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# 100 prisoners

100 prisoners
You are encouraged to solve this task according to the task description, using any language you may know.

The Problem
• 100 prisoners are individually numbered 1 to 100
• A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.
• Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.
• Prisoners start outside the room
• They can decide some strategy before any enter the room.
• Prisoners enter the room one by one, can open a drawer, inspect the card number in the drawer, then close the drawer.
• A prisoner can open no more than 50 drawers.
• A prisoner tries to find his own number.
• A prisoner finding his own number is then held apart from the others.
• If all 100 prisoners find their own numbers then they will all be pardoned. If any don't then all sentences stand.

1. Simulate several thousand instances of the game where the prisoners randomly open drawers
2. Simulate several thousand instances of the game where the prisoners use the optimal strategy mentioned in the Wikipedia article, of:
• First opening the drawer whose outside number is his prisoner number.
• If the card within has his number then he succeeds otherwise he opens the drawer with the same number as that of the revealed card. (until he opens his maximum).

Show and compare the computed probabilities of success for the two strategies, here, on this page.

References
1. The unbelievable solution to the 100 prisoner puzzle standupmaths (Video).
2. wp:100 prisoners problem
3. 100 Prisoners Escape Puzzle DataGenetics.
4. Random permutation statistics#One hundred prisoners on Wikipedia.

## 11l

Translation of: Python
`F play_random(n)   V pardoned = 0   V in_drawer = Array(0.<100)   V sampler = Array(0.<100)   L 0 .< n      random:shuffle(&in_drawer)      V found = 0B      L(prisoner) 100         found = 0B         L(reveal) random:sample(sampler, 50)            V card = in_drawer[reveal]            I card == prisoner               found = 1B               L.break         I !found            L.break      I found         pardoned++   R Float(pardoned) / n * 100 F play_optimal(n)   V pardoned = 0   V in_drawer = Array(0.<100)   L 0 .< n      random:shuffle(&in_drawer)      V found = 0B      L(prisoner) 100         V reveal = prisoner         found = 0B         L 50            V card = in_drawer[reveal]            I card == prisoner               found = 1B               L.break            reveal = card         I !found            L.break      I found         pardoned++   R Float(pardoned) / n * 100 V n = 100'000print(‘ Simulation count: ’n)print(‘ Random play wins: #2.1% of simulations’.format(play_random(n)))print(‘Optimal play wins: #2.1% of simulations’.format(play_optimal(n)))`
Output:
``` Simulation count: 100000
Random play wins:  0.0% of simulations
Optimal play wins: 31.1% of simulations
```

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
` /* ARM assembly AARCH64 Raspberry PI 3B *//*  program prisonniex64.s   */  /*******************************************//* Constantes file                         *//*******************************************//* for this file see task include a file in language AArch64 assembly*/.include "../includeConstantesARM64.inc" .equ NBDOORS,   100.equ NBLOOP, 1000 /*********************************//* Initialized data              *//*********************************/.datasMessResult:        .asciz "Random strategie  : @ sur 1000 \n"sMessResultOPT:     .asciz "Optimal strategie : @ sur 1000 \n"szCarriageReturn:   .asciz "\n"/*********************************//* UnInitialized data            *//*********************************/.bsssZoneConv:        .skip 24tbDoors:          .skip 8 * NBDOORS tbTest:           .skip 8 * NBDOORS/*********************************//*  code section                 *//*********************************/.text.global main main:                                 // entry of program      ldr x1,qAdrtbDoors    mov x2,#01:                                    // loop init doors table    add x3,x2,#1    str x3,[x1,x2,lsl #3]    add x2,x2,#1    cmp x2,#NBDOORS    blt 1b     mov x9,#0                         // loop counter    mov x10,#0                        // counter successes random strategie    mov x11,#0                        // counter successes optimal strategie2:    ldr x0,qAdrtbDoors    mov x1,#NBDOORS    bl knuthShuffle     ldr x0,qAdrtbDoors    bl aleaStrategie    cmp x0,#NBDOORS    cinc x10,x10,eq     ldr x0,qAdrtbDoors    bl optimaStrategie    cmp x0,#NBDOORS    cinc x11,x11,eq     add x9,x9,#1    cmp x9,#NBLOOP    blt 2b     mov x0,x10                        // result display    ldr x1,qAdrsZoneConv    bl conversion10                   // call decimal conversion    ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv              // insert conversion in message    bl strInsertAtCharInc    bl affichageMess     mov x0,x11                        // result display    ldr x1,qAdrsZoneConv    bl conversion10                   // call decimal conversion    ldr x0,qAdrsMessResultOPT    ldr x1,qAdrsZoneConv              // insert conversion in message    bl strInsertAtCharInc    bl affichageMess 100:                                  // standard end of the program     mov x0,0                          // return code    mov x8,EXIT                       // request to exit program    svc 0                             // perform the system call qAdrszCarriageReturn:     .quad szCarriageReturnqAdrsMessResult:          .quad sMessResultqAdrsMessResultOPT:       .quad sMessResultOPTqAdrtbDoors:              .quad tbDoorsqAdrtbTest:               .quad tbTestqAdrsZoneConv:            .quad sZoneConv/******************************************************************//*            random door test strategy                           */ /******************************************************************//* x0 contains the address of table */aleaStrategie:    stp x1,lr,[sp,-16]!          // save  registres    stp x2,x3,[sp,-16]!          // save  registres    stp x4,x5,[sp,-16]!          // save  registres    stp x6,x7,[sp,-16]!          // save  registres    stp x8,x9,[sp,-16]!          // save  registres    ldr x6,qAdrtbTest            // table doors tests address    mov x8,x0                    // save table doors address    mov x4,#0                    // counter number of successes    mov x2,#0                    // prisonners indice1:    bl razTable                  // zero to table doors tests    mov x5,#0                    // counter of door tests     add x7,x2,#12:    mov x0,#1    mov x1,#NBDOORS    bl extRandom                 // random test    ldr x3,[x6,x0,lsl #3]        // doors also tested ?    cmp x3,#0     bne 2b                       // yes    ldr x3,[x8,x0,lsl #3]        // load N° door    cmp x3,x7                    // compar N° door N° prisonner    cinc x4,x4,eq    beq 3f    mov x3,#1                    // top test table item     str x3,[x6,x0,lsl #3]    add x5,x5,#1    cmp x5,#NBDOORS / 2          // number tests maxi ?    blt 2b                       // no -> loop3:    add x2,x2,#1                 // other prisonner    cmp x2,#NBDOORS    blt 1b     mov x0,x4                    // return number of successes 100:    ldp x8,x9,[sp],16           // restaur des  2 registres    ldp x6,x7,[sp],16           // restaur des  2 registres    ldp x4,x5,[sp],16           // restaur des  2 registres    ldp x2,x3,[sp],16           // restaur des  2 registres    ldp x1,lr,[sp],16           // restaur des  2 registres    ret/******************************************************************//*     raz test table                                             */ /******************************************************************/razTable:    stp x0,lr,[sp,-16]!        // save  registres    stp x1,x2,[sp,-16]!        // save  registres    ldr x0,qAdrtbTest    mov x1,#0                  // item indice    mov x2,#01:    str x2,[x0,x1,lsl #3]      // store zero à item    add x1,x1,#1    cmp x1,#NBDOORS    blt 1b100:    ldp x1,x2,[sp],16          // restaur des  2 registres    ldp x0,lr,[sp],16          // restaur des  2 registres    ret/******************************************************************//*            random door test strategy                           */ /******************************************************************//* x0 contains the address of table */optimaStrategie:    stp x1,lr,[sp,-16]!          // save  registres    stp x2,x3,[sp,-16]!          // save  registres    stp x4,x5,[sp,-16]!          // save  registres    mov x4,#0                    // counter number of successes    mov x2,#0                    // counter prisonner1:    mov x5,#0                    // counter test    mov x1,x2                    // first test = N° prisonner2:    ldr x3,[x0,x1,lsl #3]        // load N° door    cmp x3,x2    cinc x4,x4,eq                // equal -> succes    beq 3f    mov x1,x3                    // new test with N° door    add x5,x5,#1                     cmp x5,#NBDOORS / 2          // test number maxi ?    blt 2b3:    add x2,x2,#1                 // other prisonner    cmp x2,#NBDOORS    blt 1b     mov x0,x4100:    ldp x4,x5,[sp],16          // restaur des  2 registres    ldp x2,x3,[sp],16          // restaur des  2 registres    ldp x1,lr,[sp],16          // restaur des  2 registres    ret/******************************************************************//*     knuth Shuffle                                  */ /******************************************************************//* x0 contains the address of table *//* x1 contains the number of elements */knuthShuffle:    stp x1,lr,[sp,-16]!          // save  registres    stp x2,x3,[sp,-16]!          // save  registres    stp x4,x5,[sp,-16]!          // save  registres    stp x6,x7,[sp,-16]!         // save  registers    mov x5,x0                   // save table address    mov x6,x1                   // save number of elements    mov x2,0                    // start index1:    mov x0,0    mov x1,x2                   // generate aleas    bl extRandom    ldr x3,[x5,x2,lsl #3]        // swap number on the table    ldr x4,[x5,x0,lsl #3]    str x4,[x5,x2,lsl #3]    str x3,[x5,x0,lsl #3]    add x2,x2,#1                 // next number    cmp x2,x6                    // end ?    blt 1b                       // no -> loop100:    ldp x6,x7,[sp],16           // restaur des  2 registres    ldp x4,x5,[sp],16           // restaur des  2 registres    ldp x2,x3,[sp],16           // restaur des  2 registres    ldp x1,lr,[sp],16           // restaur des  2 registres    ret /******************************************************************//*     random number                                          */ /******************************************************************//*  x0 contains inferior value *//*  x1 contains maxi value *//*  x0 return random number */extRandom:    stp x1,lr,[sp,-16]!        // save  registers    stp x2,x8,[sp,-16]!        // save  registers    stp x3,x4,[sp,-16]!        // save  registers    stp x19,x20,[sp,-16]!      // save  registers    sub sp,sp,16               // reserve 16 octets on stack    mov x19,x0    add x20,x1,1    mov x0,sp                  // store result on stack    mov x1,8                   // length 8 bytes    mov x2,0    mov x8,278                 //  call system Linux 64 bits Urandom    svc 0    mov x0,sp                  // load résult on stack    ldr x0,[x0]    sub x2,x20,x19             // calculation of the range of values     udiv x1,x0,x2              // calculation range modulo    msub x0,x1,x2,x0    add  x0,x0,x19             // and add inferior value100:    add sp,sp,16               // alignement stack     ldp x19,x20,[sp],16        // restaur  2 registers    ldp x3,x4,[sp],16          // restaur  2 registers    ldp x2,x8,[sp],16          // restaur  2 registers    ldp x1,lr,[sp],16          // restaur  2 registers    ret                        // return to address lr x30/********************************************************//*        File Include fonctions                        *//********************************************************//* for this file see task include a file in language AArch64 assembly */.include "../includeARM64.inc" `
```Random strategie  : 0 sur 1000
Optimal strategie : 305 sur 1000
```

` package Prisoners is    type Win_Percentage is digits 2 range 0.0 .. 100.0;   type Drawers is array (1 .. 100) of Positive;    function Play_Game     (Repetitions : in Positive;      Strategy    :    not null access function        (Cupboard     : in Drawers; Max_Prisoners : Integer;         Max_Attempts :    Integer; Prisoner_Number : Integer) return Boolean)      return Win_Percentage;   -- Play the game with a specified number of repetitions, the chosen strategy   -- is passed to this function    function Optimal_Strategy     (Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;      Prisoner_Number :    Integer) return Boolean;    function Random_Strategy     (Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;      Prisoner_Number :    Integer) return Boolean; end Prisoners; `
` pragma Ada_2012;with Ada.Numerics.Discrete_Random;with Ada.Text_IO; use Ada.Text_IO; package body Prisoners is    subtype Drawer_Range is Positive range 1 .. 100;   package Random_Drawer is new Ada.Numerics.Discrete_Random (Drawer_Range);   use Random_Drawer;    -- Helper procedures to initialise and shuffle the drawers    procedure Swap (A, B : Positive; Cupboard : in out Drawers) is      Temp : Positive;   begin      Temp         := Cupboard (B);      Cupboard (B) := Cupboard (A);      Cupboard (A) := Temp;   end Swap;    procedure Shuffle (Cupboard : in out Drawers) is      G : Generator;   begin      Reset (G);      for I in Cupboard'Range loop         Swap (I, Random (G), Cupboard);      end loop;   end Shuffle;    procedure Initialise_Drawers (Cupboard : in out Drawers) is   begin      for I in Cupboard'Range loop         Cupboard (I) := I;      end loop;      Shuffle (Cupboard);   end Initialise_Drawers;    -- The two strategies for playing the game    function Optimal_Strategy     (Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;      Prisoner_Number :    Integer) return Boolean   is      Current_Card : Positive;   begin      Current_Card := Cupboard (Prisoner_Number);      if Current_Card = Prisoner_Number then         return True;      else         for I in Integer range 1 .. Max_Attempts loop            Current_Card := Cupboard (Current_Card);            if Current_Card = Prisoner_Number then               return True;            end if;         end loop;      end if;      return False;   end Optimal_Strategy;    function Random_Strategy     (Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;      Prisoner_Number :    Integer) return Boolean   is      Current_Card : Positive;      G            : Generator;   begin      Reset (G);      Current_Card := Cupboard (Prisoner_Number);      if Current_Card = Prisoner_Number then         return True;      else         for I in Integer range 1 .. Max_Attempts loop            Current_Card := Cupboard (Random (G));            if Current_Card = Prisoner_Number then               return True;            end if;         end loop;      end if;      return False;   end Random_Strategy;    function Prisoners_Attempts     (Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;      Strategy :    not null access function        (Cupboard     : in Drawers; Max_Prisoners : Integer;         Max_Attempts :    Integer; Prisoner_Number : Integer) return Boolean)      return Boolean   is   begin      for Prisoner_Number in Integer range 1 .. Max_Prisoners loop         if not Strategy             (Cupboard, Max_Prisoners, Max_Attempts, Prisoner_Number)         then            return False;         end if;      end loop;      return True;   end Prisoners_Attempts;    -- The function to play the game itself    function Play_Game     (Repetitions : in Positive;      Strategy    :    not null access function        (Cupboard     : in Drawers; Max_Prisoners : Integer;         Max_Attempts :    Integer; Prisoner_Number : Integer) return Boolean)      return Win_Percentage   is      Cupboard            : Drawers;      Win, Game_Count     : Natural          := 0;      Number_Of_Prisoners : constant Integer := 100;      Max_Attempts        : constant Integer := 50;   begin      loop         Initialise_Drawers (Cupboard);         if Prisoners_Attempts             (Cupboard     => Cupboard, Max_Prisoners => Number_Of_Prisoners,              Max_Attempts => Max_Attempts, Strategy => Strategy)         then            Win := Win + 1;         end if;         Game_Count := Game_Count + 1;         exit when Game_Count = Repetitions;      end loop;      return Win_Percentage ((Float (Win) / Float (Repetitions)) * 100.0);   end Play_Game; end Prisoners; `
` with Prisoners;   use Prisoners;with Ada.Text_IO; use Ada.Text_IO; procedure Main is   Wins : Win_Percentage;   package Win_Percentage_IO is new Float_IO (Win_Percentage);begin   Wins := Play_Game (100_000, Optimal_Strategy'Access);   Put ("Optimal Strategy = ");   Win_Percentage_IO.Put (Wins, 2, 2, 0);   Put ("%");   New_Line;   Wins := Play_Game (100_000, Random_Strategy'Access);   Put ("Random Strategy = ");   Win_Percentage_IO.Put (Wins, 2, 2, 0);   Put ("%");end Main; `
Output:
```Optimal Strategy = 31.80%
Random Strategy =  0.00%
```

## APL

Works with: GNU APL version 1.8
` ∇ R ← random Nnc; N; n; c  (N n c) ← Nnc  R ← ∧/{∨/⍵=c[n?N]}¨⍳N∇ ∇ R ← follow Nnc; N; n; c; b  (N n c) ← Nnc  b ← n N⍴⍳N  R ← ∧/∨⌿b={⍺⊢c[⍵]}⍀n N⍴c∇ ∇ R ← M timesSimPrisoners Nn; N; n; m; c; r; s  (N n) ← Nn  R ← 0 0  m ← M  LOOP: c←N?N         r ← random N n c  s ← follow N n c  R ← R + r,s        →((m←m-1)>0)/LOOP  R ← R ÷ M∇ 5000 timesSimPrisoners 100 50  `

## Applesoft BASIC

This is modified from the 100_prisoners#Commodore_BASIC listing. Here are some noted differences between the BASICs and platforms:

• UPPER CASE, for the 1970's Apple II and Apple II+
• GET in Applesoft waits for a keypress, so : IF K\$ = "" THEN 1110 is not needed
• CLear Screen: PRINT CHR\$ (147); on Commodore BASIC, HOME in Applesoft
• "{LEFT-CRSR}" is CHR\$(8) on Apple II, but numbers printed in Applesoft don't have spaces appended to them
• but spaces need to be added in front and after numbers in Applesoft
•  ; is optional for string concatenation
• Replace bare PRINT statement with M\$ embedded in PRINT statements to visually compact the listing

And, minor speed tweaks:

• Remove REMs, adjust line numbers, move the two compacted methods to the beginning of the program
• Rename some two character variable names to single character names: 's/DR(/D(/' 's/IG(/J(/'
• Start at 0 and go up to 99, but don't regress into off by one bugs
• Inline the shuffle subroutine and hoist it out of the methods
• Embed the results in the loop because feedback can be helpful, otherwise it looks like the program froze

Actual test of 4000 trials for each method were run on the KEGSMAC emulator with MHz set to No Limit.

`0 GOTO 9 1 FOR X = 0 TO N:J(X) = X: NEXT: FOR I = 0 TO N:FOR X = 0 TO N:T = J(X):NP =  INT ( RND (1) * H):J(X) = J(NP):J(NP) = T: NEXT :FOR G = 1 TO W:IF D(J(G)) = I THEN IP = IP + 1: NEXT I: RETURN 2 NEXT G:RETURN  3 FOR I = 0 TO N:NG = I: FOR G = 0 TO W:CD = D(NG):IF CD = I THEN IP = IP + 1: NEXT I: RETURN 4 NG = CD:IF CD = I THEN STOP5 NEXT G: RETURN  9 H=100:N=H-1:DIM D(99),J(99):FOR I = 0 TO N:D(I) = I: NEXT:W=INT(H/2)-1:M\$=CHR\$(13):M\$(1)="RANDOM GUESSING":M\$(2)="CHAINED NUMBER PICKING" 1000 FOR Q = 0 TO 1 STEP 0 : HOME : PRINT "100 PRISONERS"M\$: INPUT "HOW MANY TRIALS FOR EACH METHOD? ";  TT1010     VTAB 2:CALL-958:PRINT M\$"RESULTS:"M\$1020     FOR M = 1 TO 2: SU(M) = 0:FA(M) = 01030         FOR TN = 1 TO TT1040             VTAB 4:PRINT M\$ "   OUT OF " TT " TRIALS, THE RESULTS ARE"M\$"   AS FOLLOWS...";1050             IP = 0: X =  RND ( - TI): FOR I = 0 TO N:R =  INT ( RND (1) * N):T = D(I):D(I) = D(R):D(R) = T: NEXT1060             ON M GOSUB 1,3 : SU(M) = SU(M) + (IP = H):FA(M) = FA(M) + (IP < H)1070             FOR Z = 1 TO 21071                 PRINT M\$M\$Z". "M\$(Z)":"M\$1073                 PRINT "   "SU(Z)" SUCCESSES"TAB(21)1074                 PRINT "   "FA(Z)" FAILURES"M\$1075                 PRINT "   "(SU(Z) / TT) * 100"% SUCCESS RATE.";:CALL-8681090     NEXT Z,TN,M 1100     PRINT M\$M\$"AGAIN?"1110     GET K\$1120     Q = K\$ <> "Y" AND K\$ <> CHR\$(ASC("Y") + 32) : NEXT Q `
Output:
```100 PRISONERS

RESULTS:

OUT OF 4000 TRIALS, THE RESULTS ARE
AS FOLLOWS...

1. RANDOM GUESSING:

0 SUCCESSES         4000 FAILURES

0% SUCCESS RATE.

2. CHAINED NUMBER PICKING:

1278 SUCCESSES      2722 FAILURES

31.95% SUCCESS RATE.
```

## ARM Assembly

Works with: as version Raspberry Pi
` /* ARM assembly Raspberry PI  *//*  program prisonniers.s   */  /* REMARK 1 : this program use routines in a include file    see task Include a file language arm assembly    for the routine affichageMess conversion10    see at end of this program the instruction include *//* for constantes see task include a file in arm assembly *//************************************//* Constantes                       *//************************************/.include "../constantes.inc" .equ NBDOORS,   100.equ NBLOOP, 1000 /*********************************//* Initialized data              *//*********************************/.datasMessResult:        .asciz "Random strategie  : @ sur 1000 \n"sMessResultOPT:     .asciz "Optimal strategie : @ sur 1000 \n"szCarriageReturn:   .asciz "\n".align 4iGraine:  .int 123456/*********************************//* UnInitialized data            *//*********************************/.bsssZoneConv:        .skip 24tbDoors:          .skip 4 * NBDOORS tbTest:           .skip 4 * NBDOORS/*********************************//*  code section                 *//*********************************/.text.global main main:                                 @ entry of program      ldr r1,iAdrtbDoors    mov r2,#01:                                    @ loop init doors table    add r3,r2,#1    str r3,[r1,r2,lsl #2]    add r2,r2,#1    cmp r2,#NBDOORS    blt 1b     mov r9,#0                         @ loop counter    mov r10,#0                        @ counter successes random strategie    mov r11,#0                        @ counter successes optimal strategie2:    ldr r0,iAdrtbDoors    mov r1,#NBDOORS    bl knuthShuffle     ldr r0,iAdrtbDoors    bl aleaStrategie    cmp r0,#NBDOORS    addeq r10,r10,#1     ldr r0,iAdrtbDoors    bl optimaStrategie    cmp r0,#NBDOORS    addeq r11,r11,#1     add r9,r9,#1    cmp r9,#NBLOOP    blt 2b     mov r0,r10                        @ result display    ldr r1,iAdrsZoneConv    bl conversion10                   @ call decimal conversion    ldr r0,iAdrsMessResult    ldr r1,iAdrsZoneConv              @ insert conversion in message    bl strInsertAtCharInc    bl affichageMess     mov r0,r11                        @ result display    ldr r1,iAdrsZoneConv    bl conversion10                   @ call decimal conversion    ldr r0,iAdrsMessResultOPT    ldr r1,iAdrsZoneConv              @ insert conversion in message    bl strInsertAtCharInc    bl affichageMess 100:                                  @ standard end of the program     mov r0, #0                        @ return code    mov r7, #EXIT                     @ request to exit program    svc #0                            @ perform the system call iAdrszCarriageReturn:     .int szCarriageReturniAdrsMessResult:          .int sMessResultiAdrsMessResultOPT:        .int sMessResultOPTiAdrtbDoors:              .int tbDoorsiAdrtbTest:               .int tbTestiAdrsZoneConv:            .int sZoneConv/******************************************************************//*            random door test strategy                           */ /******************************************************************//* r0 contains the address of table */aleaStrategie:    push {r1-r7,lr}              @ save registers    ldr r6,iAdrtbTest            @ table doors tests address    mov r1,r0                    @ save table doors address    mov r4,#0                    @ counter number of successes    mov r2,#0                    @ prisonners indice1:    bl razTable                  @ zero to table doors tests    mov r5,#0                    @ counter of door tests     add r7,r2,#12:    mov r0,#NBDOORS - 1    bl genereraleas              @ random test    add r0,r0,#1    ldr r3,[r6,r0,lsl #2]        @ doors also tested ?    cmp r3,#0     bne 2b                       @ yes    ldr r3,[r1,r0,lsl #2]        @ load N° door    cmp r3,r7                    @ compar N° door N° prisonner    addeq r4,r4,#1               @ succes    beq 3f    mov r3,#1                    @ top test table item     str r3,[r6,r0,lsl #2]    add r5,r5,#1    cmp r5,#NBDOORS / 2          @ number tests maxi ?    blt 2b                       @ no -> loop3:    add r2,r2,#1                 @ other prisonner    cmp r2,#NBDOORS    blt 1b     mov r0,r4                    @ return number of successes 100:    pop {r1-r7,lr}    bx lr                        @ return /******************************************************************//*     raz test table                                             */ /******************************************************************/razTable:    push {r0-r2,lr}              @ save registers    ldr r0,iAdrtbTest    mov r1,#0                    @ item indice    mov r2,#01:    str r2,[r0,r1,lsl #2]        @ store zero à item    add r1,r1,#1    cmp r1,#NBDOORS    blt 1b100:    pop {r0-r2,lr}    bx lr                        @ return /******************************************************************//*            random door test strategy                           */ /******************************************************************//* r0 contains the address of table */optimaStrategie:    push {r1-r7,lr}              @ save registers    mov r4,#0                    @ counter number of successes    mov r2,#0                    @ counter prisonner1:    mov r5,#0                    @ counter test    mov r1,r2                    @ first test = N° prisonner2:    ldr r3,[r0,r1,lsl #2]        @ load N° door    cmp r3,r2    addeq r4,r4,#1               @ equal -> succes    beq 3f    mov r1,r3                    @ new test with N° door    add r5,r5,#1                     cmp r5,#NBDOORS / 2          @ test number maxi ?    blt 2b3:    add r2,r2,#1                 @ other prisonner    cmp r2,#NBDOORS    blt 1b     mov r0,r4100:    pop {r1-r7,lr}    bx lr                        @ return /******************************************************************//*     knuth Shuffle                                  */ /******************************************************************//* r0 contains the address of table *//* r1 contains the number of elements */knuthShuffle:    push {r2-r5,lr}                   @ save registers    mov r5,r0                         @ save table address    mov r2,#0                         @ start index1:    mov r0,r2                         @ generate aleas    bl genereraleas    ldr r3,[r5,r2,lsl #2]             @ swap number on the table    ldr r4,[r5,r0,lsl #2]    str r4,[r5,r2,lsl #2]    str r3,[r5,r0,lsl #2]    add r2,#1                         @ next number    cmp r2,r1                         @ end ?    blt 1b                            @ no -> loop100:    pop {r2-r5,lr}    bx lr                             @ return /***************************************************//*   Generation random number                  *//***************************************************//* r0 contains limit  */genereraleas:    push {r1-r4,lr}                   @ save registers     ldr r4,iAdriGraine    ldr r2,[r4]    ldr r3,iNbDep1    mul r2,r3,r2    ldr r3,iNbDep1    add r2,r2,r3    str r2,[r4]                       @ maj de la graine pour l appel suivant     cmp r0,#0    beq 100f    mov r1,r0                         @ divisor    mov r0,r2                         @ dividende    bl division    mov r0,r3                         @ résult = remainder 100:                                  @ end function    pop {r1-r4,lr}                    @ restaur registers    bx lr                             @ return/*****************************************************/iAdriGraine: .int iGraineiNbDep1:     .int 0x343FDiNbDep2:     .int 0x269EC3 /***************************************************//*      ROUTINES INCLUDE                           *//***************************************************/.include "../affichage.inc" `
```Random strategie  : 0           sur 1000
Optimal strategie : 303         sur 1000
```

## AutoHotkey

`NumOfTrials := 20000randomFailTotal := 0, strategyFailTotal := 0prisoners := [], drawers := [], Cards := []loop, 100	prisoners[A_Index] := A_Index				; create prisoners	, drawers[A_Index] := true				; create drawers loop, % NumOfTrials{	loop, 100		Cards[A_Index] := A_Index			; create cards for this iteration	loop, 100	{		Random, rnd, 1, Cards.count()		drawers[A_Index] := Cards.RemoveAt(rnd)		; randomly place cards in drawers	}	;-------------------------------------------	; randomly open drawers	RandomList := []	loop, 100		RandomList[A_Index] := A_Index	Fail := false	while (A_Index <=100) && !Fail	{		thisPrisoner := A_Index		res := ""		while (thisCard <> thisPrisoner) && !Fail		{			Random, rnd, 1, % RandomList.Count()	; choose random number			NextDrawer := RandomList.RemoveAt(rnd)	; remove drawer from random list (don't choose more than once)			thisCard := drawers[NextDrawer]		; get card from this drawer			if (A_Index > 50)				Fail := true		}		if Fail			randomFailTotal++	}	;-------------------------------------------	; use optimal strategy	Fail := false	while (A_Index <=100) && !Fail	{		counter := 1, thisPrisoner := A_Index		NextDrawer := drawers[thisPrisoner]		; 1st trial, drawer whose outside number is prisoner number		while (drawers[NextDrawer] <> thisPrisoner) && !Fail		{				NextDrawer := drawers[NextDrawer]	; drawer with the same number as that of the revealed card			if ++counter > 50				Fail := true		}		if Fail			strategyFailTotal++	}}MsgBox %  "Number Of Trials = " NumOfTrials		. "`nOptimal Strategy:`t" (1 - strategyFailTotal/NumOfTrials) *100 " % success rate" 		. "`nRandom Trials:`t" (1 - randomFailTotal/NumOfTrials) *100 " % success rate"`
Outputs:
```Number Of Trials = 20000
Optimal Strategy:	33.275000 % success rate
Random Trials   :	0.000000 % success rate```

## BASIC256

Works with: BASIC256 version 2.0.0.11
` O = 50N = 2*Oiterations = 10000 REM From the numbers 0 to N-1 inclusive, pick O of them.function shuffle(N, O) dim array(N) for i = 0 to N-1  array[i] = i next i for i = 0 to O-1  swapindex = i + rand*(N-i)  swapvalue = array[swapindex]  array[swapindex] = array[i]  array[i] = swapvalue next i return arrayend function REM given N drawers with O to open, prisoner P chooses randomly: does he choose well?function chooserandom(drawers, N, O, p)  choices = shuffle(N, O)  for i = 0 to O-1   if drawers[choices[i]] = p then return true  next i  return falseend function REM N prisoners randomly choose O drawers to open: do they all choose well?function allchooserandom(N, O) drawers = shuffle(N, N) for p = 0 to N-1  goodchoice = chooserandom(drawers, N, O, p)  if not goodchoice then return false next p return trueend function REM given N drawers with O to open, prisoner P chooses smartly: does he choose well?function choosesmart(drawers, N, O, p) numopened = 0 i = p while numopened < O  numopened += 1  if drawers[i] = p then return true  i = drawers[i] end while return falseend function REM N prisoners smartly choose O drawers to open: do they all choose well?function allchoosesmart(N, O) drawers = shuffle(N, N) for p = 0 to N-1  goodchoice = choosesmart(drawers, N, O, p)  if not goodchoice then return false next p return trueend function clsprint N; " prisoners choosing ";O;" drawers, ";iterations;" iterations:" total = 0for iteration = 1 to iterations if allchooserandom(N, O) then total += 1next iteration print "Random choices: "; total;" out of ";iterationsprint "Observed ratio: "; total/iterations; ", expected ratio: "; (O/N)^N total = 0for iteration = 1 to iterations if allchoosesmart(N, O) then total += 1next iteration print "Smart choices: "; total;" out of ";iterationsprint "Observed ratio: "; total/iterations; ", expected ratio with N=2*O: greater than about 0.30685": REM for N=100, O=50 particularly, about 0.3118 `
Output:
```100 prisoners choosing 50 drawers, 10000 iterations:
Random choices: 0 out of 10000
Observed ratio: 0.0, expected ratio: 0.0
Smart choices: 3052 out of 10000
Observed ratio: 0.3052, expected ratio with N=2*O: greater than about 0.30685
```

## BCPL

`get "libhdr" manifest \$(     seed = 12345   // for pseudorandom number generator    size = 100     // amount of drawers and prisoners    tries = 50     // amount of tries each prisoner may make    simul = 2000   // amount of simulations to run\$) let randto(n) = valof\$(  static \$( state = seed \$)    let mask = 1    mask := (mask<<1)|1 repeatuntil mask > n    state := random(state) repeatuntil ((state >> 8) & mask) < n     resultis (state >> 8) & mask\$) // initialize drawerslet placeCards(d, n) be\$(  for i=0 to n-1 do d!i := i;    for i=0 to n-2 do    \$(  let j = i+randto(n-i)        let k = d!i        d!i := d!j        d!j := k    \$)\$) // random strategy (prisoner 'p' tries to find his own number)let randoms(d, p, t) = valof\$(  for n = 1 to t do        if d!randto(size) = p then resultis true    resultis false \$) // optimal strategylet optimal(d, p, t) = valof\$(  let last = p    for n = 1 to t do        test d!last = p             then resultis true            else last := d!last    resultis false\$) // run a simulation given a strategylet simulate(d, strat, n, t) = valof\$(  placeCards(d, n)    for p = 0 to n-1 do        if not strat(d, p, t) then resultis false    resultis true\$) // run many simulations and count the successeslet runSimulations(d, strat, n, amt, t) = valof\$(  let succ = 0    for i = 1 to amt do        if simulate(d, strat, n, t) do            succ := succ + 1    resultis succ\$) let run(d, name, strat, n, amt, t) be\$(  let s = runSimulations(d, strat, n, amt, t);    writef("%S: %I5 of %I5, %N percent.*N", name, s, amt, s*10/(amt/10))\$) let start() be\$(  let d = vec size-1    run(d, " Random", randoms, size, simul, tries)    run(d, "Optimal", optimal, size, simul, tries)\$)`
Output:
``` Random:     0 of  2000, 0 percent.
Optimal:   698 of  2000, 34 percent.```

## C

` #include<stdbool.h>#include<stdlib.h>#include<stdio.h>#include<time.h> #define LIBERTY false#define DEATH true typedef struct{	int cardNum;	bool hasBeenOpened;}drawer; drawer *drawerSet; void initialize(int prisoners){	int i,j,card;	bool unique; 	drawerSet = ((drawer*)malloc(prisoners * sizeof(drawer))) -1; 	card = rand()%prisoners + 1;	drawerSet = (drawer){.cardNum = card, .hasBeenOpened = false}; 	for(i=1 + 1;i<prisoners + 1;i++){		unique = false;		while(unique==false){			for(j=0;j<i;j++){				if(drawerSet[j].cardNum == card){					card = rand()%prisoners + 1;					break;				}			}			if(j==i){				unique = true;			}		}		drawerSet[i] = (drawer){.cardNum = card, .hasBeenOpened = false};	} } void closeAllDrawers(int prisoners){	int i;	for(i=1;i<prisoners + 1;i++)		drawerSet[i].hasBeenOpened = false;} bool libertyOrDeathAtRandom(int prisoners,int chances){	int i,j,chosenDrawer; 	for(i= 1;i<prisoners + 1;i++){		bool foundCard = false;		for(j=0;j<chances;j++){			do{				chosenDrawer = rand()%prisoners + 1;			}while(drawerSet[chosenDrawer].hasBeenOpened==true);			if(drawerSet[chosenDrawer].cardNum == i){				foundCard = true;				break;			}			drawerSet[chosenDrawer].hasBeenOpened = true;		}		closeAllDrawers(prisoners);		if(foundCard == false)			return DEATH;	} 	return LIBERTY;} bool libertyOrDeathPlanned(int prisoners,int chances){	int i,j,chosenDrawer;	for(i=1;i<prisoners + 1;i++){		chosenDrawer = i;		bool foundCard = false;		for(j=0;j<chances;j++){			drawerSet[chosenDrawer].hasBeenOpened = true; 			if(drawerSet[chosenDrawer].cardNum == i){				foundCard = true;				break;			}			if(chosenDrawer == drawerSet[chosenDrawer].cardNum){				do{                    chosenDrawer = rand()%prisoners + 1;				}while(drawerSet[chosenDrawer].hasBeenOpened==true);			}			else{				chosenDrawer = drawerSet[chosenDrawer].cardNum;			} 		} 		closeAllDrawers(prisoners);		if(foundCard == false)			return DEATH;	} 	return LIBERTY;} int main(int argc,char** argv){	int prisoners, chances;	unsigned long long int trials,i,count = 0;        char* end; 	if(argc!=4)		return printf("Usage : %s <Number of prisoners> <Number of chances> <Number of trials>",argv); 	prisoners = atoi(argv);	chances = atoi(argv);	trials = strtoull(argv,&end,10); 	srand(time(NULL)); 	printf("Running random trials...");	for(i=0;i<trials;i+=1L){		initialize(prisoners); 		count += libertyOrDeathAtRandom(prisoners,chances)==DEATH?0:1;	} 	printf("\n\nGames Played : %llu\nGames Won : %llu\nChances : %lf %% \n\n",trials,count,(100.0*count)/trials);         count = 0; 	printf("Running strategic trials...");	for(i=0;i<trials;i+=1L){		initialize(prisoners); 		count += libertyOrDeathPlanned(prisoners,chances)==DEATH?0:1;	} 	printf("\n\nGames Played : %llu\nGames Won : %llu\nChances : %lf %% \n\n",trials,count,(100.0*count)/trials);	return 0;}  `
```\$ gcc 100prisoners.c && ./a.out 100 50 10000
Running random trials...

Games Played : 10000
Games Won : 0
Chances : 0.000000 %

Running strategic trials...

Games Played : 10000
Games Won : 3051
Chances : 30.510000 %
```

## C#

Translation of: D
`using System;using System.Linq; namespace Prisoners {    class Program {        static bool PlayOptimal() {            var secrets = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();             for (int p = 0; p < 100; p++) {                bool success = false;                 var choice = p;                for (int i = 0; i < 50; i++) {                    if (secrets[choice] == p) {                        success = true;                        break;                    }                    choice = secrets[choice];                }                 if (!success) {                    return false;                }            }             return true;        }         static bool PlayRandom() {            var secrets = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();             for (int p = 0; p < 100; p++) {                var choices = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();                 bool success = false;                for (int i = 0; i < 50; i++) {                    if (choices[i] == p) {                        success = true;                        break;                    }                }                 if (!success) {                    return false;                }            }             return true;        }         static double Exec(uint n, Func<bool> play) {            uint success = 0;            for (uint i = 0; i < n; i++) {                if (play()) {                    success++;                }            }            return 100.0 * success / n;        }         static void Main() {            const uint N = 1_000_000;            Console.WriteLine("# of executions: {0}", N);            Console.WriteLine("Optimal play success rate: {0:0.00000000000}%", Exec(N, PlayOptimal));            Console.WriteLine(" Random play success rate: {0:0.00000000000}%", Exec(N, PlayRandom));        }    }}`
Output:
```# of executions: 1000000
Optimal play success rate: 31.21310000000%
Random play success rate: 0.00000000000%```

## C++

`#include <cstdlib>   // for rand#include <algorithm> // for random_shuffle#include <iostream>  // for output using namespace std; class cupboard {public:    cupboard() {        for (int i = 0; i < 100; i++)            drawers[i] = i;        random_shuffle(drawers, drawers + 100);    }     bool playRandom();    bool playOptimal(); private:    int drawers;}; bool cupboard::playRandom() {    bool openedDrawers = { 0 };    for (int prisonerNum = 0; prisonerNum < 100; prisonerNum++) { // loops through prisoners numbered 0 through 99        bool prisonerSuccess = false;        for (int i = 0; i < 100 / 2; i++) {  // loops through 50 draws for each prisoner            int drawerNum = rand() % 100;            if (!openedDrawers[drawerNum]) {                openedDrawers[drawerNum] = true;                break;            }            if (drawers[drawerNum] == prisonerNum) {                prisonerSuccess = true;                break;            }        }        if (!prisonerSuccess)            return false;    }    return true;} bool cupboard::playOptimal() {    for (int prisonerNum = 0; prisonerNum < 100; prisonerNum++) {        bool prisonerSuccess = false;        int checkDrawerNum = prisonerNum;        for (int i = 0; i < 100 / 2; i++) {            if (drawers[checkDrawerNum] == prisonerNum) {                prisonerSuccess = true;                break;            } else                checkDrawerNum = drawers[checkDrawerNum];        }        if (!prisonerSuccess)            return false;    }    return true;} double simulate(char strategy) {    int numberOfSuccesses = 0;    for (int i = 0; i < 10000; i++) {        cupboard d;        if ((strategy == 'R' && d.playRandom()) || (strategy == 'O' && d.playOptimal())) // will run playRandom or playOptimal but not both because of short-circuit evaluation            numberOfSuccesses++;    }     return numberOfSuccesses * 100.0 / 10000;} int main() {    cout << "Random strategy:  " << simulate('R') << " %" << endl;    cout << "Optimal strategy: " << simulate('O') << " %" << endl;    system("PAUSE"); // for Windows    return 0;}`
Output:
```Random strategy:  0 %
Optimal strategy: 31.54 %```

## Clojure

`(ns clojure-sandbox.prisoners) (defn random-drawers []  "Returns a list of shuffled numbers"  (-> 100      range      shuffle)) (defn search-50-random-drawers [prisoner-number drawers]  "Select 50 random drawers and return true if the prisoner's number was found"  (->> drawers      shuffle ;; Put drawer contents in random order      (take 50) ;; Select first 50, equivalent to selecting 50 random drawers      (filter (fn [x] (= x prisoner-number))) ;; Filter to include only those that match prisoner number      count      (= 1))) ;; Returns true if the number of matching numbers is 1 (defn search-50-optimal-drawers [prisoner-number drawers]  "Open 50 drawers according to the agreed strategy, returning true if prisoner's number was found"  (loop [next-drawer prisoner-number ;; The drawer index to start on is the prisoner's number         drawers-opened 0] ;; To keep track of how many have been opened as 50 is the maximum    (if (= drawers-opened 50)      false ;; If 50 drawers have been opened, the prisoner's number has not been found      (let [result (nth drawers next-drawer)] ;; Open the drawer given by next number        (if (= result prisoner-number) ;; If prisoner number has been found          true ;; No need to keep opening drawers - return true          (recur result (inc drawers-opened))))))) ;; Restart the loop using the resulting number as the drawer number (defn try-luck [drawers drawer-searching-function]  "Returns 1 if all prisoners find their number otherwise 0"  (loop [prisoners (range 100)] ;; Start with 100 prisoners    (if (empty? prisoners) ;; If they've all gone and found their number      1 ;; Return true- they'll all live      (let [res (-> prisoners                    first                    (drawer-searching-function drawers))] ;; Otherwise, have the first prisoner open drawers according to the specified method        (if (false? res) ;; If this prisoner didn't find their number          0 ;; no prisoners will be freed so we can return false and stop          (recur (rest prisoners))))))) ;; Otherwise they've found the number, so we remove them from the queue and repeat with the others (defn simulate-100-prisoners []  "Simulates all prisoners searching the same drawers by both strategies, returns map showing whether each was successful"  (let [drawers (random-drawers)] ;; Create 100 drawers with randomly ordered prisoner numbers    {:random (try-luck drawers search-50-random-drawers) ;; True if all prisoners found their number using random strategy     :optimal (try-luck drawers search-50-optimal-drawers)})) ;; True if all prisoners found their number using optimal strategy (defn simulate-n-runs [n]  "Simulate n runs of the 100 prisoner problem and returns a success count for each search method"  (loop [random-successes 0         optimal-successes 0         run-count 0]    (if (= n run-count) ;; If we've done the loop n times      {:random-successes random-successes ;; return results       :optimal-successes optimal-successes       :run-count run-count}      (let [next-result (simulate-100-prisoners)] ;; Otherwise, run for another batch of prisoners        (recur (+ random-successes (:random next-result)) ;; Add result of run to the total successs count               (+ optimal-successes (:optimal next-result))               (inc run-count)))))) ;; increment run count and run again (defn -main [& args]  "For 5000 runs, print out the success frequency for both search methods"  (let [{:keys [random-successes optimal-successes run-count]} (simulate-n-runs 5000)]    (println (str "Probability of survival with random search: " (float (/ random-successes run-count))))    (println (str "Probability of survival with ordered search: " (float (/ optimal-successes run-count))))))`
Output:
```Probability of survival with random search: 0.0
Probability of survival with ordered search: 0.3062
```

## CLU

`% This program needs to be merged with PCLU's "misc" library% to use the random number generator.%% pclu -merge \$CLUHOME/lib/misc.lib -compile prisoners.clu % Seed the random number generator with the current timeinit_rng = proc ()    d: date := now()    seed: int := ((d.hour*60) + d.minute)*60 + d.second    random\$seed(seed)end init_rng % Place cards in drawers randomlymake_drawers = proc (n: int) returns (sequence[int])    d: array[int] := array[int]\$predict(1,n)     % place each card in its own drawer    for i: int in int\$from_to(1,n) do        array[int]\$addh(d,i)    end     % shuffle the cards    for i: int in int\$from_to_by(n,2,-1) do        j: int := random\$next(i)+1        t: int := d[i]        d[i] := d[j]        d[j] := t    end    return(sequence[int]\$a2s(d))end make_drawers % Random strategyrand_strat = proc (p, tries: int, d: sequence[int]) returns (bool)    n: int := sequence[int]\$size(d)    for i: int in int\$from_to(1,tries) do        if p = d[random\$next(n)+1] then return(true) end    end    return(false)end rand_strat % Optimal strategyopt_strat = proc (p, tries: int, d: sequence[int]) returns (bool)    last: int := p    for i: int in int\$from_to(1,tries) do        if d[last]=p then return(true) end        last := d[last]    end    return(false)end opt_strat % Run one simulation given a strategysimulate = proc (n, tries: int,                 strat: proctype (int,int,sequence[int]) returns (bool))           returns (bool)    d: sequence[int] := make_drawers(n)    for p: int in int\$from_to(1,n) do        % If one prisoner fails, they all hang        if ~strat(p,tries,d) then return(false) end    end    return(true)end simulate % Run many simulations and count the successesrun_simulations = proc (amount, n, tries: int,                        strat: proctype (int,int,sequence[int]) returns (bool))                  returns (int)    ok: int := 0    for i: int in int\$from_to(1,amount) do        if simulate(n,tries,strat) then            ok := ok + 1        end    end    return(ok)end run_simulations % Run simulations and show the resultsshow = proc (title: string,             amount, n, tries: int,             strat: proctype (int,int,sequence[int]) returns (bool))    po: stream := stream\$primary_output()    stream\$puts(po, title || ": ")     ok: int := run_simulations(amount, n, tries, strat)    perc: real := real\$i2r(ok)*100.0/real\$i2r(amount)     stream\$putright(po, int\$unparse(ok), 7)    stream\$puts(po, " out of ")    stream\$putright(po, int\$unparse(amount), 7)    stream\$putl(po, ", " || f_form(perc, 3, 2) || "%")end show  start_up = proc ()    prisoners   = 100    tries       = 50    simulations = 50000     init_rng()     show(" Random", simulations, prisoners, tries, rand_strat)    show("Optimal", simulations, prisoners, tries, opt_strat)end start_up`
Output:
``` Random:       0 out of   50000, 0.00%
Optimal:   15541 out of   50000, 31.08%```

## Commodore BASIC

It should be noted that this is a very time consuming process for a ~1 MHz 8-bit computer. Evaluating 1000 trials of each method with the algorithm below takes about 3.5 hours on the BASIC system clock (TIME\$) of a stock NTSC Commodore 64, even with screen blanking. (Screen blanking seems to achieve only a 3% improvement in speed.) Actual test of 4000 trials for each method were run on the VICE emulator with warp speed engaged, otherwise the user would have had to wait a day and a half for results.

Another concern is when the prisoner's number is found. When this happens it becomes unnecessary to use whatever guesses are remaining; we should simply move on to the next prisoner. Furthermore, if any prisoner uses all 50 guesses with no luck, then everyone is out of luck and the trial is over, which means no other prisoner needs to make the attempt.

This potentially could cause problems on the stack with unfinished guessing (or prisoner) loops, especially where stack limits are extremely small however, a few things are happening to prevent this (See C64-Wiki "NEXT: Early Exits..." for reference.):

1. The prisoner loop, and each prisoner's 50-guesses loop, are contained within a subroutine. The RETURN at the end of either subroutine terminates any unfinished loops and keeps the stack clean.
2. When the NEXT belonging to loop 'i' is encountered, any inner loops ('g') are terminated.
3. Similar to above, any new loop using an existing loop's variable terminates the old loop, and any nested loops within it.

The key here is avoiding the use of GOTO as a means of exiting a loop early.

` 10 rem 100 prisoners20 rem set arrays30 rem dr = drawers containing card values40 rem ig = a list of numbers 1 through 100, shuffled to become the 41 rem guess sequence for each inmate - method 150 dim dr(100),ig(100)55 rem initialize drawers with own card in each drawer60 for i=1 to 100:dr(i)=i:next  1000 print chr\$(147);"how many trials for each method";:input tt1010 for m=1 to 2:su(m)=0:fa(m)=01015 for tn=1 to tt1020 on m gosub 2000,30001025 rem ip = number of inmates who passed1030 if ip=100 then su(m)=su(m)+11040 if ip<100 then fa(m)=fa(m)+11045 next tn1055 next m 1060 print chr\$(147);"Results:":print1070 print "Out of";tt;"trials, the results are"1071 print "as follows...":print1072 print "1. Random Guessing:"1073 print "  ";su(1);"successes"1074 print "  ";fa(1);"failures"1075 print "  ";su(1)/tn;"{left-crsr}% success rate.":print1077 print "2. Chained Number Picking:"1078 print "  ";su(2);"successes"1079 print "  ";fa(2);"failures"1080 print "  ";(su(2)/tn)*100;"{left-crsr}% success rate.":print1100 print:print "Again?"1110 get k\$:if k\$="" then 11101120 if k\$="y" then 10001500 end 2000 rem random guessing method2005 for x=1 to 100:ig(x)=x:next:ip=0:gosub 40002007 for i=1 to 1002010 for x=1 to 100:t=ig(x):np=int(rnd(1)*100)+1:ig(x)=ig(np):ig(np)=t:next2015 for g=1 to 502020 if dr(ig(g))=i then ip=ip+1:next i:return2025 next g2030 return 3000 rem chained method3005 ip=0:gosub 40003007 rem iterate through each inmate3010 fori=1to1003015 ng=i:forg=1to503020 cd=dr(ng)3025 ifcd=ithenip=ip+1:nexti:return3030 ifcd<>ithenng=cd3035 nextg:return 4000 rem shuffle the drawer cards randomly4010 x=rnd(-ti)4020 for i=1 to 1004030 r=int(rnd(1)*100)+1:t=dr(i):dr(i)=dr(r):dr(r)=t:next4040 return `
Output:
```Results:

Out of 4000 trials the percentage of
success is as follows...

1. Random Guessing:
0 successes
4000 failures
0% success rate.

2. Chained Number Picking:
1274 successes
2726 failures
31.85% success rate.
```

## Common Lisp

Translation of: Racket
` (defparameter *samples* 10000)(defparameter *prisoners* 100)(defparameter *max-guesses* 50) (defun range (n)  "Returns a list from 0 to N."  (loop     for i below n     collect i)) (defun nshuffle (list)  "Returns a shuffled LIST."  (loop     for i from (length list) downto 2     do (rotatef (nth (random i) list)                 (nth (1- i) list)))  list) (defun build-drawers ()  "Returns a list of shuffled drawers."  (nshuffle (range *prisoners*))) (defun strategy-1 (drawers p)  "Returns T if P is found in DRAWERS under *MAX-GUESSES* using a random strategy."  (loop     for i below *max-guesses*     thereis (= p (nth (random *prisoners*) drawers)))) (defun strategy-2 (drawers p)  "Returns T if P is found in DRAWERS under *MAX-GUESSES* using an optimal strategy."  (loop     for i below *max-guesses*     for j = p then (nth j drawers)     thereis (= p (nth j drawers)))) (defun 100-prisoners-problem (strategy &aux (drawers (build-drawers)))  "Returns T if all prisoners find their number using the given STRATEGY."  (every (lambda (e) (eql T e))         (mapcar (lambda (p) (funcall strategy drawers p)) (range *prisoners*)))) (defun sampling (strategy)  (loop     repeat *samples*     for result = (100-prisoners-problem strategy)      count result)) (defun compare-strategies ()  (format t "Using a random strategy in ~4,2F % of the cases the prisoners are free.~%" (* (/ (sampling #'strategy-1) *samples*) 100))  (format t "Using an optimal strategy in ~4,2F % of the cases the prisoners are free.~%" (* (/ (sampling #'strategy-2) *samples*) 100))) `
Output:
```CL-USER> (compare-strategies)
Using a random strategy in 0.00 % of the cases the prisoners are free.
Using an optimal strategy in 31.34 % of the cases the prisoners are free.```

## Cowgol

`include "cowgol.coh";include "argv.coh"; # Parametersconst Drawers     := 100;   # Amount of drawers (and prisoners)const Attempts    := 50;    # Amount of attempts a prisoner may makeconst Simulations := 2000;  # Amount of simulations to run typedef NSim is int(0, Simulations); # Random number generatorrecord RNG is    x: uint8;    a: uint8;    b: uint8;    c: uint8;    state @at(0): int32;end record; sub RandomByte(r: [RNG]): (byte: uint8) is     r.x := r.x + 1;    r.a := r.a ^ r.c ^ r.x;    r.b := r.b + r.a;    r.c := r.c + (r.b >> 1) ^ r.a;    byte := r.c;end sub; sub RandomUpTo(r: [RNG], limit: uint8): (rslt: uint8) is    var x: uint8 := 1;    while x < limit loop        x := x << 1;    end loop;    x := x - 1;     loop        rslt := RandomByte(r) & x;        if rslt < limit then            break;        end if;    end loop;end sub; # Drawers (though marked 0..99 instead of 1..100)var drawers: uint8[Drawers];typedef Drawer is @indexof drawers;typedef Prisoner is Drawer; # Place cards randomly in drawerssub InitDrawers(r: [RNG]) is    var x: Drawer := 0;    while x < Drawers loop        drawers[x] := x;        x := x + 1;    end loop;     x := 0;    while x < Drawers - 1 loop        var y := x + RandomUpTo(r, Drawers-x);        var t := drawers[x];        drawers[x] := drawers[y];        drawers[y] := t;        x := x + 1;    end loop;end sub; # A prisoner can apply a strategy and either succeed or notinterface Strategy(p: Prisoner, r: [RNG]): (success: uint8); # The stupid strategy: open drawers randomly.sub Stupid implements Strategy is    # Let's assume the prisoner is smart enough not to reopen an open drawer    var opened: Drawer[Drawers];    MemZero(&opened, @bytesof opened);     # Open random drawers    success := 0;    var triesLeft: uint8 := Attempts;    while triesLeft != 0 loop        var d := RandomUpTo(r, Drawers); # grab a random drawer        if opened[d] != 0 then            continue; # Ignore it if a drawer was already open        else            triesLeft := triesLeft - 1;            opened[d] := 1;            if drawers[d] == p then # found it!                success := 1;                return;            end if;        end if;    end loop;end sub; # The optimal strategy: open the drawer for each numbersub Optimal implements Strategy is    var current := p;    var triesLeft: uint8 := Attempts;    success := 0;    while triesLeft != 0 loop        current := drawers[current];        if current == p then            success := 1;            return;        end if;        triesLeft := triesLeft - 1;    end loop;end sub; # Run a simulationsub Simulate(s: Strategy, r: [RNG]): (success: uint8) is    InitDrawers(r); # place cards randomly in drawer    var p: Prisoner := 0;    success := 1; # if they all succeed the simulation succeeds    while p < Drawers loop # but for each prisoner...         if s(p, r) == 0 then # if he fails, the simulation fails            success := 0;            return;        end if;        p := p + 1;    end loop;end sub; # Run an amount of simulations and report the amount of successessub Run(n: NSim, s: Strategy, r: [RNG]): (successes: NSim) is    successes := 0;    while n > 0 loop        successes := successes + Simulate(s, r) as NSim;        n := n - 1;    end loop;end sub; # Initialize RNG with number given on command line (defaults to 0)var rng: RNG; rng.state := 0;ArgvInit();var arg := ArgvNext();if arg != 0 as [uint8] then    (rng.state, arg) := AToI(arg);end if; sub RunAndPrint(name: [uint8], strat: Strategy) is    print(name);    print(" strategy: ");    var succ := Run(Simulations, strat, &rng) as uint32;    print_i32(succ);    print(" out of ");    print_i32(Simulations);    print(" - ");    print_i32(succ * 100 / Simulations);    print("%\n");end sub; RunAndPrint("Stupid", Stupid);RunAndPrint("Optimal", Optimal);`
Output:
```Stupid strategy: 0 out of 2000 - 0%
Optimal strategy: 634 out of 2000 - 31%```

## Crystal

Based on the Ruby implementation

`prisoners = (1..100).to_aN = 100_000generate_rooms = ->{ (1..100).to_a.shuffle } res = N.times.count do  rooms = generate_rooms.call  prisoners.all? { |pr| rooms[1, 100].sample(50).includes?(pr) }endputs "Random strategy : %11.4f %%" % (res.fdiv(N) * 100) res = N.times.count do  rooms = generate_rooms.call  prisoners.all? do |pr|    cur_room = pr    50.times.any? do      cur_room = rooms[cur_room - 1]      found = (cur_room == pr)      found    end  endendputs "Optimal strategy: %11.4f %%" % (res.fdiv(N) * 100)`
Output:
```Random strategy :      0.0000 %
Optimal strategy:     31.3190 %```

## D

Translation of: Kotlin
`import std.array;import std.random;import std.range;import std.stdio;import std.traits; bool playOptimal() {    auto secrets = iota(100).array.randomShuffle();     prisoner:    foreach (p; 0..100) {        auto choice = p;        foreach (_; 0..50) {            if (secrets[choice] == p) continue prisoner;            choice = secrets[choice];        }        return false;    }     return true;} bool playRandom() {    auto secrets = iota(100).array.randomShuffle();     prisoner:    foreach (p; 0..100) {        auto choices = iota(100).array.randomShuffle();        foreach (i; 0..50) {            if (choices[i] == p) continue prisoner;        }        return false;    }     return true;} double exec(const size_t n, bool function() play) {    size_t success = 0;    for (int i = n; i > 0; i--) {        if (play()) {            success++;        }    }    return 100.0 * success / n;} void main() {    enum N = 1_000_000;    writeln("# of executions: ", N);    writefln("Optimal play success rate: %11.8f%%", exec(N, &playOptimal));    writefln(" Random play success rate: %11.8f%%", exec(N, &playRandom));}`
Output:
```# of executions: 1000000
Optimal play success rate: 31.16100000%
Random play success rate:  0.00000000%```

See #Pascal.

## EasyLang

`for i range 100  drawer[] &= i  sampler[] &= i.subr shuffle_drawer  for i = len drawer[] downto 2    r = random i    swap drawer[r] drawer[i - 1]  ..subr play_random  call shuffle_drawer  found = 1  prisoner = 0  while prisoner < 100 and found = 1    found = 0    i = 0    while i < 50 and found = 0      r = random (100 - i)      card = drawer[sampler[r]]      swap sampler[r] sampler[100 - i - 1]      if card = prisoner        found = 1      .      i += 1    .    prisoner += 1  ..subr play_optimal  call shuffle_drawer  found = 1  prisoner = 0  while prisoner < 100 and found = 1    reveal = prisoner    found = 0    i = 0    while i < 50 and found = 0      card = drawer[reveal]      if card = prisoner        found = 1      .      reveal = card      i += 1    .    prisoner += 1  ..n = 10000pardoned = 0for round range n  call play_random  pardoned += found.print "random: " & 100.0 * pardoned / n & "%"# pardoned = 0for round range n  call play_optimal  pardoned += found.print "optimal: " & 100.0 * pardoned / n & "%"`
Output:
```random: 0.000%
optimal: 30.800%
```

## Elixir

Translation of: Ruby
`defmodule HundredPrisoners do  def optimal_room(_, _, _, []), do: []  def optimal_room(prisoner, current_room, rooms, [_ | tail]) do    found = Enum.at(rooms, current_room - 1) == prisoner    next_room = Enum.at(rooms, current_room - 1)    [found] ++ optimal_room(prisoner, next_room, rooms, tail)  end   def optimal_search(prisoner, rooms) do    Enum.any?(optimal_room(prisoner, prisoner, rooms, Enum.to_list(1..50)))  endend prisoners = 1..100n = 1..10_000generate_rooms = fn -> Enum.shuffle(1..100) end random_strategy = Enum.count(n,   fn _ ->   rooms = generate_rooms.()  Enum.all?(prisoners, fn pr -> pr in (rooms |> Enum.take_random(50)) end)end) IO.puts "Random strategy: #{random_strategy} / #{n |> Range.size}" optimal_strategy = Enum.count(n,  fn _ ->  rooms = generate_rooms.()  Enum.all?(prisoners,     fn pr -> HundredPrisoners.optimal_search(pr, rooms) end)end) IO.puts "Optimal strategy: #{optimal_strategy} / #{n |> Range.size}"`
Output:
```Random strategy: 0 / 10000
Optimal strategy: 3110 / 10000
```

## F#

`let rnd = System.Random()let shuffled min max =    [|min..max|] |> Array.sortBy (fun _ -> rnd.Next(min,max+1)) let drawers () = shuffled 1 100 // strategy randomizing drawer openinglet badChoices (drawers' : int array) =    Seq.init 100 (fun _ -> shuffled 1 100 |> Array.take 50) // selections for each prisoner    |> Seq.map (fun indexes -> indexes |> Array.map(fun index -> drawers'.[index-1])) // transform to cards    |> Seq.mapi (fun i cards -> cards |> Array.contains i) // check if any card matches prisoner number    |> Seq.contains false // true means not all prisoners got their cardslet outcomeOfRandom runs =    let pardons = Seq.init runs (fun _ -> badChoices (drawers ()))                  |> Seq.sumBy (fun badChoice -> if badChoice |> not then 1.0 else 0.0)    pardons/ float runs // strategy optimizing drawer openinglet smartChoice max prisoner (drawers' : int array) =    prisoner    |> Seq.unfold (fun selection ->        let card = drawers'.[selection-1]        Some (card, card))    |> Seq.take max    |> Seq.contains prisonerlet smartChoices (drawers' : int array) =    seq { 1..100 }    |> Seq.map (fun prisoner -> smartChoice 50 prisoner drawers')    |> Seq.filter (fun result -> result |> not) // remove all but false results    |> Seq.isEmpty // empty means all prisoners got their cardslet outcomeOfOptimize runs =    let pardons = Seq.init runs (fun _ -> smartChoices (drawers()))                  |> Seq.sumBy (fun smartChoice' -> if smartChoice' then 1.0 else 0.0)    pardons/ float runs printfn \$"Using Random Strategy: {(outcomeOfRandom 20000):p2}"printfn \$"Using Optimum Strategy: {(outcomeOfOptimize 20000):p2}" `
Output:
```Using Random Strategy: 0.00%
Using Optimum Strategy: 31.06%
```

## Factor

`USING: arrays formatting fry io kernel math random sequences ; : setup ( -- seq seq ) 100 <iota> dup >array randomize ; : rand ( -- ? )    setup [ 50 sample member? not ] curry find nip >boolean not ; : trail ( m seq -- n )    50 pick '[ [ nth ] keep over _ = ] replicate [ t = ] any?    2nip ; : optimal ( -- ? ) setup [ trail ] curry [ and ] map-reduce ; : simulate ( m quot -- x )    dupd replicate [ t = ] count swap /f 100 * ; inline "Simulation count: 10,000" print10,000 [ rand ] simulate "Random play success: "10,000 [ optimal ] simulate "Optimal play success: "[ write "%.2f%%\n" printf ] [email protected]`
Output:
```Simulation count: 10,000
Random play success: 0.00%
Optimal play success: 31.11%
```

## FOCAL

`01.10 T %5.02," RANDOM";S CU=001.20 F Z=1,2000;D 5;S CU=CU+SU01.30 T CU/20,!,"OPTIMAL";S CU=001.40 F Z=1,2000;D 6;S CU=CU+SU01.50 T CU/20,!01.60 Q 02.01 C-- PUT CARDS IN RANDOM DRAWERS02.10 F X=1,100;S D(X)=X02.20 F X=1,99;D 2.3;S B=D(X);S D(X)=D(A);S D(A)=B02.30 D 2.4;S A=X+FITR(A*(101-X))02.40 S A=FABS(FRAN()*10);S A=A-FITR(A) 03.01 C-- PRISONER X TRIES UP TO 50 RANDOM DRAWERS03.10 S TR=50;S SU=003.20 D 2.4;I (X-D(A))3.3,3.4,3.303.30 S TR=TR-1;I (TR),3.5,3.203.40 S SU=1;R03.50 S SU=0 04.01 C-- PRISONER X TRIES OPTIMAL METHOD04.10 S TR=50;S SU=0;S A=X04.20 I (X-D(A))4.3,4.4,4.304.30 S TR=TR-1;S A=D(A);I (TR),4.5,4.204.40 S SU=1;R04.50 S SU=0 05.01 C-- PRISONERS TRY RANDOM METHOD UNTIL ONE FAILS05.10 D 2;S X=105.20 I (X-101)5.3,5.405.30 D 3;S X=X+1;I (SU),5.4,5.205.40 R 06.01 C-- PRISONERS TRY OPTIMAL METHOD UNTIL ONE FAILS06.10 D 2;S X=106.20 I (X-101)6.3,6.406.30 D 4;S X=X+1;I (SU),6.4,6.206.40 R`
Output:
``` RANDOM=   0.00
OPTIMAL=  30.10```

## Forth

ANS Forth has no in-built facility for random numbers, but libraries are available.

Works with: ANS Forth

Here is a solution using ran4.seq from The Forth Scientific Library, available here.

Run the two strategies (random and follow the card number) 10,000 times each, and show number or successes.

`INCLUDE ran4.seq 100      CONSTANT #drawers#drawers CONSTANT #players100000   CONSTANT #tries CREATE drawers  #drawers CELLS ALLOT                    \ index 0..#drawers-1 : drawer[]                              ( n -- addr )   \ return address of drawer n    CELLS drawers +; : random_drawer                         ( -- n )        \ n=0..#drawers-1 random drawer     RAN4 ( d ) XOR ( n ) #drawers MOD; : random_drawer[]                       ( -- addr )     \ return address of random drawer    random_drawer drawer[]; : swap_indirect                         ( addr1 addr2 -- )  \ swaps the values at the two addresses    2DUP @ SWAP @                       ( addr1 addr2 n2 n1 )    ROT ! SWAP !                        \ store n1 at addr2 and n2 at addr1; : init_drawers                          ( -- ) \ shuffle cards into drawers    #drawers 0 DO        I I drawer[] !                  \ store cards in order    LOOP    #drawers 0 DO        I drawer[]  random_drawer[]     ( addr-drawer-i addr-drawer-rnd )        swap_indirect    LOOP; : random_turn                           ( player - f )    #drawers 2 / 0 DO		random_drawer 		drawer[] @ 		OVER = IF			DROP TRUE UNLOOP EXIT	\ found his number		THEN	LOOP 	DROP FALSE; 0 VALUE player : cycle_turn                            ( player - f )	DUP TO player			( next-drawer )    #drawers 2 / 0 DO		drawer[] @		DUP player = IF 			DROP TRUE UNLOOP EXIT	\ found his number		THEN	LOOP 	DROP FALSE; : turn                                  ( strategy player - f )    SWAP 0= IF                          \ random play         random_turn    ELSE        cycle_turn    THEN; : play                                  ( strategy -- f ) \ return true if prisioners survived    init_drawers    #players 0 DO        DUP I turn        0= IF            DROP FALSE UNLOOP EXIT 	\ this player did not survive, UNLOOP, return false        THEN    LOOP     DROP TRUE                           \ all survived, return true; : trie					( strategy - nr-saved )	0				( strategy nr-saved )	#tries 0 DO		OVER play IF 1+ THEN	LOOP	NIP; 0 trie . CR	\ random strategy1 trie . CR	\ follow the card number strategy`

output:

```0
30009
```

## Fortran

`SUBROUTINE SHUFFLE_ARRAY(INT_ARRAY)    ! Takes an input array and shuffles the elements by swapping them    ! in pairs in turn 10 times    IMPLICIT NONE     INTEGER, DIMENSION(100), INTENT(INOUT) :: INT_ARRAY    INTEGER, PARAMETER :: N_PASSES = 10    ! Local Variables     INTEGER :: TEMP_1, TEMP_2   ! Temporaries for swapping elements    INTEGER :: I, J, PASS       ! Indices variables    REAL :: R                   ! Randomly generator value     CALL RANDOM_SEED()  ! Seed the random number generator     DO PASS=1, N_PASSES        DO I=1, SIZE(INT_ARRAY)             ! Get a random index to swap with            CALL RANDOM_NUMBER(R)            J = CEILING(R*SIZE(INT_ARRAY))             ! In case generated index value            ! exceeds array size            DO WHILE (J > SIZE(INT_ARRAY))                J = CEILING(R*SIZE(INT_ARRAY))            END DO             !  Swap the two elements            TEMP_1 = INT_ARRAY(I)            TEMP_2 = INT_ARRAY(J)            INT_ARRAY(I) = TEMP_2            INT_ARRAY(J) = TEMP_1        ENDDO    ENDDOEND SUBROUTINE SHUFFLE_ARRAY SUBROUTINE RUN_RANDOM(N_ROUNDS)    ! Run the 100 prisoner puzzle simulation N_ROUNDS times    ! in the scenario where each prisoner selects a drawer at random    IMPLICIT NONE     INTEGER, INTENT(IN) :: N_ROUNDS ! Number of simulations to run in total     INTEGER :: ROUND, PRISONER, CHOICE, I       ! Iteration variables    INTEGER :: N_SUCCESSES                      ! Number of successful trials    REAL(8) :: TOTAL                            ! Total number of trials as real    LOGICAL :: NUM_FOUND = .FALSE.              ! Prisoner has found their number     INTEGER, DIMENSION(100) :: CARDS, CHOICES   ! Arrays representing card allocations                                                ! to draws and drawer choice order     ! Both cards and choices are randomly assigned.    ! This being the drawer (allocation represented by index),    ! and what drawer to pick for Nth/50 choice    ! (take first 50 elements of 100 element array)    CARDS = (/(I, I=1, 100, 1)/)    CHOICES = (/(I, I=1, 100, 1)/)     N_SUCCESSES = 0    TOTAL = REAL(N_ROUNDS)     ! Run the simulation for N_ROUNDS rounds    ! when a prisoner fails to find their number    ! after 50 trials, set that simulation to fail    ! and start the next round    ROUNDS_LOOP: DO ROUND=1, N_ROUNDS        CALL SHUFFLE_ARRAY(CARDS)        PRISONERS_LOOP: DO PRISONER=1, 100            NUM_FOUND = .FALSE.            CALL SHUFFLE_ARRAY(CHOICES)            CHOICE_LOOP: DO CHOICE=1, 50                IF(CARDS(CHOICE) == PRISONER) THEN                    NUM_FOUND = .TRUE.                    EXIT CHOICE_LOOP                ENDIF            ENDDO CHOICE_LOOP            IF(.NOT. NUM_FOUND) THEN                EXIT PRISONERS_LOOP            ENDIF        ENDDO PRISONERS_LOOP        IF(NUM_FOUND) THEN            N_SUCCESSES = N_SUCCESSES + 1        ENDIF    ENDDO ROUNDS_LOOP     WRITE(*, '(A, F0.3, A)') "Random drawer selection method success rate: ", &        100*N_SUCCESSES/TOTAL, "%" END SUBROUTINE RUN_RANDOM SUBROUTINE RUN_OPTIMAL(N_ROUNDS)    ! Run the 100 prisoner puzzle simulation N_ROUNDS times in the scenario    ! where each prisoner selects firstly the drawer with their number and then    ! subsequently the drawer matching the number of the card present     ! within that current drawer    IMPLICIT NONE     INTEGER, INTENT(IN) :: N_ROUNDS     INTEGER :: ROUND, PRISONER, CHOICE, I   ! Iteration variables    INTEGER :: CURRENT_DRAW                 ! ID of the current draw    INTEGER :: N_SUCCESSES                  ! Number of successful trials    REAL(8) :: TOTAL                        ! Total number of trials as real    LOGICAL :: NUM_FOUND = .FALSE.          ! Prisoner has found their number     INTEGER, DIMENSION(100) :: CARDS        ! Array representing card allocations     ! Cards are randomly assigned to a drawer     ! (allocation represented by index),    CARDS = (/(I, I=1, 100, 1)/)     N_SUCCESSES = 0    TOTAL = REAL(N_ROUNDS)     ! Run the simulation for N_ROUNDS rounds    ! when a prisoner fails to find their number    ! after 50 trials, set that simulation to fail    ! and start the next round    ROUNDS_LOOP: DO ROUND=1, N_ROUNDS        CARDS = (/(I, I=1, 100, 1)/)        CALL SHUFFLE_ARRAY(CARDS)        PRISONERS_LOOP: DO PRISONER=1, 100            CURRENT_DRAW = PRISONER            NUM_FOUND = .FALSE.            CHOICE_LOOP: DO CHOICE=1, 50                IF(CARDS(CURRENT_DRAW) == PRISONER) THEN                    NUM_FOUND = .TRUE.                    EXIT CHOICE_LOOP                ELSE                    CURRENT_DRAW = CARDS(CURRENT_DRAW)                ENDIF            ENDDO CHOICE_LOOP            IF(.NOT. NUM_FOUND) THEN                EXIT PRISONERS_LOOP            ENDIF        ENDDO PRISONERS_LOOP        IF(NUM_FOUND) THEN            N_SUCCESSES = N_SUCCESSES + 1        ENDIF    ENDDO ROUNDS_LOOP    WRITE(*, '(A, F0.3, A)') "Optimal drawer selection method success rate: ", &        100*N_SUCCESSES/TOTAL, "%" END SUBROUTINE RUN_OPTIMAL PROGRAM HUNDRED_PRISONERS    ! Run the two scenarios for the 100 prisoners puzzle of random choice    ! and optimal choice (choice based on drawer contents)    IMPLICIT NONE    INTEGER, PARAMETER :: N_ROUNDS = 50000    WRITE(*,'(A, I0, A)') "Running simulation for ", N_ROUNDS, " trials..."    CALL RUN_RANDOM(N_ROUNDS)    CALL RUN_OPTIMAL(N_ROUNDS)END PROGRAM HUNDRED_PRISONERS`

output:

```Running simulation for 50000 trials...
Random drawer selection method success rate: .000%
Optimal drawer selection method success rate: 31.360%
```

## FreeBASIC

`#include once "knuthshuf.bas"   'use the routines in https://rosettacode.org/wiki/Knuth_shuffle#FreeBASIC function gus( i as long, strat as boolean ) as long    if strat then return i    return 1+int(rnd*100)end function sub trials( byref c_success as long, byref c_fail as long, byval strat as boolean )        dim as long i, j, k, guess, drawer(1 to 100)    for i = 1 to 100        drawer(i) = i    next i    for j = 1 to 1000000 'one million trials of prisoners        knuth_up( drawer() )  'shuffles the cards in the drawers            for i = 1 to 100 'prisoner number            guess = gus(i, strat)            for k = 1 to 50 'each prisoner gets 50 tries                if drawer(guess) = i then goto next_prisoner                guess = gus(drawer(guess), strat)            next k            c_fail += 1            goto next_trial            next_prisoner:        next i        c_success += 1        next_trial:    next jend sub randomize timerdim as long c_fail=0, c_success=0 trials( c_success, c_fail, false ) print using "For prisoners guessing randomly we had ####### successes and ####### failures.";c_success;c_fail c_success = 0c_fail = 0 trials( c_success, c_fail, true ) print using "For prisoners using the strategy we had ####### successes and ####### failures.";c_success;c_fail`

## Gambas

Implementation of the '100 Prisoners' program written in VBA. Tested in Gambas 3.15.2

`' Gambas module file Public DrawerArray As Long[]Public NumberFromDrawer As LongPublic FoundOwnNumber As Long Public Sub Main()   Dim NumberOfPrisoners As Long  Dim Selections As Long  Dim Tries As Long   Print "Number of prisoners (default, 100)?"  Try Input NumberOfPrisoners  If Error Then NumberOfPrisoners = 100   Print "Number of selections (default, half of prisoners)?"   Try Input Selections  If Error Then Selections = NumberOfPrisoners / 2   Print "Number of tries (default, 1000)?"  Try Input Tries  If Error Then Tries = 1000   Dim AllFoundOptimal As Long = 0  Dim AllFoundRandom As Long = 0  Dim AllFoundRandomMem As Long = 0   Dim i As Long  Dim OptimalCount As Long  Dim RandomCount As Long  Dim RandomMenCount As Long   Dim fStart As Float = Timer   For i = 1 To Tries    OptimalCount = HundredPrisoners_Optimal(NumberOfPrisoners, Selections)    RandomCount = HundredPrisoners_Random(NumberOfPrisoners, Selections)    RandomMenCount = HundredPrisoners_Random_Mem(NumberOfPrisoners, Selections)     If OptimalCount = NumberOfPrisoners Then AllFoundOptimal += 1    If RandomCount = NumberOfPrisoners Then AllFoundRandom += 1    If RandomMenCount = NumberOfPrisoners Then AllFoundRandomMem += 1  Next   Dim fTime As Float = Timer - fStart  fTime = Round(ftime, -1)   Print  Print "Result with " & NumberOfPrisoners & " prisoners, " & Selections & " selections and " & Tries & " tries. "  Print  Print "Optimal: " & AllFoundOptimal & " of " & Tries & ": " & Str(AllFoundOptimal / Tries * 100) & " %"  Print "Random: " & AllFoundRandom & " of " & Tries & ": " & Str(AllFoundRandom / Tries * 100) & " %"  Print "RandomMem: " & AllFoundRandomMem & " of " & Tries & ": " & Str(AllFoundRandomMem / Tries * 100) & " %"  Print  Print "Elapsed Time: " & fTime & " sec"  Print  Print "Trials/sec: " & Round(Tries / fTime, -1) End Function HundredPrisoners_Optimal(NrPrisoners As Long, NrSelections As Long) As Long   DrawerArray = New Long[NrPrisoners]  Dim Counter As Long   For Counter = 0 To DrawerArray.Max    DrawerArray[Counter] = Counter + 1  Next   DrawerArray.Shuffle()   Dim i As Long  Dim j As Long  FoundOwnNumber = 0   For i = 1 To NrPrisoners    For j = 1 To NrSelections      If j = 1 Then NumberFromDrawer = DrawerArray[i - 1]       If NumberFromDrawer = i Then        FoundOwnNumber += 1        Break      Endif      NumberFromDrawer = DrawerArray[NumberFromDrawer - 1]    Next  Next  Return FoundOwnNumber End Function HundredPrisoners_Random(NrPrisoners As Long, NrSelections As Long) As Long   Dim RandomDrawer As Long  Dim Counter As Long   DrawerArray = New Long[NrPrisoners]   For Counter = 0 To DrawerArray.Max    DrawerArray[Counter] = Counter + 1  Next   DrawerArray.Shuffle()   Dim i As Long  Dim j As Long  FoundOwnNumber = 0   Randomize   For i = 1 To NrPrisoners    For j = 1 To NrSelections      RandomDrawer = CLong(Rand(NrPrisoners - 1))      NumberFromDrawer = DrawerArray[RandomDrawer]      If NumberFromDrawer = i Then        FoundOwnNumber += 1        Break      Endif    Next  Next  Return FoundOwnNumber End Function HundredPrisoners_Random_Mem(NrPrisoners As Long, NrSelections As Long) As Long   Dim SelectionArray As New Long[NrPrisoners]  Dim Counter As Long   DrawerArray = New Long[NrPrisoners]   For Counter = 0 To DrawerArray.Max    DrawerArray[Counter] = Counter + 1   Next   For Counter = 0 To SelectionArray.Max    SelectionArray[Counter] = Counter + 1   Next   DrawerArray.Shuffle()   Dim i As Long  Dim j As Long  FoundOwnNumber = 0   For i = 1 To NrPrisoners    SelectionArray.Shuffle()    For j = 1 To NrSelections      NumberFromDrawer = DrawerArray[SelectionArray[j - 1] - 1]      If NumberFromDrawer = i Then        FoundOwnNumber += 1        Break      Endif      NumberFromDrawer = DrawerArray[NumberFromDrawer - 1]    Next  Next  Return FoundOwnNumber End`
Output:
```Number of prisoners (default, 100)?
100
Number of selections (default, half of prisoners)?
50
Number of tries (default, 1000)?

Result with 100 prisoners, 50 selections and 1000 tries.

Optimal: 311 of 1000: 31,1 %
Random: 0 of 1000: 0 %
RandomMem: 0 of 1000: 0 %

Elapsed Time: 8.7 sec

Trials/sec: 114.9```

## Go

`package main import (    "fmt"    "math/rand"    "time") // Uses 0-based numbering rather than 1-based numbering throughout.func doTrials(trials, np int, strategy string) {    pardoned := 0trial:    for t := 0; t < trials; t++ {        var drawers int        for i := 0; i < 100; i++ {            drawers[i] = i        }        rand.Shuffle(100, func(i, j int) {            drawers[i], drawers[j] = drawers[j], drawers[i]        })    prisoner:        for p := 0; p < np; p++ {            if strategy == "optimal" {                prev := p                for d := 0; d < 50; d++ {                    this := drawers[prev]                    if this == p {                        continue prisoner                    }                    prev = this                }            } else {                // Assumes a prisoner remembers previous drawers (s)he opened                // and chooses at random from the others.                var opened bool                for d := 0; d < 50; d++ {                    var n int                    for {                        n = rand.Intn(100)                        if !opened[n] {                            opened[n] = true                            break                        }                    }                    if drawers[n] == p {                        continue prisoner                    }                }            }            continue trial        }        pardoned++    }    rf := float64(pardoned) / float64(trials) * 100    fmt.Printf("  strategy = %-7s  pardoned = %-6d relative frequency = %5.2f%%\n\n", strategy, pardoned, rf)} func main() {    rand.Seed(time.Now().UnixNano())    const trials = 100000    for _, np := range []int{10, 100} {        fmt.Printf("Results from %d trials with %d prisoners:\n\n", trials, np)        for _, strategy := range string{"random", "optimal"} {            doTrials(trials, np, strategy)        }    }}`
Output:
```Results from 100000 trials with 10 prisoners:

strategy = random   pardoned = 99     relative frequency =  0.10%

strategy = optimal  pardoned = 31205  relative frequency = 31.20%

Results from 100000 trials with 100 prisoners:

strategy = random   pardoned = 0      relative frequency =  0.00%

strategy = optimal  pardoned = 31154  relative frequency = 31.15%
```

## Groovy

Translation of: Java
`import java.util.function.Functionimport java.util.stream.Collectorsimport java.util.stream.IntStream class Prisoners {    private static boolean playOptimal(int n) {        List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList())        Collections.shuffle(secretList)         prisoner:        for (int i = 0; i < secretList.size(); ++i) {            int prev = i            for (int j = 0; j < secretList.size() / 2; ++j) {                if (secretList.get(prev) == i) {                    continue prisoner                }                prev = secretList.get(prev)            }            return false        }        return true    }     private static boolean playRandom(int n) {        List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList())        Collections.shuffle(secretList)         prisoner:        for (Integer i : secretList) {            List<Integer> trialList = IntStream.range(0, n).boxed().collect(Collectors.toList())            Collections.shuffle(trialList)             for (int j = 0; j < trialList.size() / 2; ++j) {                if (Objects.equals(trialList.get(j), i)) {                    continue prisoner                }            }             return false        }        return true    }     private static double exec(int n, int p, Function<Integer, Boolean> play) {        int succ = 0        for (int i = 0; i < n; ++i) {            if (play.apply(p)) {                succ++            }        }        return (succ * 100.0) / n    }     static void main(String[] args) {        final int n = 100_000        final int p = 100        System.out.printf("# of executions: %d\n", n)        System.out.printf("Optimal play success rate: %f%%\n", exec(n, p, Prisoners.&playOptimal))        System.out.printf("Random play success rate: %f%%\n", exec(n, p, Prisoners.&playRandom))    }}`
Output:
```# of executions: 100000
Optimal play success rate: 31.215000%
Random play success rate: 0.000000%```

`import System.Randomimport Control.Monad.State numRuns        = 10000numPrisoners   = 100numDrawerTries = 50type Drawers   = [Int]type Prisoner  =  Inttype Prisoners = [Int] main = do  gen <- getStdGen  putStrLn \$ "Chance of winning when choosing randomly: "  ++ (show \$ evalState runRandomly gen)  putStrLn \$ "Chance of winning when choosing optimally: " ++ (show \$ evalState runOptimally gen)  runRandomly :: State StdGen DoublerunRandomly =  let runResults = replicateM numRuns \$ do         drawers <- state \$ shuffle [1..numPrisoners]         allM (\prisoner -> openDrawersRandomly drawers prisoner numDrawerTries) [1..numPrisoners]   in  ((/ fromIntegral numRuns) . fromIntegral . sum . map fromEnum) `liftM` runResults openDrawersRandomly :: Drawers -> Prisoner -> Int -> State StdGen BoolopenDrawersRandomly drawers prisoner triesLeft = go triesLeft []  where go 0 _ = return False        go triesLeft seenDrawers = do          try <- state \$ randomR (1, numPrisoners)          case try of            x | x == prisoner        -> return True              | x `elem` seenDrawers -> go triesLeft seenDrawers              | otherwise            -> go (triesLeft - 1) (x:seenDrawers) runOptimally :: State StdGen DoublerunOptimally =  let runResults = replicateM numRuns \$ do         drawers <- state \$ shuffle [1..numPrisoners]         return \$ all (\prisoner -> openDrawersOptimally drawers prisoner numDrawerTries) [1..numPrisoners]   in  ((/ fromIntegral numRuns) . fromIntegral . sum . map fromEnum) `liftM` runResults openDrawersOptimally :: Drawers -> Prisoner -> Int -> BoolopenDrawersOptimally drawers prisoner triesLeft = go triesLeft prisoner  where go 0 _ = False        go triesLeft drawerToTry =          let thisDrawer = drawers !! (drawerToTry - 1)           in if thisDrawer == prisoner then True else go (triesLeft - 1) thisDrawer  -- Haskel stdlib is lacking big time, so here some necessary 'library' functions -- make a list of 'len' random values in range 'range' from 'gen'randomLR :: Integral a => Random b => a -> (b, b) -> StdGen -> ([b], StdGen)randomLR 0 range gen = ([], gen)randomLR len range gen =  let (x, newGen) = randomR range gen      (xs, lastGen) = randomLR (len - 1) range newGen  in (x : xs, lastGen)  -- shuffle a list by a generatorshuffle :: [a] -> StdGen -> ([a], StdGen)shuffle list gen = (shuffleByNumbers numbers list, finalGen)  where    n = length list    (numbers, finalGen) = randomLR n (0, n-1) gen    shuffleByNumbers :: [Int] -> [a] -> [a]    shuffleByNumbers [] _ = []    shuffleByNumbers _ [] = []    shuffleByNumbers (i:is) xs = let (start, x:rest) = splitAt (i `mod` length xs) xs                                 in x : shuffleByNumbers is (start ++ rest) -- short-circuit monadic allallM :: Monad m => (a -> m Bool) -> [a] -> m BoolallM func [] = return TrueallM func (x:xs) = func x >>= \res -> if res then allM func xs else return False `
Output:
```Chance of winning when choosing randomly: 0.0
Chance of winning when choosing optimally: 0.3188```

## J

` NB. game is solvable by optimal strategy when the length (#) of theNB. longest (>./) cycle (C.) is at most 50.opt=: 50 >: [: >./ [: > [: #&.> C. NB. for each prisoner randomly open 50 boxes ((50?100){y) and see if NB. the right card is there (p&e.). if not return 0.rand=: monad definefor_p. i.100 do. if. -.p e.(50?100){y do. 0 return. end.end. 1) NB. use both strategies on the same shuffles y times.simulate=: monad define'o r'=. y %~ 100 * +/ ((rand,opt)@?~)"0 y # 100('strategy';'win rate'),('random';(":o),'%'),:'optimal';(":r),'%')`
Output:
```   simulate 10000000
┌────────┬────────┐
│strategy│win rate│
├────────┼────────┤
│random  │0%      │
├────────┼────────┤
│optimal │31.1816%│
└────────┴────────┘
```

## Janet

` (math/seedrandom (os/cryptorand 8)) (defn drawers  "create list and shuffle it"  [prisoners]  (var x (seq [i :range [0 prisoners]] i))  (loop [i :down [(- prisoners 1) 0]]    (var j (math/floor (* (math/random) (+ i 1))))    (var k (get x i))    (put x i (get x j))    (put x j k))  x) (defn optimal-play  "optimal decision path"  [prisoners drawers]  (var result 0)  (loop [i :range [0 prisoners]]    (var choice i)    (loop [j :range [0 50] :until (= (get drawers choice) i)]      (set choice (get drawers choice)))    (cond      (= (get drawers choice) i) (++ result)      (break)))  result) (defn random-play  "random decision path"  [prisoners d]  (var result 0)  (var options (drawers prisoners))  (loop [i :range [0 prisoners]]    (var choice 0)    (loop [j :range [0 (/ prisoners 2)] :until (= (get d j) (get options i))]      (set choice j))    (cond      (= (get d choice) (get options i)) (++ result)      (break)))  result) (defn main [& args]  (def prisoners 100)  (var optimal-success 0)  (var random-success 0)  (var sims 10000)  (for i 0 sims    (var d (drawers prisoners))    (if (= (optimal-play prisoners d) prisoners)      (++ optimal-success))    (if (= (random-play prisoners d) prisoners)      (++ random-success)))  (printf "Simulation count:  %d" sims)  (printf "Optimal play wins: %.1f%%" (* (/ optimal-success sims) 100))  (printf "Random play wins:  %.1f%%" (* (/ random-success sims) 100))) `

Output:

```Simulation count:  10000
Optimal play wins: 33.1%
Random play wins:  0.0%
```

## Java

Translation of: Kotlin
`import java.util.Collections;import java.util.List;import java.util.Objects;import java.util.function.Function;import java.util.function.Supplier;import java.util.stream.Collectors;import java.util.stream.IntStream; public class Main {    private static boolean playOptimal(int n) {        List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList());        Collections.shuffle(secretList);         prisoner:        for (int i = 0; i < secretList.size(); ++i) {            int prev = i;            for (int j = 0; j < secretList.size() / 2; ++j) {                if (secretList.get(prev) == i) {                    continue prisoner;                }                prev = secretList.get(prev);            }            return false;        }        return true;    }     private static boolean playRandom(int n) {        List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList());        Collections.shuffle(secretList);         prisoner:        for (Integer i : secretList) {            List<Integer> trialList = IntStream.range(0, n).boxed().collect(Collectors.toList());            Collections.shuffle(trialList);             for (int j = 0; j < trialList.size() / 2; ++j) {                if (Objects.equals(trialList.get(j), i)) {                    continue prisoner;                }            }             return false;        }        return true;    }     private static double exec(int n, int p, Function<Integer, Boolean> play) {        int succ = 0;        for (int i = 0; i < n; ++i) {            if (play.apply(p)) {                succ++;            }        }        return (succ * 100.0) / n;    }     public static void main(String[] args) {        final int n = 100_000;        final int p = 100;        System.out.printf("# of executions: %d\n", n);        System.out.printf("Optimal play success rate: %f%%\n", exec(n, p, Main::playOptimal));        System.out.printf("Random play success rate: %f%%\n", exec(n, p, Main::playRandom));    }}`
Output:
```# of executions: 100000
Optimal play success rate: 31.343000%
Random play success rate: 0.000000%```

## JavaScript

Translation of: C#
Works with: Node.js
` const _ = require('lodash'); const numPlays = 100000; const setupSecrets = () => {	// setup the drawers with random cards	let secrets = []; 	for (let i = 0; i < 100; i++) {		secrets.push(i);	} 	return _.shuffle(secrets);} const playOptimal = () => { 	let secrets = setupSecrets();  	// Iterate once per prisoner	loop1:	for (let p = 0; p < 100; p++) { 		// whether the prisoner succeedss		let success = false; 		// the drawer number the prisoner chose		let choice = p;  		// The prisoner can choose up to 50 cards		loop2:		for (let i = 0; i < 50; i++) { 			// if the card in the drawer that the prisoner chose is his card			if (secrets[choice] === p){				success = true;				break loop2;			} 			// the next drawer the prisoner chooses will be the number of the card he has.			choice = secrets[choice]; 		}	// each prisoner gets 50 chances  		if (!success) return false; 	} // iterate for each prisoner  	return true;} const playRandom = () => { 	let secrets = setupSecrets(); 	// iterate for each prisoner 	for (let p = 0; p < 100; p++) { 		let choices = setupSecrets(); 		let success = false; 		for (let i = 0; i < 50; i++) { 			if (choices[i] === p) {				success = true;				break;			}		} 		if (!success) return false;	} 	return true;} const execOptimal = () => { 	let success = 0; 	for (let i = 0; i < numPlays; i++) { 		if (playOptimal()) success++; 	} 	return 100.0 * success / 100000;} const execRandom = () => { 	let success = 0; 	for (let i = 0; i < numPlays; i++) { 		if (playRandom()) success++; 	} 	return 100.0 * success / 100000;} console.log("# of executions: " + numPlays);console.log("Optimal Play Success Rate: " + execOptimal());console.log("Random Play Success Rate: " + execRandom()); `

### School example

Works with: JavaScript version Node.js 16.13.0 (LTS)
`"use strict"; // Simulate several thousand instances of the game:const gamesCount = 2000; // ...where the prisoners randomly open drawers.const randomResults = playGame(gamesCount, randomStrategy); // ...where the prisoners use the optimal strategy mentioned in the Wikipedia article.const optimalResults = playGame(gamesCount, optimalStrategy); // Show and compare the computed probabilities of success for the two strategies.console.log(`Games count: \${gamesCount}`);console.log(`Probability of success with "random" strategy: \${computeProbability(randomResults, gamesCount)}`);console.log(`Probability of success with "optimal" strategy: \${computeProbability(optimalResults, gamesCount)}`); function playGame(gamesCount, strategy, prisonersCount = 100) {    const results = new Array();     for (let game = 1; game <= gamesCount; game++) {        // A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.        // Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.        const drawers = initDrawers(prisonersCount);         // A prisoner tries to find his own number.        // Prisoners start outside the room.        // They can decide some strategy before any enter the room.        let found = 0;        for (let prisoner = 1; prisoner <= prisonersCount; prisoner++, found++)            if (!find(prisoner, drawers, strategy)) break;         // If all 100 findings find their own numbers then they will all be pardoned. If any don't then all sentences stand.        results.push(found == prisonersCount);    }     return results;} function find(prisoner, drawers, strategy) {    // A prisoner can open no more than 50 drawers.    const openMax = Math.floor(drawers.length / 2);     // Prisoners start outside the room.    let card;    for (let open = 0; open < openMax; open++) {        // A prisoner tries to find his own number.        card = strategy(prisoner, drawers, card);         // A prisoner finding his own number is then held apart from the others.        if (card == prisoner)            break;    }     return (card == prisoner);} function randomStrategy(prisoner, drawers, card) {    // Simulate the game where the prisoners randomly open drawers.     const min = 0;    const max = drawers.length - 1;     return drawers[draw(min, max)];} function optimalStrategy(prisoner, drawers, card) {    // Simulate the game where the prisoners use the optimal strategy mentioned in the Wikipedia article.     // First opening the drawer whose outside number is his prisoner number.    // If the card within has his number then he succeeds...    if (typeof card === "undefined")        return drawers[prisoner - 1];     // ...otherwise he opens the drawer with the same number as that of the revealed card.    return drawers[card - 1];} function initDrawers(prisonersCount) {    const drawers = new Array();    for (let card = 1; card <= prisonersCount; card++)        drawers.push(card);     return shuffle(drawers);} function shuffle(drawers) {    const min = 0;    const max = drawers.length - 1;    for (let i = min, j; i < max; i++)     {        j = draw(min, max);        if (i != j)            [drawers[i], drawers[j]] = [drawers[j], drawers[i]];    }     return drawers;} function draw(min, max) {    // See: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/random    return Math.floor(Math.random() * (max - min + 1)) + min;} function computeProbability(results, gamesCount) {    return Math.round(results.filter(x => x == true).length * 10000 / gamesCount) / 100;}`

Output:

```Games count: 2000
Probability of success with "random" strategy: 0
Probability of success with "optimal" strategy: 33.2```

## jq

Works with: jq

jq does not have a built-in PRNG and so the jq program used here presupposes an external source of entropy such as /dev/urandom. The output shown below was obtained by invoking jq as follows:

`export LC_ALL=C< /dev/urandom tr -cd '0-9' | fold -w 1 | jq -MRcnr -f 100-prisoners.jq`

In the following jq program:

• `np` is the number of prisoners
• the number of drawers is `np` and the maximum number of draws per prisoner is `np/2|floor`

Preliminaries

`def count(s): reduce s as \$x (0; .+1); # Output: a PRN in range(0;\$n) where \$n is .def prn:  if . == 1 then 0  else . as \$n  | ((\$n-1)|tostring|length) as \$w  | [limit(\$w; inputs)] | join("") | tonumber  | if . < \$n then . else (\$n | prn) end  end; def knuthShuffle:  length as \$n  | if \$n <= 1 then .    else {i: \$n, a: .}    | until(.i ==  0;        .i += -1        | (.i + 1 | prn) as \$j        | .a[.i] as \$t        | .a[.i] = .a[\$j]        | .a[\$j] = \$t)    | .a     end;`

np Prisoners

`# Output: if all the prisoners succeed, emit true, otherwise falsedef optimalStrategy(\$drawers; np):  # Does prisoner \$p succeed?  def succeeds(\$p):    first( foreach range(0; np/2) as \$d ({prev: \$p};             .curr = (\$drawers[.prev])             | if .curr == \$p               then .success = true               else .prev = .curr               end;             select(.success))) // false;   all( range(0; np); succeeds(.) ); # Output: if all the prisoners succeed, emit true, otherwise falsedef randomStrategy(\$drawers; np):  (np/2) as \$maxd  # Does prisoner \$p succeed?  | def succeeds(\$p):      {success: false }      | first(.d = 0              | .opened = []              | until( (.d >= \$maxd) or .success;                  (np|prn) as \$n                  | if .opened[\$n] then .                    else .opened[\$n] = true                    | .d += 1                    | .success = \$drawers[\$n] == \$p                    end )              | select(.success) ) // false;   all( range(0; np); succeeds(.) );  def run(strategy; trials; np):  count(range(0; trials)    | ([range(0;np)] | knuthShuffle) as \$drawers    | select (if strategy == "optimal"              then optimalStrategy(\$drawers; np)              else randomStrategy(\$drawers; np)              end ) ); def task(\$trials):  def percent: "\(10000 * . | round / 100)%";  def summary(strategy):    "With \(strategy) strategy: pardoned = \(.), relative frequency = \(./\$trials | percent)";   (10, 100) as \$np  | "Results from \(\$trials) trials with \(\$np) prisoners:",    (run("random";  \$trials; \$np) | summary("random")),    (run("optimal"; \$trials; \$np) | summary("optimal")),    ""; task(100000)`
Output:
```Results from 100000 trials with 10 prisoners:
With random strategy: pardoned = 92, relative frequency = 0.09%
With optimal strategy: pardoned = 31212, relative frequency = 31.21%

Results from 100000 trials with 100 prisoners:
With random strategy: pardoned = 0, relative frequency = 0%
With optimal strategy: pardoned = 31026, relative frequency = 31.03%
```

## Julia

Translation of: Python
`using Random, Formatting function randomplay(n, numprisoners=100)    pardoned, indrawer, found = 0, collect(1:numprisoners), false    for i in 1:n        shuffle!(indrawer)        for prisoner in 1:numprisoners            found = false            for reveal in randperm(numprisoners)[1:div(numprisoners, 2)]                indrawer[reveal] == prisoner && (found = true) && break            end            !found && break        end        found && (pardoned += 1)    end    return 100.0 * pardoned / nend function optimalplay(n, numprisoners=100)    pardoned, indrawer, found = 0, collect(1:numprisoners), false    for i in 1:n        shuffle!(indrawer)        for prisoner in 1:numprisoners            reveal = prisoner            found = false            for j in 1:div(numprisoners, 2)                card = indrawer[reveal]                card == prisoner && (found = true) && break                reveal = card            end            !found && break        end        found && (pardoned += 1)    end    return 100.0 * pardoned / n end const N = 100_000println("Simulation count: \$N")println("Random play wins: ", format(randomplay(N), precision=8), "% of simulations.")println("Optimal play wins: ", format(optimalplay(N), precision=8), "% of simulations.") `
Output:
```Simulation count: 100000
Random play wins: 0.00000000% of simulations.
Optimal play wins: 31.18100000% of simulations.
```

## Kotlin

`val playOptimal: () -> Boolean = {    val secrets = (0..99).toMutableList()    var ret = true    secrets.shuffle()    prisoner@ for(i in 0 until 100){        var prev = i        draw@ for(j in 0 until  50){            if (secrets[prev] == i) continue@prisoner            prev = secrets[prev]        }        ret = false        break@prisoner    }    ret} val playRandom: ()->Boolean = {    var ret = true    val secrets = (0..99).toMutableList()    secrets.shuffle()    prisoner@ for(i in 0 until 100){        val opened = mutableListOf<Int>()        val genNum : () ->Int = {            var r = (0..99).random()            while (opened.contains(r)) {                r = (0..99).random()            }            r        }        for(j in 0 until 50){            val draw = genNum()            if ( secrets[draw] == i) continue@prisoner            opened.add(draw)        }        ret = false        break@prisoner    }    ret} fun exec(n:Int, play:()->Boolean):Double{    var succ = 0    for (i in IntRange(0, n-1)){        succ += if(play()) 1 else 0    }    return (succ*100.0)/n} fun main() {    val N = 100_000    println("# of executions: \$N")    println("Optimal play success rate: \${exec(N, playOptimal)}%")    println("Random play success rate: \${exec(N, playRandom)}%")}`
Output:
```# of executions: 100000
Optimal play success rate: 31.451%
Random play success rate: 0.0%
```

## Lua

Translation of: lang
`function shuffle(tbl)  for i = #tbl, 2, -1 do    local j = math.random(i)    tbl[i], tbl[j] = tbl[j], tbl[i]  end  return tblend function playOptimal()    local secrets = {}    for i=1,100 do        secrets[i] = i    end    shuffle(secrets)     for p=1,100 do        local success = false         local choice = p        for i=1,50 do            if secrets[choice] == p then                success = true                break            end            choice = secrets[choice]        end         if not success then            return false        end    end     return trueend function playRandom()    local secrets = {}    for i=1,100 do        secrets[i] = i    end    shuffle(secrets)     for p=1,100 do        local choices = {}        for i=1,100 do            choices[i] = i        end        shuffle(choices)         local success = false        for i=1,50 do            if choices[i] == p then                success = true                break            end        end         if not success then            return false        end    end     return trueend function exec(n,play)    local success = 0    for i=1,n do        if play() then            success = success + 1        end    end    return 100.0 * success / nend function main()    local N = 1000000    print("# of executions: "..N)    print(string.format("Optimal play success rate: %f", exec(N, playOptimal)))    print(string.format("Random play success rate: %f", exec(N, playRandom)))end main()`
Output:
```# of executions: 1000000
Optimal play success rate: 31.237500
Random play success rate: 0.000000```

## Maple

Don"t bother to simulate the random method: each prisoner has a probability p to win with:

`p:=simplify(1-product(1-1/(2*n-k),k=0..n-1));# p=1/2`

Since all prisoners' attempts are independent, the probability that they all win is:

`p^100;evalf(%); # 1/1267650600228229401496703205376# 7.888609052e-31`

Even with billions of simulations, chances are we won't find even one successful escape.

On the other hand, if they try the optimal strategy, then their success is governed by the cycle decomposition of the permutation of numbers in boxes. That is, the function f(i)=j where i is the number on the box, and j the number in the box, is a permutation of 1..100. This permutation has a cycle decomposition. It's not difficult to see that all prisoners with a number in the same cycle, need the same number of attempts before finding their number, and it's the cycle length. Hence, for all prisoners to escape, the maximum cycle length must not exceed 50.

Here is a simulation based on this, assuming that the permutation of numbers in boxes is random:

`a:=[seq(max(GroupTheory[PermCycleType](Perm(Statistics[Shuffle]([\$1..100])))),i=1..100000)]:nops(select(n->n<=50,a))/nops(a);evalf(%);# 31239/100000# 0.3123900000`

The probability of success is now better than 30%, which is far better than the random approach.

It can be proved that the probability with the second strategy is in fact:

`1-(harmonic(100)-harmonic(50));evalf(%); # 21740752665556690246055199895649405434183/69720375229712477164533808935312303556800# 0.3118278207`

## Mathematica/Wolfram Language

`ClearAll[PlayRandom, PlayOptimal]PlayRandom[n_] :=  Module[{pardoned = 0, sampler, indrawer, found, reveal},  sampler = indrawer = Range;  Do[   indrawer //= RandomSample;   found = 0;   Do[    reveal = RandomSample[sampler, 50];    If[MemberQ[indrawer[[reveal]], p],     found++;     ]    ,    {p, 100}    ];   If[found == 100, pardoned++];   ,   {n}   ];  N[pardoned/n]  ]PlayOptimal[n_] :=  Module[{pardoned = 0, indrawer, reveal, found, card},  indrawer = Range;  Do[   indrawer //= RandomSample;   Do[    reveal = p;    found = False;    Do[     card = indrawer[[reveal]];     If[card == p,      found = True;      Break[];      ];     reveal = card;     ,     {g, 50}     ];    If[! found, Break[]];    ,    {p, 100}    ];   If[found, pardoned++];   ,   {n}   ];  N[pardoned/n]  ];PlayRandomPlayOptimal`
Output:
```0.
0.3116```

## MATLAB

`function [randSuccess,idealSuccess]=prisoners(numP,numG,numT)    %numP is the number of prisoners    %numG is the number of guesses    %numT is the number of trials    randSuccess=0;     %Random    for trial=1:numT        drawers=randperm(numP);        won=1;        for i=1:numP            correct=0;            notopened=drawers;            for j=1:numG                ind=randi(numel(notopened));                m=notopened(ind);                if m==i                    correct=1;                    break;                end                notopened(ind)=[];            end            if correct==0                won=0;                break;            end        end        randSuccess=randSuccess*(trial-1)/trial+won/trial;    end      %Ideal    idealSuccess=0;     for trial=1:numT        drawers=randperm(numP);        won=1;        for i=1:numP            correct=0;            guess=i;            for j=1:numG                m=drawers(guess);                if m==i                    correct=1;                    break;                end                guess=m;            end            if correct==0                won=0;                break;            end        end        idealSuccess=idealSuccess*(trial-1)/trial+won/trial;    end    disp(['Probability of success with random strategy: ' num2str(randSuccess*100) '%']);    disp(['Probability of success with ideal strategy: ' num2str(idealSuccess*100) '%']);end`
Output:
```>> [randSuccess,idealSuccess]=prisoners(100,50,10000);
Probability of success with random strategy: 0%
Probability of success with ideal strategy: 31.93%```

## MiniScript

Translation of: Python
`playRandom = function(n)    // using 0-99 instead of 1-100    pardoned = 0    numInDrawer = range(99)    choiceOrder = range(99)    for round in range(1, n)    	numInDrawer.shuffle        choiceOrder.shuffle        for prisoner in range(99)            found = false            for card in choiceOrder[:50]                if card == prisoner then                    found = true                    break                end if            end for            if not found then break        end for        if found then pardoned = pardoned + 1    end for    return pardoned / n * 100end function playOptimal = function(n)    // using 0-99 instead of 1-100    pardoned = 0    numInDrawer = range(99)    for round in range(1, n)    	numInDrawer.shuffle        for prisoner in range(99)            found = false	    drawer = prisoner            for i in range(1,50)                card = numInDrawer[drawer]                if card == prisoner then                    found = true                    break                end if                drawer = card            end for            if not found then break        end for        if found then pardoned = pardoned + 1    end for    return pardoned / n * 100end function print "Random:  " + playRandom(10000) + "%"print "Optimal: " + playOptimal(10000) + "%"`
Output:
```Random:  0%
Optimal: 31.06%```

## Nim

Imperative style.

`import random, sequtils, strutils type  Sample = tuple    succ: int    fail: int const  numPrisoners = 100  numDrawsEachPrisoner = numPrisoners div 2  numDrawings: Positive = 1_000_000 div 1 proc `\$`(s: Sample): string =  "Succs: \$#\tFails: \$#\tTotal: \$#\tSuccess Rate: \$#%." % [\$s.succ, \$s.fail, \$(s.succ + s.fail), \$(s.succ.float / (s.succ + s.fail).float * 100.0)] proc prisonersWillBeReleasedSmart(): bool =  result = true  var drawers = toSeq(0..<numPrisoners)  drawers.shuffle  for prisoner in 0..<numPrisoners:    var drawer = prisoner    block inner:      for _ in 0..<numDrawsEachPrisoner:        if drawers[drawer] == prisoner: break inner        drawer = drawers[drawer]      return false proc prisonersWillBeReleasedRandom(): bool =  result = true  var drawers = toSeq(0..<numPrisoners)  drawers.shuffle  for prisoner in 0..<numPrisoners:    var selectDrawer = toSeq(0..<numPrisoners)    selectDrawer.shuffle    block inner:      for i in 0..<numDrawsEachPrisoner:        if drawers[selectDrawer[i]] == prisoner: break inner      return false proc massDrawings(prisonersWillBeReleased: proc(): bool): Sample =  var success = 0  for i in 1..numDrawings:    if prisonersWillBeReleased():      inc(success)  return (success, numDrawings - success) randomize()echo \$massDrawings(prisonersWillBeReleasedSmart)echo \$massDrawings(prisonersWillBeReleasedRandom)`
Output:
```Succs: 312225   Fails: 687775   Total: 1000000  Success Rate: 31.2225%.
Succs: 0        Fails: 1000000  Total: 1000000  Success Rate: 0.0%.```

## Pascal

Works with: Free Pascal

searching the longest cycle length as stated on talk page and increment an counter for that cycle length.

`program Prisoners100; const  rounds  = 100000; type  tValue = Uint32;  tPrisNum = array of tValue;var  drawers,  PrisonersChoice : tPrisNum; procedure shuffle(var N:tPrisNum);var  i,j,lmt : nativeInt;  tmp: tValue;Begin  lmt := High(N);  For i := lmt downto 1 do  begin    //take on from index i..limit    j := random(i+1);    //exchange with i    tmp := N[i];N[i]:= N[j];N[j]:= tmp;  end;end; function PardonedRandom(maxTestNum: NativeInt):boolean;var  PrisNum,TestNum,Lmt : NativeUint;  Pardoned : boolean;Begin  IF maxTestNum <=0 then  Begin    PardonedRandom := false;    EXIT;  end;  Lmt := High(drawers);  IF (maxTestNum >= Lmt) then  Begin    PardonedRandom := true;    EXIT;  end;   shuffle(drawers);  PrisNum := 0;  repeat    //every prisoner uses his own list of drawers    shuffle(PrisonersChoice);    TestNum := 0;    repeat      Pardoned := drawers[PrisonersChoice[TestNum]] = PrisNum;      inc(TestNum);    until Pardoned OR (TestNum>=maxTestNum);    IF Not(Pardoned) then      BREAK;    inc(PrisNum);  until PrisNum>=Lmt;  PardonedRandom:= Pardoned;end; function PardonedOptimized(maxTestNum: NativeUint):boolean;var  PrisNum,TestNum,NextNum,Cnt,Lmt : NativeUint;  Pardoned : boolean;Begin  IF maxTestNum <=0 then  Begin    PardonedOptimized := false;    EXIT;  end;  Lmt := High(drawers);  IF (maxTestNum >= Lmt) then  Begin    PardonedOptimized := true;    EXIT;  end;   shuffle(drawers);  Lmt := High(drawers);  IF maxTestNum >= Lmt then  Begin    PardonedOptimized := true;    EXIT;  end;  PrisNum := 0;  repeat    Cnt := 0;    NextNum := PrisNum;    repeat      TestNum := NextNum;      NextNum := drawers[TestNum];      inc(cnt);      Pardoned := NextNum = PrisNum;    until Pardoned OR (cnt >=maxTestNum);     IF Not(Pardoned) then      BREAK;    inc(PrisNum);  until PrisNum>Lmt;  PardonedOptimized := Pardoned;end; procedure CheckRandom(testCount : NativeUint);var  i,cnt : NativeInt;Begin  cnt := 0;  For i := 1 to rounds do    IF PardonedRandom(TestCount) then      inc(cnt);  writeln('Randomly  ',cnt/rounds*100:7:2,'% get pardoned out of ',rounds,' checking max ',TestCount);end; procedure CheckOptimized(testCount : NativeUint);var  i,cnt : NativeInt;Begin  cnt := 0;  For i := 1 to rounds do    IF PardonedOptimized(TestCount) then      inc(cnt);  writeln('Optimized ',cnt/rounds*100:7:2,'% get pardoned out of ',rounds,' checking max ',TestCount);end; procedure OneCompareRun(PrisCnt:NativeInt);var  i,lmt :nativeInt;begin  setlength(drawers,PrisCnt);  For i := 0 to PrisCnt-1 do    drawers[i] := i;  PrisonersChoice := copy(drawers);   //test  writeln('Checking ',PrisCnt,' prisoners');   lmt := PrisCnt;  repeat    CheckOptimized(lmt);    dec(lmt,PrisCnt DIV 10);  until lmt < 0;  writeln;   lmt := PrisCnt;  repeat    CheckRandom(lmt);    dec(lmt,PrisCnt DIV 10);  until lmt < 0;  writeln;  writeln;end; Begin  //init  randomize;  OneCompareRun(20);  OneCompareRun(100);end.`
Output:
```Checking 20 prisoners
Optimized  100.00% get pardoned out of 100000 checking max 20
Optimized   89.82% get pardoned out of 100000 checking max 18
Optimized   78.25% get pardoned out of 100000 checking max 16
Optimized   65.31% get pardoned out of 100000 checking max 14
Optimized   50.59% get pardoned out of 100000 checking max 12
Optimized   33.20% get pardoned out of 100000 checking max 10
Optimized   15.28% get pardoned out of 100000 checking max 8
Optimized    3.53% get pardoned out of 100000 checking max 6
Optimized    0.10% get pardoned out of 100000 checking max 4
Optimized    0.00% get pardoned out of 100000 checking max 2
Optimized    0.00% get pardoned out of 100000 checking max 0

Randomly   100.00% get pardoned out of 100000 checking max 20
Randomly    13.55% get pardoned out of 100000 checking max 18
Randomly     1.38% get pardoned out of 100000 checking max 16
Randomly     0.12% get pardoned out of 100000 checking max 14
Randomly     0.00% get pardoned out of 100000 checking max 12
Randomly     0.00% get pardoned out of 100000 checking max 10
Randomly     0.00% get pardoned out of 100000 checking max 8
Randomly     0.00% get pardoned out of 100000 checking max 6
Randomly     0.00% get pardoned out of 100000 checking max 4
Randomly     0.00% get pardoned out of 100000 checking max 2
Randomly     0.00% get pardoned out of 100000 checking max 0

Checking 100 prisoners
Optimized  100.00% get pardoned out of 100000 checking max 100
Optimized   89.48% get pardoned out of 100000 checking max 90
Optimized   77.94% get pardoned out of 100000 checking max 80
Optimized   64.48% get pardoned out of 100000 checking max 70
Optimized   49.35% get pardoned out of 100000 checking max 60
Optimized   31.10% get pardoned out of 100000 checking max 50
Optimized   13.38% get pardoned out of 100000 checking max 40
Optimized    2.50% get pardoned out of 100000 checking max 30
Optimized    0.05% get pardoned out of 100000 checking max 20
Optimized    0.00% get pardoned out of 100000 checking max 10
Optimized    0.00% get pardoned out of 100000 checking max 0

Randomly   100.00% get pardoned out of 100000 checking max 100
Randomly     0.01% get pardoned out of 100000 checking max 90
Randomly     0.00% get pardoned out of 100000 checking max 80
Randomly     0.00% get pardoned out of 100000 checking max 70
Randomly     0.00% get pardoned out of 100000 checking max 60
Randomly     0.00% get pardoned out of 100000 checking max 50
Randomly     0.00% get pardoned out of 100000 checking max 40
Randomly     0.00% get pardoned out of 100000 checking max 30
Randomly     0.00% get pardoned out of 100000 checking max 20
Randomly     0.00% get pardoned out of 100000 checking max 10
Randomly     0.00% get pardoned out of 100000 checking max 0```

### Alternative for optimized

`program Prisoners100;{\$IFDEF FPC}  {\$MODE DELPHI}{\$OPTIMIZATION ON,ALL}{\$ELSE}  {\$APPTYPE CONSOLE}{\$ENDIF}type  tValue  = NativeUint;  tpValue = pNativeUint;  tPrisNum = array of tValue; const  rounds  = 1000000;  cAlreadySeen = High(tValue);var  drawers,  Visited,  CntToPardoned : tPrisNum;  PrisCount : NativeInt; procedure shuffle(var N:tPrisNum;lmt : nativeInt = 0);var  pN : tpValue;  i,j : nativeInt;  tmp: tValue;Begin  pN := @N;  if lmt = 0 then    lmt := High(N);  For i := lmt downto 1 do  begin    //take one from index [0..i]    j := random(i+1);    //exchange with i    tmp := pN[i];pN[i]:= pN[j];pN[j]:= tmp;  end;end; procedure CopyDrawers2Visited;//drawers and Visited are of same size, so only moving valuesBegin  Move(drawers,Visited,SizeOf(tValue)*PrisCount);end; function GetMaxCycleLen:NativeUint;var  pVisited : tpValue;  cycleLen,MaxCycLen,Num,NumBefore : NativeUInt;Begin  CopyDrawers2Visited;  pVisited := @Visited;  MaxCycLen := 0;  cycleLen := MaxCycLen;  Num := MaxCycLen;  repeat    NumBefore := Num;    Num := pVisited[Num];    pVisited[NumBefore] := cAlreadySeen;    inc(cycleLen);    IF (Num= NumBefore) or (Num = cAlreadySeen) then    begin      IF Num = cAlreadySeen then        dec(CycleLen);      IF MaxCycLen < cycleLen then        MaxCycLen := cycleLen;      Num := 0;      while (Num< PrisCount) AND (pVisited[Num] = cAlreadySeen) do        inc(Num);      //all cycles found      IF Num >= PrisCount then        BREAK;      cycleLen :=0;    end;  until false;  GetMaxCycleLen := MaxCycLen-1;end; procedure CheckOptimized(testCount : NativeUint);var  factor: extended;  i,sum,digit,delta : NativeInt;Begin  For i := 1 to rounds do  begin    shuffle(drawers);    inc(CntToPardoned[GetMaxCycleLen]);  end;   digit := 0;  sum := rounds;  while sum > 100 do  Begin    inc(digit);    sum := sum DIV 10;  end;  factor := 100.0/rounds;   delta :=0;  sum := 0;  For i := 0 to High(drawers) do  Begin    inc(sum,CntToPardoned[i]);    dec(delta);    IF delta <= 0 then    Begin      writeln(sum*factor:Digit+5:Digit,'% get pardoned checking max ',i+1);      delta := delta+Length(drawers) DIV 10;    end;  end;end; procedure OneCompareRun(PrisCnt:NativeInt);var  i,lmt :nativeInt;begin  PrisCount := PrisCnt;  setlength(drawers,PrisCnt);  For i := 0 to PrisCnt-1 do    drawers[i] := i;  setlength(Visited,PrisCnt);  setlength(CntToPardoned,PrisCnt);  //test  writeln('Checking ',PrisCnt,' prisoners for ',rounds,' rounds');  lmt := PrisCnt;  CheckOptimized(lmt);  writeln;   setlength(CntToPardoned,0);  setlength(Visited,0);  setlength(drawers,0);end; Begin  randomize;  OneCompareRun(10);  OneCompareRun(100);  OneCompareRun(1000);end.`
Output:
```Checking 10 prisoners for 1000000 rounds
0.0000% get pardoned checking max 1
0.2584% get pardoned checking max 2
4.7431% get pardoned checking max 3
17.4409% get pardoned checking max 4
35.4983% get pardoned checking max 5
52.1617% get pardoned checking max 6
66.4807% get pardoned checking max 7
78.9761% get pardoned checking max 8
90.0488% get pardoned checking max 9
100.0000% get pardoned checking max 10

Checking 100 prisoners for 1000000 rounds
0.0000% get pardoned checking max 1
0.0000% get pardoned checking max 10
0.0459% get pardoned checking max 20
2.5996% get pardoned checking max 30
13.5071% get pardoned checking max 40
31.2258% get pardoned checking max 50
49.3071% get pardoned checking max 60
64.6128% get pardoned checking max 70
77.8715% get pardoned checking max 80
89.5385% get pardoned checking max 90
100.0000% get pardoned checking max 100

Checking 1000 prisoners for 1000000 rounds
0.0000% get pardoned checking max 1
0.0000% get pardoned checking max 100
0.0374% get pardoned checking max 200
2.3842% get pardoned checking max 300
13.1310% get pardoned checking max 400
30.7952% get pardoned checking max 500
48.9710% get pardoned checking max 600
64.3555% get pardoned checking max 700
77.6950% get pardoned checking max 800
89.4515% get pardoned checking max 900
100.0000% get pardoned checking max 1000

real    0m9,975s```

## Perl

Translation of: Raku
`use strict;use warnings;use feature 'say';use List::Util 'shuffle'; sub simulation {    my(\$population,\$trials,\$strategy) = @_;    my \$optimal   = \$strategy =~ /^o/i ? 1 : 0;    my @prisoners = 0..\$population-1;    my \$half      = int \$population / 2;    my \$pardoned  = 0;     for (1..\$trials) {        my @drawers = shuffle @prisoners;        my \$total = 0;        for my \$prisoner (@prisoners) {            my \$found = 0;            if (\$optimal) {                my \$card = \$drawers[\$prisoner];                if (\$card == \$prisoner) {                    \$found = 1;                } else {                    for (1..\$half-1) {                        \$card = \$drawers[\$card];                        (\$found = 1, last) if \$card == \$prisoner                    }                }            } else {                for my \$card ( (shuffle @drawers)[0..\$half]) {                    (\$found = 1, last) if \$card == \$prisoner                }            }            last unless \$found;            \$total++;        }        \$pardoned++ if \$total == \$population;    }    \$pardoned / \$trials * 100} my \$population = 100;my \$trials     = 10000;say " Simulation count: \$trials\n" .(sprintf " Random strategy pardons: %6.3f%% of simulations\n", simulation \$population, \$trials, 'random' ) .(sprintf "Optimal strategy pardons: %6.3f%% of simulations\n", simulation \$population, \$trials, 'optimal'); \$population = 10;\$trials     = 100000;say " Simulation count: \$trials\n" .(sprintf " Random strategy pardons: %6.3f%% of simulations\n", simulation \$population, \$trials, 'random' ) .(sprintf "Optimal strategy pardons: %6.3f%% of simulations\n", simulation \$population, \$trials, 'optimal');`
Output:
``` Simulation count: 10000
Random strategy pardons:  0.000% of simulations
Optimal strategy pardons: 31.510% of simulations

Simulation count: 1000000
Random strategy pardons:  0.099% of simulations
Optimal strategy pardons: 35.420% of simulations```

## PicoLisp

Built so you could easily build and test your own strategies.

`(de shuffle (Lst)   (by '(NIL (rand)) sort Lst) ) # Extend this class with a `next-guess>` method and a `str>` method.(class +Strategy +Entity)(dm prev-drawer> (Num)   (=: prev Num) ) (class +Random +Strategy)(dm T (Prisoner)   (=: guesses (nth (shuffle (range 1 100)) 51)) )(dm next-guess> ()   (pop (:: guesses)) )(dm str> ()   "Random" ) (class +Optimal +Strategy)(dm T (Prisoner)   (=: prisoner-id Prisoner) )(dm next-guess> ()   (or (: prev) (: prisoner-id)) )(dm str> ()   "Optimal/Wikipedia" )  (de test-strategy (Strategy)   "Simulate one round of 100 prisoners who use `Strategy`"   (let Drawers (shuffle (range 1 100))      (for Prisoner (range 1 100)         (NIL # Break and return NIL if any prisoner fails their test.            (let Strat (new (list Strategy) Prisoner)               (do 50 # Try 50 iterations of `Strat`. Break and return T iff success.                  (T (= Prisoner (prev-drawer> Strat (get Drawers (next-guess> Strat))))                     T ) ) ) )         T ) ) ) (de test-strategy-n-times (Strategy N)   "Simulate `N` rounds of 100 prisoners who use `Strategy`"   (let Successes 0      (do N         (when (test-strategy Strategy)            (inc 'Successes) ) )      (prinl "We have a " (/ (* 100 Successes) N) "% success rate with " N " trials.")      (prinl "This is using the " (str> Strategy) " strategy.") ) )`

Then run

`(test-strategy-n-times '+Random 10000)(test-strategy-n-times '+Optimal 10000)`
Output:
```We have a 0% success rate with 10000 trials.
This is using the Random strategy.
We have a 31% success rate with 10000 trials.
This is using the Optimal/Wikipedia strategy.```

## Phix

```function play(integer prisoners, iterations, bool optimal)
sequence drawers = shuffle(tagset(prisoners))
integer pardoned = 0
bool found = false
for i=1 to iterations do
drawers = shuffle(drawers)
for prisoner=1 to prisoners do
found = false
integer drawer = iff(optimal?prisoner:rand(prisoners))
for j=1 to prisoners/2 do
drawer = drawers[drawer]
if drawer==prisoner then found = true exit end if
if not optimal then drawer = rand(prisoners) end if
end for
end for
pardoned += found
end for
return 100*pardoned/iterations
end function

constant iterations = 100_000
printf(1,"Simulation count: %d\n",iterations)
for prisoners=10 to 100 by 90 do
atom random = play(prisoners,iterations,false),
optimal = play(prisoners,iterations,true)
printf(1,"Prisoners:%d, random:%g, optimal:%g\n",{prisoners,random,optimal})
end for
```
Output:
```Simulation count: 100000
Prisoners:10, random:0.006, optimal:35.168
Prisoners:100, random:0, optimal:31.098
```

## Phixmonti

Translation of: Yabasic
`/# Rosetta Code problem: http://rosettacode.org/wiki/100_prisonersby Galileo, 05/2022 #/ include ..\Utilitys.pmt def random rand * 1 + int enddef def shuffle    len var l    l for var a        l random var b        b get var p        a get b set        p a set    endforenddef def play var optimal var iterations var prisoners    0 var pardoned     ( prisoners for endfor )     iterations for drop        shuffle        prisoners for var prisoner            false var found            optimal if prisoner else prisoners random endif            prisoners 2 / int for drop                get dup prisoner == if true var found exitfor                else                    optimal not if drop prisoners random endif                endif            endfor            found not if exitfor endif            drop        endfor        pardoned found + var pardoned    endfor    drop    pardoned 100 * iterations /enddef "Please, be patient ..." ? ( "Optimal: " 100 10000 true play  " Random: " 100 10000 false play  " Prisoners: " prisoners ) lprint`
Output:
```Please, be patient ...
Optimal: 31.65 Random: 0 Prisoners: 100
=== Press any key to exit ===```

## PL/M

`100H:/* PARAMETERS */DECLARE N\$DRAWERS  LITERALLY '100';  /* AMOUNT OF DRAWERS */DECLARE N\$ATTEMPTS LITERALLY '50';   /* ATTEMPTS PER PRISONER */DECLARE N\$SIMS     LITERALLY '2000'; /* N. OF SIMULATIONS TO RUN */ DECLARE RAND\$SEED  LITERALLY '193';  /* RANDOM SEED */ /* CP/M CALLS */BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;EXIT: PROCEDURE; CALL BDOS(0, 0); END EXIT;PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9, S); END PRINT; /* PRINT NUMBER */PRINT\$NUMBER: PROCEDURE (N);    DECLARE S (6) BYTE INITIAL ('.....\$');    DECLARE (P, N) ADDRESS, C BASED P BYTE;    P = .S(5);DIGIT:    P = P - 1;    C = N MOD 10 + '0';    N = N / 10;    IF N > 0 THEN GO TO DIGIT;    CALL PRINT(P);END PRINT\$NUMBER; /* RANDOM NUMBER GENERATOR */RAND\$BYTE: PROCEDURE BYTE;    DECLARE (X, A, B, C) BYTE         INITIAL (RAND\$SEED, RAND\$SEED, RAND\$SEED, RAND\$SEED);    X = X+1;    A = A XOR C XOR X;    B = B+A;    C = C+SHR(B,1)+A;    RETURN C;END RAND\$BYTE; /* GENERATE RANDOM NUMBER FROM 0 TO MAX */RAND\$MAX: PROCEDURE (MAX) BYTE;    DECLARE (X, R, MAX) BYTE;    X = 1;    DO WHILE X < MAX;        X = SHL(X,1);    END;    X = X-1;    DO WHILE 1;        R = RAND\$BYTE AND X;        IF R < MAX THEN RETURN R;    END;END RAND\$MAX; /* PLACE CARDS RANDOMLY IN DRAWERS */INIT\$DRAWERS: PROCEDURE (DRAWERS);    DECLARE DRAWERS ADDRESS, (D BASED DRAWERS, I, J, K) BYTE;    DO I=0 TO N\$DRAWERS-1;        D(I) = I;    END;    DO I=0 TO N\$DRAWERS-1;        J = I + RAND\$MAX(N\$DRAWERS-I);        K = D(I);        D(I) = D(J);        D(J) = K;    END;END INIT\$DRAWERS; /* PRISONER OPENS RANDOM DRAWERS */RANDOM\$STRATEGY: PROCEDURE (DRAWERS, P) BYTE;    DECLARE DRAWERS ADDRESS, D BASED DRAWERS BYTE;    DECLARE (P, I, TRIES) BYTE;     /* KEEP TRACK OF WHICH DRAWERS HAVE BEEN OPENED */    DECLARE OPEN (N\$DRAWERS) BYTE;    DO I=0 TO N\$DRAWERS-1;        OPEN(I) = 0;    END;     /* OPEN RANDOM DRAWERS */    TRIES = N\$ATTEMPTS;    DO WHILE TRIES > 0;        IF NOT OPEN(I := RAND\$MAX(N\$DRAWERS)) THEN DO;            /* IF WE FIND OUR NUMBER, SUCCESS */            IF D(I) = P THEN RETURN 1;            OPEN(I) = 1;                TRIES = TRIES - 1;        END;    END;     RETURN 0; /* WE DID NOT FIND OUR NUMBER */END RANDOM\$STRATEGY; /* PRISONER USES OPTIMAL STRATEGY */OPTIMAL\$STRATEGY: PROCEDURE (DRAWERS, P) BYTE;    DECLARE DRAWERS ADDRESS, D BASED DRAWERS BYTE;    DECLARE (P, I, TRIES) BYTE;    TRIES = N\$ATTEMPTS;    I = P;    DO WHILE TRIES > 0;        I = D(I); /* OPEN DRAWER W/ CURRENT NUMBER */        IF I = P THEN RETURN 1; /* DID WE FIND IT? */        TRIES = TRIES - 1;    END;    RETURN 0;END OPTIMAL\$STRATEGY; /* RUN A SIMULATION */DECLARE RANDOM LITERALLY '0';DECLARE OPTIMAL LITERALLY '1';SIMULATE: PROCEDURE (STRAT) BYTE;    DECLARE (STRAT, P, R) BYTE;     /* PLACE CARDS IN DRAWERS */    DECLARE DRAWERS (N\$DRAWERS) BYTE;    CALL INIT\$DRAWERS(.DRAWERS);     /* TRY EACH PRISONER */    DO P=0 TO N\$DRAWERS-1;        DO CASE STRAT;            R = RANDOM\$STRATEGY(.DRAWERS, P);            R = OPTIMAL\$STRATEGY(.DRAWERS, P);        END;         /* IF ONE PRISONER FAILS THEY ALL HANG */        IF NOT R THEN RETURN 0;    END;     RETURN 1; /* IF THEY ALL SUCCEED NONE HANG */END SIMULATE; /* RUN MANY SIMULATIONS AND COUNT THE SUCCESSES */RUN\$SIMULATIONS: PROCEDURE (N, STRAT) ADDRESS;    DECLARE STRAT BYTE, (I, N, SUCC) ADDRESS;    SUCC = 0;    DO I=1 TO N;        SUCC = SUCC + SIMULATE(STRAT);    END;    RETURN SUCC;END RUN\$SIMULATIONS; /* RUN AND PRINT SIMULATIONS */RUN\$AND\$PRINT: PROCEDURE (NAME, STRAT, N);    DECLARE (NAME, N, S) ADDRESS, STRAT BYTE;    CALL PRINT(NAME);    CALL PRINT(.' STRATEGY: \$');    S = RUN\$SIMULATIONS(N, STRAT);    CALL PRINT\$NUMBER(S);    CALL PRINT(.' OUT OF \$');    CALL PRINT\$NUMBER(N);    CALL PRINT(.' - \$');    CALL PRINT\$NUMBER( S*10 / (N/10) );    CALL PRINT(.(37,13,10,'\$'));END RUN\$AND\$PRINT; CALL RUN\$AND\$PRINT(.'RANDOM\$', RANDOM, N\$SIMS);CALL RUN\$AND\$PRINT(.'OPTIMAL\$', OPTIMAL, N\$SIMS);CALL EXIT;EOF`
Output:
```RANDOM STRATEGY: 0 OUT OF 2000 - 0%
OPTIMAL STRATEGY: 653 OUT OF 2000 - 32%```

## Pointless

`optimalSeq(drawers, n) =  iterate(ind => drawers[ind - 1], n)  |> takeUntil(ind => drawers[ind - 1] == n) optimalTrial(drawers) =  range(1, 100)  |> map(optimalSeq(drawers)) randomSeq(drawers, n) =  iterate(ind => randRange(1, 100), randRange(1, 100))  |> takeUntil(ind => drawers[ind - 1] == n) randomTrial(drawers) =  range(1, 100)  |> map(randomSeq(drawers)) checkLength(seq) =  length(take(51, seq)) <= 50 numTrials = 3000 runTrials(trialFunc) =  for t in range(1, numTrials)  yield    range(1, 100)    |> shuffle    |> toArray    |> trialFunc    |> map(checkLength)    |> all countSuccess(trialFunc) =  runTrials(trialFunc)  |> filter(id)  |> length optimalCount = countSuccess(optimalTrial)randomCount = countSuccess(randomTrial) output =  format("optimal: {} / {} = {} prob\nrandom: {} / {} = {} prob", [    optimalCount, numTrials, optimalCount / numTrials,    randomCount, numTrials, randomCount / numTrials,  ])  |> println`
Output:
```optimal: 923 / 3000 = 0.30766666666666664 prob
random: 0 / 3000 = 0.0 prob```

## PowerShell

Translation of: Chris
` ### Clear Screen from old OutputClear-Host Function RandomOpening ()   {    \$Prisoners = 1..100 | Sort-Object {Get-Random}    \$Cupboard = 1..100 | Sort-Object {Get-Random}    ## Loop for the Prisoners    \$Survived = \$true    for (\$I=1;\$I -le 100;\$i++)      {          \$OpeningListe = 1..100 | Sort-Object {Get-Random}          \$Gefunden = \$false          ## Loop for the trys of every prisoner          for (\$X=1;\$X -le 50;\$X++)            {                \$OpenNumber = \$OpeningListe[\$X]                IF (\$Cupboard[\$OpenNumber] -eq \$Prisoners[\$I])                  {                      \$Gefunden = \$true                  }                ## Cancel loop if prisoner found his number (yeah i know, dirty way ^^ )                  IF (\$Gefunden)                  {                    \$X = 55                  }            }          IF (\$Gefunden -eq \$false)            {              \$I = 120              \$Survived = \$false            }                  }    Return \$Survived  }   Function StrategyOpening ()   {    \$Prisoners = 1..100 | Sort-Object {Get-Random}    \$Cupboard = 1..100 | Sort-Object {Get-Random}    \$Survived = \$true    for (\$I=1;\$I -le 100;\$i++)      {          \$Gefunden = \$false          \$OpeningNumber = \$Prisoners[\$I-1]          for (\$X=1;\$X -le 50;\$X++)            {                IF (\$Cupboard[\$OpeningNumber-1] -eq \$Prisoners[\$I-1])                  {                      \$Gefunden = \$true                  }                else                   {                    \$OpeningNumber = \$Cupboard[\$OpeningNumber-1]                                    }                 IF (\$Gefunden)                  {                    \$X = 55                  }            }          IF (\$Gefunden -eq \$false)            {              \$I = 120              \$Survived = \$false            }                  }    Return \$Survived  } \$MaxRounds = 10000 Function TestRandom  {    \$WinnerRandom = 0    for (\$Round = 1; \$Round -le \$MaxRounds;\$Round++)      {        IF ((\$Round%1000) -eq 0)          {            \$Time = Get-Date            Write-Host "Currently we are at rount \$Round at \$Time"          }        \$Rueckgabewert = RandomOpening        IF (\$Rueckgabewert)          {            \$WinnerRandom++          }      }     \$Prozent = (100/\$MaxRounds)*\$WinnerRandom    Write-Host "There are \$WinnerRandom survivors whit random opening. This is \$Prozent percent"  } Function TestStrategy  {    \$WinnersStrategy = 0       for (\$Round = 1; \$Round -le \$MaxRounds;\$Round++)        {          IF ((\$Round%1000) -eq 0)            {              \$Time = Get-Date              Write-Host "Currently we are at \$Round at \$Time"            }          \$Rueckgabewert = StrategyOpening          IF (\$Rueckgabewert)            {              \$WinnersStrategy++            }        }     \$Prozent = (100/\$MaxRounds)*\$WinnersStrategy    Write-Host "There are \$WinnersStrategy survivors whit strategic opening. This is \$Prozent percent"  } Function Main ()   {    Clear-Host    TestRandom    TestStrategy  } Main `
Output:
```# of executions: 10000
There are 0 survivors whit random opening. This is 0 percent
There are 3104 survivors whit strategic opening. This is 31,04 percent"
```

## Processing

`IntList drawers = new IntList();int trials = 100000;int succes_count; void setup() {  for (int i = 0; i < 100; i++) {    drawers.append(i);  }  println(trials + " trials\n");   //Random strategy  println("Random strategy");  succes_count = trials;  for (int i = 0; i < trials; i++) {    drawers.shuffle();    for (int prisoner = 0; prisoner < 100; prisoner++) {      boolean found = false;      for (int attempt = 0; attempt < 50; attempt++) {        if (drawers.get(int(random(drawers.size()))) == prisoner) {          found = true;          break;        }      }      if (!found) {        succes_count--;        break;      }    }  }  println(" Succeses: " + succes_count);  println(" Succes rate: " + 100.0 * succes_count / trials + "%\n");   //Optimal strategy  println("Optimal strategy");  succes_count = trials;  for (int i = 0; i < trials; i++) {    drawers.shuffle();    for (int prisoner = 0; prisoner < 100; prisoner++) {      boolean found = false;      int next = prisoner;      for (int attempt = 0; attempt < 50; attempt++) {        next = drawers.get(next);        if (next == prisoner) {          found = true;          break;        }      }      if (!found) {        succes_count--;        break;      }    }  }  println(" Succeses: " + succes_count);  print(" Succes rate: " + 100.0 * succes_count / trials + "%");}`
Output:
```100000 trials

Random strategy
Succeses: 0
Succes rate: 0.0%

Optimal strategy
Succeses: 31134
Succes rate: 31.134%```

## PureBasic

`#PRISONERS=100#DRAWERS  =100#LOOPS    = 50#MAXPROBE = 10000OpenConsole() Dim p1(#PRISONERS,#DRAWERS)Dim p2(#PRISONERS,#DRAWERS)Dim d(#DRAWERS) For i=1 To #DRAWERS : d(i)=i : NextStart:For probe=1 To #MAXPROBE  RandomizeArray(d(),1,100)  c1=0 : c2=0   For m=1 To #PRISONERS    p2(m,1)=d(m) : If d(m)=m : p2(m,0)=1 : EndIf    For n=1 To #LOOPS      p1(m,n)=d(Random(100,1))      If p1(m,n)=m : p1(m,0)=1 : EndIf      If n>1 : p2(m,n)=d(p2(m,n-1)) : If p2(m,n)=m : p2(m,0)=1 : EndIf : EndIf    Next n  Next m   For m=1 To #PRISONERS    If p1(m,0) : c1+1 : p1(m,0)=0 : EndIf     If p2(m,0) : c2+1 : p2(m,0)=0 : EndIf  Next m   If c1=#PRISONERS : w1+1 : EndIf  If c2=#PRISONERS : w2+1 : EndIfNext probePrint("TRIALS: "+Str(#MAXPROBE))Print("  RANDOM= "+StrF(100*w1/#MAXPROBE,2)+"%   STATEGY= "+StrF(100*w2/#MAXPROBE,2)+"%")PrintN(~"\tFIN =q.") : inp\$=Input()w1=0 : w2=0If inp\$<>"q" : Goto Start : EndIf`
Output:
```TRIALS: 10000  RANDOM= 0.00%   STATEGY= 30.83%	FIN =q.

TRIALS: 10000  RANDOM= 0.00%   STATEGY= 31.60%	FIN =q.

TRIALS: 10000  RANDOM= 0.00%   STATEGY= 31.20%	FIN =q.```

## Python

### Procedural

`import random def play_random(n):    # using 0-99 instead of ranges 1-100    pardoned = 0    in_drawer = list(range(100))    sampler = list(range(100))    for _round in range(n):        random.shuffle(in_drawer)        found = False        for prisoner in range(100):            found = False            for reveal in random.sample(sampler, 50):                card = in_drawer[reveal]                if card == prisoner:                    found = True                    break            if not found:                break        if found:            pardoned += 1    return pardoned / n * 100   # % def play_optimal(n):    # using 0-99 instead of ranges 1-100    pardoned = 0    in_drawer = list(range(100))    for _round in range(n):        random.shuffle(in_drawer)        for prisoner in range(100):            reveal = prisoner            found = False            for go in range(50):                card = in_drawer[reveal]                if card == prisoner:                    found = True                    break                reveal = card            if not found:                break        if found:            pardoned += 1    return pardoned / n * 100   # % if __name__ == '__main__':    n = 100_000    print(" Simulation count:", n)    print(f" Random play wins: {play_random(n):4.1f}% of simulations")    print(f"Optimal play wins: {play_optimal(n):4.1f}% of simulations")`
Output:
``` Simulation count: 100000
Random play wins:  0.0% of simulations
Optimal play wins: 31.1% of simulations```

Or, an alternative procedural approach:

`# http://rosettacode.org/wiki/100_prisoners import random  def main():    NUM_DRAWERS = 10    NUM_REPETITIONS = int(1E5)     print('{:15}: {:5} ({})'.format('approach', 'wins', 'ratio'))    for approach in PrisionersGame.approaches:        num_victories = 0        for _ in range(NUM_REPETITIONS):            game = PrisionersGame(NUM_DRAWERS)            num_victories += PrisionersGame.victory(game.play(approach))         print('{:15}: {:5} ({:.2%})'.format(            approach.__name__, num_victories, num_victories / NUM_REPETITIONS))  class PrisionersGame:    """docstring for PrisionersGame"""    def __init__(self, num_drawers):        assert num_drawers % 2 == 0        self.num_drawers = num_drawers        self.max_attempts = int(self.num_drawers / 2)        self.drawer_ids = list(range(1, num_drawers + 1))        shuffled = self.drawer_ids[:]        random.shuffle(shuffled)        self.drawers = dict(zip(self.drawer_ids, shuffled))     def play_naive(self, player_number):        """ Randomly open drawers """        for attempt in range(self.max_attempts):            if self.drawers[random.choice(self.drawer_ids)] == player_number:                return True         return False     def play_naive_mem(self, player_number):        """ Randomly open drawers but avoiding repetitions """        not_attemped = self.drawer_ids[:]        for attempt in range(self.max_attempts):            guess = random.choice(not_attemped)            not_attemped.remove(guess)             if self.drawers[guess] == player_number:                return True         return False     def play_optimum(self, player_number):        """ Open the drawer that matches the player number and then open the drawer        with the revealed number.        """        prev_attempt = player_number        for attempt in range(self.max_attempts):            if self.drawers[prev_attempt] == player_number:                return True            else:                prev_attempt = self.drawers[prev_attempt]         return False     @classmethod    def victory(csl, results):        """Defines a victory of a game: all players won"""        return all(results)     approaches = [play_naive, play_naive_mem, play_optimum]     def play(self, approach):        """Plays this game and returns a list of booleans with        True if a player one, False otherwise"""        return [approach(self, player) for player in self.drawer_ids]  if __name__ == '__main__':    main()`
Output:
```With 10 drawers (100k runs)
approach       : wins  (ratio)
play_naive     :    14 (0.01%)
play_naive_mem :    74 (0.07%)
play_optimum   : 35410 (35.41%)

With 100 drawers (10k runs)
approach       : wins  (ratio)
play_naive     :     0 (0.00%)
play_naive_mem :     0 (0.00%)
play_optimum   :  3084 (30.84%)```

### Functional

There is some inefficiency entailed in repeatedly re-calculating the fixed sequence of drawers defined by index-chasing in the optimal strategy. Parts of the same paths from drawer to drawer are followed by several different prisoners.

We can avoid redundant recalculation by first obtaining the full set of drawer-chasing cycles that are defined by the sequence of any given shuffle.

We may also notice that the collective fate of the prisoners turns on whether any of the cyclical paths formed by a given shuffle are longer than 50 items. If a shuffle produces a single over-sized cycle, then not every prisoner will be able to reach their card in 50 moves.

The computation below returns a survival failure as soon as a cycle of more than 50 items is found for any given shuffle:

Works with: Python version 3.7
`'''100 Prisoners''' from random import randint, sample  # allChainedPathsAreShort :: Int -> IO (0|1)def allChainedPathsAreShort(n):    '''1 if none of the index-chasing cycles in a shuffled       sample of [1..n] cards are longer than half the       sample size. Otherwise, 0.    '''    limit = n // 2    xs = range(1, 1 + n)    shuffled = sample(xs, k=n)     # A cycle of boxes, drawn from a shuffled    # sample, which includes the given target.    def cycleIncluding(target):        boxChain = [target]        v = shuffled[target - 1]        while v != target:            boxChain.append(v)            v = shuffled[v - 1]        return boxChain     # Nothing if the target list is empty, or if the cycle which contains the    # first target is larger than half the sample size.    # Otherwise, just a cycle of enchained boxes containing the first target    # in the list, tupled with the residue of any remaining targets which    # fall outside that cycle.    def boxCycle(targets):        if targets:            boxChain = cycleIncluding(targets)            return Just((                difference(targets[1:])(boxChain),                boxChain            )) if limit >= len(boxChain) else Nothing()        else:            return Nothing()     # No cycles longer than half of total box count ?    return int(n == sum(map(len, unfoldr(boxCycle)(xs))))  # randomTrialResult :: RandomIO (0|1) -> Int -> (0|1)def randomTrialResult(coin):    '''1 if every one of the prisoners finds their ticket       in an arbitrary half of the sample. Otherwise 0.    '''    return lambda n: int(all(        coin(x) for x in range(1, 1 + n)    ))  # TEST ----------------------------------------------------# main :: IO ()def main():    '''Two sampling techniques constrasted with 100 drawers       and 100 prisoners, over 100,000 trial runs.    '''    halfOfDrawers = randomRInt(0)(1)     def optimalDrawerSampling(x):        return allChainedPathsAreShort(x)     def randomDrawerSampling(x):        return randomTrialResult(halfOfDrawers)(x)     # kSamplesWithNBoxes :: Int -> Int -> String    def kSamplesWithNBoxes(k):        tests = range(1, 1 + k)        return lambda n: '\n\n' + fTable(            str(k) + ' tests of optimal vs random drawer-sampling ' +            'with ' + str(n) + ' boxes: \n'        )(fName)(lambda r: '{:.2%}'.format(r))(            lambda f: sum(f(n) for x in tests) / k        )([            optimalDrawerSampling,            randomDrawerSampling,        ])     print(kSamplesWithNBoxes(10000)(10))     print(kSamplesWithNBoxes(10000)(100))     print(kSamplesWithNBoxes(100000)(100))  # ------------------------DISPLAY-------------------------- # fTable :: String -> (a -> String) -># (b -> String) -> (a -> b) -> [a] -> Stringdef fTable(s):    '''Heading -> x display function -> fx display function ->       f -> xs -> tabular string.    '''    def go(xShow, fxShow, f, xs):        ys = [xShow(x) for x in xs]        w = max(map(len, ys))        return s + '\n' + '\n'.join(map(            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),            xs, ys        ))    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(        xShow, fxShow, f, xs    )  # fname :: (a -> b) -> Stringdef fName(f):    '''Name bound to the given function.'''    return f.__name__  # ------------------------GENERIC ------------------------- # Just :: a -> Maybe adef Just(x):    '''Constructor for an inhabited Maybe (option type) value.       Wrapper containing the result of a computation.    '''    return {'type': 'Maybe', 'Nothing': False, 'Just': x}  # Nothing :: Maybe adef Nothing():    '''Constructor for an empty Maybe (option type) value.       Empty wrapper returned where a computation is not possible.    '''    return {'type': 'Maybe', 'Nothing': True}  # difference :: Eq a => [a] -> [a] -> [a]def difference(xs):    '''All elements of xs, except any also found in ys.'''    return lambda ys: list(set(xs) - set(ys))  # randomRInt :: Int -> Int -> IO () -> Intdef randomRInt(m):    '''The return value of randomRInt is itself       a function. The returned function, whenever       called, yields a a new pseudo-random integer       in the range [m..n].    '''    return lambda n: lambda _: randint(m, n)  # unfoldr(lambda x: Just((x, x - 1)) if 0 != x else Nothing())(10)# -> [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]# unfoldr :: (b -> Maybe (a, b)) -> b -> [a]def unfoldr(f):    '''Dual to reduce or foldr.       Where catamorphism reduces a list to a summary value,       the anamorphic unfoldr builds a list from a seed value.       As long as f returns Just(a, b), a is prepended to the list,       and the residual b is used as the argument for the next       application of f.       When f returns Nothing, the completed list is returned.    '''    def go(v):        xr = v, v        xs = []        while True:            mb = f(xr)            if mb.get('Nothing'):                return xs            else:                xr = mb.get('Just')                xs.append(xr)        return xs    return lambda x: go(x)  # MAIN ---if __name__ == '__main__':    main()`
Output:
```10000 tests of optimal vs random drawer-sampling with 10 boxes:

optimalDrawerSampling -> 35.47%
randomDrawerSampling -> 0.09%

10000 tests of optimal vs random drawer-sampling with 100 boxes:

optimalDrawerSampling -> 30.40%
randomDrawerSampling -> 0.00%

100000 tests of optimal vs random drawer-sampling with 100 boxes:

optimalDrawerSampling -> 31.17%
randomDrawerSampling -> 0.00%```

## R

`t = 100000 #number of trialssuccess.r = rep(0,t) #this will keep track of how many prisoners find their ticket on each trial for the random methodsuccess.o = rep(0,t) #this will keep track of how many prisoners find their ticket on each trial for the optimal method #random methodfor(i in 1:t){  escape = rep(F,100)  ticket = sample(1:100)  for(j in 1:length(prisoner)){    escape[j] = j %in% sample(ticket,50)  }  success.r[i] = sum(escape)} #optimal methodfor(i in 1:t){  escape = rep(F,100)  ticket = sample(1:100)  for(j in 1:100){    boxes = 0    current.box = j    while(boxes<50 && !escape[j]){      boxes=boxes+1      escape[j] = ticket[current.box]==j      current.box = ticket[current.box]    }  }  success.o[i] = sum(escape)} cat("Random method resulted in a success rate of ",100*mean(success.r==100),    "%.\nOptimal method resulted in a success rate of ",100*mean(success.o==100),"%.",sep="")`
Output:
```Random method resulted in a success rate of 0%.
Optimal method resulted in a success rate of 31.129%.```

## QB64

` Const Found = -1, Searching = 0, Status = 1, Tries = 2Const Attempt = 1, Victories = 2, RandomW = 1, ChainW = 2Randomize Timer Dim Shared Prisoners(1 To 100, Status To Tries) As Integer, Drawers(1 To 100) As Integer, Results(1 To 2, 1 To 2) As IntegerPrint "100 prisoners"Print "Random way to search..."For a = 1 To 2000    Init    Results(RandomW, Attempt) = Results(RandomW, Attempt) + 1    RandomWay    If verify% Then Results(RandomW, Victories) = Results(RandomW, Victories) + 1Next Print: Print "Chain way to search..."For a = 1 To 2000    Init    Results(ChainW, Attempt) = Results(ChainW, Attempt) + 1    ChainWay    If verify% Then Results(ChainW, Victories) = Results(ChainW, Victories) + 1NextPrint: Print "Results: "Print " Attempts "; Results(RandomW, Attempt); " "; "Victories "; Results(RandomW, Victories); " Ratio:"; Results(RandomW, Victories); "/"; Results(RandomW, Attempt)PrintPrint " Attempts "; Results(ChainW, Attempt); " "; "Victories "; Results(ChainW, Victories); " Ratio:"; Results(ChainW, Victories); "/"; Results(ChainW, Attempt)End Function verify%    Dim In As Integer    Print "veryfing "    verify = 0    For In = 1 To 100        If Prisoners(In, Status) = Searching Then Exit For    Next    If In = 101 Then verify% = FoundEnd Function Sub ChainWay    Dim In As Integer, ChainChoice As Integer    Print "Chain search"    For In = 1 To 100        ChainChoice = In        Do            Prisoners(In, Tries) = Prisoners(In, Tries) + 1            If Drawers(ChainChoice) = In Then Prisoners(In, Status) = Found: Exit Do            ChainChoice = Drawers(ChainChoice)        Loop Until Prisoners(In, Tries) = 50    Next InEnd Sub Sub RandomWay    Dim In As Integer, RndChoice As Integer    Print "Random search"    For In = 1 To 100        Do            Prisoners(In, Tries) = Prisoners(In, Tries) + 1            If Drawers(Int(Rnd * 100) + 1) = In Then Prisoners(In, Status) = Found: Exit Do        Loop Until Prisoners(In, Tries) = 50    Next    Print "Executed "End Sub  Sub Init    Dim I As Integer, I2 As Integer    Print "initialization"    For I = 1 To 100        Prisoners(I, Status) = Searching        Prisoners(I, Tries) = Searching        Do            Drawers(I) = Int(Rnd * 100) + 1            For I2 = 1 To I                If Drawers(I2) = Drawers(I) Then Exit For            Next            If I2 = I Then Exit Do        Loop    Next I    Print "Done "End Sub  `

## Quackery

`  [ this ] is 100prisoners.qky   [ dup size 2 / split ]                          is halve     (   [ --> [ [ )   [ stack ]                                       is successes (     --> s   )   [ [] swap times [ i join ] shuffle ]            is drawers   (   n --> [   )   [ false unrot    temp put     dup shuffle    halve drop    witheach      [ dip dup peek        temp share = if        [ dip not          conclude ] ]    drop    temp release ]                                is naive     ( [ n --> b   )   [ false unrot     dup temp put    over size 2 / times       [ dip dup peek        dup temp share = if        [ rot not unrot          conclude ] ]    2drop    temp release ]                                is smart     ( [ n --> b   )   [ ]'[ temp put    drawers    0 successes put    dup size times       [ dup i temp share do        successes tally ]    size successes take =     temp release ]                                is prisoners (   n --> b   )   [ say "100 naive prisoners were pardoned "    0 10000 times [ 100 prisoners naive + ] echo    say " times out of 10000 simulations." cr     say "100 smart prisoners were pardoned "    0 10000 times [ 100 prisoners smart + ] echo    say " times out of 10000 simulations." cr ]   is simulate  (     -->     )`

Output:

`/O>  [ \$ '100prisoners.qky' loadfile ] now!...  simulate... 100 naive prisoners were pardoned 0 times out of 10000 simulations.100 smart prisoners were pardoned 3158 times out of 10000 simulations. Stack empty.`

## Racket

`#lang racket(require srfi/1) (define current-samples (make-parameter 10000))(define *prisoners* 100)(define *max-guesses* 50) (define (evaluate-strategy instance-solved? strategy (s (current-samples)))  (/ (for/sum ((_ s) #:when (instance-solved? strategy)) 1) s)) (define (build-drawers)  (list->vector (shuffle (range *prisoners*)))) (define (100-prisoners-problem strategy)  (every (strategy (build-drawers)) (range *prisoners*))) (define ((strategy-1 drawers) p)  (any (λ (_) (= p (vector-ref drawers (random *prisoners*)))) (range *max-guesses*))) (define ((strategy-2 drawers) p)  (define-values (_ found?)    (for/fold ((d p) (found? #f)) ((_ *max-guesses*)) #:break found?      (let ((card (vector-ref drawers d))) (values card (= card p)))))  found?) (define (print-sample-percentage caption f (s (current-samples)))  (printf "~a: ~a%~%" caption (real->decimal-string (* 100 f) (- (order-of-magnitude s) 2)))) (module+ main  (print-sample-percentage "random" (evaluate-strategy 100-prisoners-problem strategy-1))  (print-sample-percentage "optimal" (evaluate-strategy 100-prisoners-problem strategy-2)))`
Output:
```random: 0.00%
optimal: 31.18%```

## Raku

(formerly Perl 6)

Works with: Rakudo version 2019.07.1

Accepts command line parameters to modify the number of prisoners and the number of simulations to run.

Also test with 10 prisoners to verify that the logic is correct for random selection. Random selection should succeed with 10 prisoners at a probability of (1/2)**10, so in 100_000 simulations, should get pardons about .0977 percent of the time.

`unit sub MAIN (:\$prisoners = 100, :\$simulations = 10000);my @prisoners = ^\$prisoners;my \$half = floor +@prisoners / 2; sub random (\$n) {    ^\$n .race.map( {        my @drawers = @prisoners.pick: *;        @prisoners.map( -> \$prisoner {            my \$found = 0;            for @drawers.pick(\$half) -> \$card {                \$found = 1 and last if \$card == \$prisoner            }            last unless \$found;            \$found        }        ).sum == @prisoners    }    ).grep( *.so ).elems / \$n * 100} sub optimal (\$n) {    ^\$n .race.map( {        my @drawers = @prisoners.pick: *;        @prisoners.map( -> \$prisoner {            my \$found = 0;            my \$card = @drawers[\$prisoner];            if \$card == \$prisoner {                \$found = 1            } else {                for ^(\$half - 1) {                    \$card = @drawers[\$card];                    \$found = 1 and last if \$card == \$prisoner                }            }            last unless \$found;            \$found        }        ).sum == @prisoners    }    ).grep( *.so ).elems / \$n * 100} say "Testing \$simulations simulations with \$prisoners prisoners.";printf " Random play wins: %.3f%% of simulations\n", random \$simulations;printf "Optimal play wins: %.3f%% of simulations\n", optimal \$simulations;`
Output:

With defaults

```Testing 10000 simulations with 100 prisoners.
Random play wins: 0.000% of simulations
Optimal play wins: 30.510% of simulations```

With passed parameters: --prisoners=10, --simulations=100000

```Testing 100000 simulations with 10 prisoners.
Random play wins: 0.099% of simulations
Optimal play wins: 35.461% of simulations
```

## Red

` Red [] K_runs: 100000repeat n 100 [append rand_arr: []  n]              ;; define array/series with numbers 1..100 ;;-------------------------------strat_optimal: function [pris ][;;-------------------------------  locker: pris                                    ;; start with locker equal to prisoner number  loop 50 [    if Board/:locker = pris [ return true ]       ;; locker with prisoner number found    locker: Board/:locker  ]  false                                           ;; number not found - fail];;-------------------------------strat_rand: function [pris ][;;-------------------------------  random rand_arr                                                 ;; define set of  random lockers  repeat n 50 [ if Board/(rand_arr/:n) = pris [ return true ]  ]  ;; try first 50, found ? then return success  false ] ;;------------------------------check_board: function [ strat][;;------------------------------repeat pris 100 [                                                   ;; for each prisoner  either  strat = 'optimal [ unless strat_optimal pris [return false ]  ]                              [ unless strat_rand pris [return false ]  ]  ]    true                                                  ;; all 100 prisoners passed test] saved: saved_rand: 0                                    ;; count all saved runs per strategyloop K_runs [  Board: random copy rand_arr                           ;; new board for every run  if  check_board 'optimal [saved: saved + 1]           ;; optimal stategy  if  check_board 'rand [saved_rand: saved_rand + 1]  ;; random strategy] print ["runs" k_runs newline  "Percent saved opt.strategy:" saved * 100.0 / k_runs ]print ["Percent saved random strategy:" saved_rand * 100.0 / k_runs ] `
Output:
```
runs 100000
Percent saved opt.strategy: 31.165
Percent saved random strategy: 0.0

```

## REXX

`/*REXX program to simulate the problem of 100 prisoners:  random,  and optimal strategy.*/parse arg men trials seed .                      /*obtain optional arguments from the CL*/if    men=='' |    men==","  then    men=    100 /*number of   prisoners   for this run.*/if trials=='' | trials==","  then trials= 100000 /*  "     "  simulations   "    "   "  */if datatype(seed, 'W')  then call random ,,seed  /*seed for the random number generator.*/try= men % 2;                swaps= men * 3      /*number tries for searching for a card*/\$.1= ' a simple ';           \$.2= "an optimal"   /*literals used for the SAY instruction*/say center(' running'  commas(trials)   "trials with"  commas(men)  'prisoners ', 70, "═")say    do strategy=1  for 2;    pardons= 0          /*perform the two types of strategies. */       do trials;             call gCards         /*do trials for a strategy;  gen cards.*/        do p=1  for men  until failure           /*have each prisoner go through process*/        if strategy==1  then failure= simple()   /*Is 1st strategy?  Use simple strategy*/                        else failure= picker()   /* " 2nd     "       "  optimal   "    */        end   /*p*/                              /*FAILURE ≡ 1?  Then a prisoner failed.*/      if #==men  then pardons= pardons + 1       /*was there a pardon of all prisoners? */      end     /*trials*/                         /*if 1 prisoner fails, then they all do*/     pc= format( pardons/trials*100, , 3);                           _= left('', pc<10)    say right('Using', 9)  \$.strategy  "strategy yields pardons "   _||pc"%  of the time."    end       /*strategy*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/commas:  parse arg _;  do c=length(_)-3  to 1  by -3; _= insert(',', _, c); end;  return _/*──────────────────────────────────────────────────────────────────────────────────────*/gCards: #= 0;                do j=1  for men;  @.j= j             /*define seq. of cards*/                             end   /*j*/                          /*same as seq. of men.*/               do swaps;             a= random(1, men)            /*get 1st rand number.*/                   do until  b\==a;  b= random(1, men)            /* "  2nd   "     "   */                   end   /*until*/                                /* [↑] ensure A ¬== B */               parse value  @.a @.b  with  @.b @.a                /*swap 2 random cards.*/               end       /*swaps*/;  return/*──────────────────────────────────────────────────────────────────────────────────────*/simple: !.= 0; do try;         do until !.?==0; ?= random(1, men) /*get random card ··· */                               end   /*until*/                    /*··· not used before.*/               if @.?==p  then do;   #= #+1;  return 0;  end      /*found his own card? */               !.?= 1                                             /*flag as being used. */               end   /*try*/;        return 1                     /*didn't find his card*//*──────────────────────────────────────────────────────────────────────────────────────*/picker: ?= p;  do try; if @.?==p  then do;   #= #+1;    return 0  /*Found his own card? */                                       end       /* [↑]  indicate success for prisoner. */               ?= @.?                            /*choose next drawer from current card.*/               end   /*try*/;        return 1    /*choose half of the number of drawers.*/`
output   when using the default inputs:
```══════════════ running 100,000 trials with 100 prisoners ══════════════

Using  a simple  strategy yields pardons   0.000%  of the time.
Using an optimal strategy yields pardons  31.186%  of the time.
```
output   when using the input of:     10
```══════════════ running 100,000 trials with 10 prisoners ══════════════

Using  a simple  strategy yields pardons   0.086%  of the time.
Using an optimal strategy yields pardons  31.204%  of the time.
```

## Ruby

`prisoners = [*1..100]N = 10_000generate_rooms = ->{ [nil]+[*1..100].shuffle } res = N.times.count do  rooms = generate_rooms[]  prisoners.all? {|pr| rooms[1,100].sample(50).include?(pr)}endputs "Random strategy : %11.4f %%" % (res.fdiv(N) * 100) res = N.times.count do  rooms = generate_rooms[]  prisoners.all? do |pr|    cur_room = pr    50.times.any? do      found = (rooms[cur_room] == pr)      cur_room = rooms[cur_room]      found    end  endendputs "Optimal strategy: %11.4f %%" % (res.fdiv(N) * 100) `
Output:
```Random strategy :      0.0000 %
Optimal strategy:     30.7400 %
```

## Rust

Fairly naive implementation. Could probably be made more idiomatic. Depends on extern rand crate.

Cargo.toml

`[dependencies]rand = '0.7.2'`

src/main.rs

`extern crate rand; use rand::prelude::*; // Do a full run of checking boxes in a random order for a single prisonerfn check_random_boxes(prisoner: u8, boxes: &[u8]) -> bool {    let checks = {        let mut b: Vec<u8> = (1u8..=100u8).collect();        b.shuffle(&mut rand::thread_rng());        b    };    checks.into_iter().take(50).any(|check| boxes[check as usize - 1] == prisoner)} // Do a full run of checking boxes in the optimized order for a single prisonerfn check_ordered_boxes(prisoner: u8, boxes: &[u8]) -> bool {    let mut next_check = prisoner;    (0..50).any(|_| {        next_check = boxes[next_check as usize - 1];        next_check == prisoner    })} fn main() {    let mut boxes: Vec<u8> = (1u8..=100u8).collect();     let trials = 100000;     let ordered_successes = (0..trials).filter(|_| {        boxes.shuffle(&mut rand::thread_rng());        (1u8..=100u8).all(|prisoner| check_ordered_boxes(prisoner, &boxes))    }).count();     let random_successes = (0..trials).filter(|_| {        boxes.shuffle(&mut rand::thread_rng());        (1u8..=100u8).all(|prisoner| check_random_boxes(prisoner, &boxes))    }).count();     println!("{} / {} ({:.02}%) successes in ordered", ordered_successes, trials, ordered_successes as f64 * 100.0 / trials as f64);    println!("{} / {} ({:.02}%) successes in random", random_successes, trials, random_successes as f64 * 100.0 / trials as f64); }`
Output:
```31106 / 100000 (31.11%) successes in ordered
0 / 100000 (0.00%) successes in random```

## Sather

`class MAIN is   shuffle (a: ARRAY{INT}) is      ARR_PERMUTE_ALG{INT, ARRAY{INT}}::shuffle(a);   end;    try_random (n: INT, drawers: ARRAY{INT}, tries: INT): BOOL is      my_tries ::= drawers.inds; shuffle(my_tries);      loop tries.times!;         if drawers[my_tries.elt!] = n then return true; end;      end;      return false;   end;    try_optimal (n: INT, drawers: ARRAY{INT}, tries: INT): BOOL is      num ::= n;      loop tries.times!;         num := drawers[num];         if num = n then return true; end;      end;      return false;   end;    stats (label: STR, rounds, successes: INT): STR is      return #FMT("<^###########>: <#######> rounds. Successes: <#######> (<##.###>%%)\n",                   label, rounds, successes, (successes.flt / rounds.flt)*100.0).str;   end;    try (name: STR, nrounds, ndrawers, npris, ntries: INT,        strategy: ROUT{INT,ARRAY{INT},INT}:BOOL)   is      drawers: ARRAY{INT} := #(ndrawers);      loop drawers.set!(drawers.ind!); end;      successes ::= 0;      loop nrounds.times!;         shuffle(drawers);         success ::= true;         loop            n ::= npris.times!;            if ~strategy.call(n, drawers, ntries) then               success := false;               break!;            end;         end;         if success then successes := successes + 1; end;      end;      #OUT + stats(name, nrounds, successes);   end;    main is      RND::seed := #TIMES.wall_time;      #OUT +"100 prisoners, 100 drawers, 50 tries:\n";      try("random",  100000, 100, 100, 50, bind(try_random(_, _, _)));      try("optimal", 100000, 100, 100, 50, bind(try_optimal(_, _, _)));       #OUT +"\n10 prisoners, 10 drawers, 5 tries:\n";      try("random",  100000, 10, 10, 5, bind(try_random(_, _, _)));      try("optimal", 100000, 10, 10, 5, bind(try_optimal(_, _, _)));   end;end;`
Output:
```100 prisoners, 100 drawers, 50 tries:
random      :  100000 rounds. Successes:       0 ( 0.000%)
optimal     :  100000 rounds. Successes:   31378 (31.378%)

10 prisoners, 10 drawers, 5 tries:
random      :  100000 rounds. Successes:     113 ( 0.113%)
optimal     :  100000 rounds. Successes:   35633 (35.633%)```

## Scala

Translation of: Java
`import scala.util.Randomimport scala.util.control.Breaks._ object Main {  def playOptimal(n: Int): Boolean = {    val secretList = Random.shuffle((0 until n).toBuffer)     for (i <- secretList.indices) {      var prev = i      breakable {        for (_ <- 0 until secretList.size / 2) {          if (secretList(prev) == i) {            break()          }          prev = secretList(prev)        }        return false      }    }     true  }   def playRandom(n: Int): Boolean = {    val secretList = Random.shuffle((0 until n).toBuffer)     for (i <- secretList.indices) {      val trialList = Random.shuffle((0 until n).toBuffer)       breakable {        for (j <- 0 until trialList.size / 2) {          if (trialList(j) == i) {            break()          }        }        return false      }    }     true  }   def exec(n: Int, p: Int, play: Int => Boolean): Double = {    var succ = 0.0    for (_ <- 0 until n) {      if (play(p)) {        succ += 1      }    }    (succ * 100.0) / n  }   def main(args: Array[String]): Unit = {    val n = 100000    val p = 100    printf("# of executions: %,d\n", n)    printf("Optimal play success rate: %f%%\n", exec(n, p, playOptimal))    printf("Random play success rate: %f%%\n", exec(n, p, playRandom))  }}`
Output:
```# of executions: 100,000
Optimal play success rate: 31.201000%
Random play success rate: 0.000000%```

## Swift

`import Foundation struct PrisonersGame {  let strategy: Strategy  let numPrisoners: Int  let drawers: [Int]   init(numPrisoners: Int, strategy: Strategy) {    self.numPrisoners = numPrisoners    self.strategy = strategy    self.drawers = (1...numPrisoners).shuffled()  }   @discardableResult  func play() -> Bool {    for num in 1...numPrisoners {      guard findNumber(num) else {        return false      }    }     return true  }   private func findNumber(_ num: Int) -> Bool {    var tries = 0    var nextDrawer = num - 1     while tries < 50 {      tries += 1       switch strategy {      case .random where drawers.randomElement()! == num:        return true      case .optimum where drawers[nextDrawer] == num:        return true      case .optimum:        nextDrawer = drawers[nextDrawer] - 1      case _:        continue      }    }     return false  }   enum Strategy {    case random, optimum  }} let numGames = 100_000let lock = DispatchSemaphore(value: 1)var done = 0 print("Running \(numGames) games for each strategy") DispatchQueue.concurrentPerform(iterations: 2) {i in  let strat = i == 0 ? PrisonersGame.Strategy.random : .optimum  var numPardoned = 0   for _ in 0..<numGames {    let game = PrisonersGame(numPrisoners: 100, strategy: strat)     if game.play() {      numPardoned += 1    }  }   print("Probability of pardon with \(strat) strategy: \(Double(numPardoned) / Double(numGames))")   lock.wait()  done += 1  lock.signal()   if done == 2 {    exit(0)  }} dispatchMain()`
Output:
```Running 100000 games for each strategy
Probability of pardon with optimum strategy: 0.31099
Probability of pardon with random strategy: 0.0```

## Tcl

Translation of: Common Lisp
`set Samples 10000set Prisoners 100set MaxGuesses 50set Strategies {random optimal} # returns a random number between 0 and N-1.proc random {n} {  expr int(rand()*\$n)} # Returns a list from 0 to N-1.proc range {n} {  set res {}  for {set i 0} {\$i < \$n} {incr i} {    lappend res \$i  }  return \$res} # Returns shuffled LIST.proc nshuffle {list} {    set len [llength \$list]    while {\$len} {        set n [expr {int(\$len * rand())}]        set tmp [lindex \$list \$n]        lset list \$n [lindex \$list [incr len -1]]        lset list \$len \$tmp    }    return \$list} # Returns a list of shuffled drawers.proc buildDrawers {} {  global Prisoners  nshuffle [range \$Prisoners]} # Returns true if P is found in DRAWERS within \$MaxGuesses attempts using a# random strategy.proc randomStrategy {drawers p} {  global Prisoners MaxGuesses  foreach i [range \$MaxGuesses] {    if {\$p == [lindex \$drawers [random \$Prisoners]]} {      return 1    }  }  return 0} # Returns true if P is found in DRAWERS within \$MaxGuesses attempts using an# optimal strategy.proc optimalStrategy {drawers p} {  global Prisoners MaxGuesses  set j \$p  foreach i [range \$MaxGuesses] {    set k [lindex \$drawers \$j]    if {\$k == \$p} {      return 1    }    set j \$k  }  return 0} # Returns true if all prisoners find their number using the given STRATEGY.proc run100prisonersProblem {strategy} {  global Prisoners  set drawers [buildDrawers]  foreach p [range \$Prisoners] {    if {![\$strategy \$drawers \$p]} {      return 0    }  }  return 1} # Runs the given STRATEGY \$Samples times and returns the number of times all# prisoners succeed.proc sampling {strategy} {  global Samples  set successes 0  foreach s [range \$Samples] {    if {[run100prisonersProblem \$strategy]} {      incr successes    }  }  return \$successes} # Returns true if the given STRING starts with a vowel.proc startsWithVowel {string} {  expr [lsearch -exact {a e i o u} [string index \$string 0]] >= 0} # Runs each of the STRATEGIES and prints a report on how well they# worked.proc compareStrategies {strategies} {  global Samples  set fmt "Using %s %s strategy, the prisoners were freed in %5.2f%% of the cases."  foreach strategy \$strategies {    set article [expr [startsWithVowel \$strategy] ? {"an"} : {"a"}]    set pct [expr [sampling \${strategy}Strategy] / \$Samples.0 * 100]    puts [format \$fmt \$article \$strategy \$pct]  }} compareStrategies \$Strategies`
Output:
```Using a random strategy, the prisoners were freed in  0.00% of the cases.
Using an optimal strategy, the prisoners were freed in 32.35% of the cases.```

## Transact-SQL

### School example

Works with: Transact-SQL version SQL Server 2017
`USE rosettacode;GO SET NOCOUNT ON;GO CREATE TABLE dbo.numbers (n INT PRIMARY KEY);GO -- NOTE If you want to play more than 10000 games, you need to extend the query generating the numbers table by adding-- next cross joins. Now the table contains enough values to solve the task and it takes less processing time. WITH sample100 AS (    SELECT TOP(100) object_id    FROM master.sys.objects)INSERT numbers    SELECT ROW_NUMBER() OVER (ORDER BY A.object_id) AS n    FROM sample100 AS A        CROSS JOIN sample100 AS B;GO CREATE TABLE dbo.drawers (drawer INT PRIMARY KEY, card INT);GO CREATE TABLE dbo.results (strategy VARCHAR(10), game INT, result BIT, PRIMARY KEY (game, strategy));GO CREATE PROCEDURE dbo.shuffleDrawers @prisonersCount INTAS BEGIN    SET NOCOUNT ON;     IF NOT EXISTS (SELECT * FROM drawers)        INSERT drawers (drawer, card)        SELECT n AS drawer, n AS card        FROM numbers        WHERE n <= @prisonersCount;     DECLARE @randoms TABLE (n INT, random INT);    DECLARE @n INT = 1;    WHILE @n <= @prisonersCount BEGIN        INSERT @randoms VALUES (@n, ROUND(RAND() * (@prisonersCount - 1), 0) + 1);         SET @n = @n + 1;    END;     WITH ordered AS (        SELECT ROW_NUMBER() OVER (ORDER BY random ASC) AS drawer,            n AS card        FROM @randoms    )    UPDATE drawers    SET card = o.card    FROM drawers AS s        INNER JOIN ordered AS o            ON o.drawer = s.drawer;ENDGO CREATE PROCEDURE dbo.find @prisoner INT, @strategy VARCHAR(10)AS BEGIN    -- A prisoner can open no more than 50 drawers.    DECLARE @drawersCount INT = (SELECT COUNT(*) FROM drawers);    DECLARE @openMax INT = @drawersCount / 2;     -- Prisoners start outside the room.    DECLARE @card INT = NULL;    DECLARE @open INT = 1;    WHILE @open <= @openMax BEGIN        -- A prisoner tries to find his own number.        IF @strategy = 'random' BEGIN            DECLARE @random INT = ROUND(RAND() * (@drawersCount - 1), 0) + 1;            SET @card = (SELECT TOP(1) card FROM drawers WHERE drawer = @random);        END        IF @strategy = 'optimal' BEGIN            IF @card IS NULL BEGIN                SET @card = (SELECT TOP(1) card FROM drawers WHERE drawer = @prisoner);            END ELSE BEGIN                SET @card = (SELECT TOP(1) card FROM drawers WHERE drawer = @card);            END        END         -- A prisoner finding his own number is then held apart from the others.        IF @card = @prisoner            RETURN 1;         SET @open = @open + 1;    END     RETURN 0;ENDGO CREATE PROCEDURE dbo.playGame @gamesCount INT, @strategy VARCHAR(10), @prisonersCount INT = 100AS BEGIN    SET NOCOUNT ON;     IF @gamesCount <> (SELECT COUNT(*) FROM results WHERE strategy = @strategy) BEGIN        DELETE results        WHERE strategy = @strategy;         INSERT results (strategy, game, result)        SELECT @strategy AS strategy, n AS game, 0 AS result        FROM numbers        WHERE n <= @gamesCount;    END     UPDATE results    SET result = 0    WHERE strategy = @strategy;     DECLARE @game INT = 1;    WHILE @game <= @gamesCount BEGIN        -- A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.        -- Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.        EXECUTE shuffleDrawers @prisonersCount;         -- A prisoner tries to find his own number.        -- Prisoners start outside the room.        -- They can decide some strategy before any enter the room.        DECLARE @prisoner INT = 1;        DECLARE @found INT = 0;        WHILE @prisoner <= @prisonersCount BEGIN            EXECUTE @found = find @prisoner, @strategy;            IF @found = 1                SET @prisoner = @prisoner + 1;            ELSE                BREAK;        END;         -- If all 100 findings find their own numbers then they will all be pardoned. If any don't then all sentences stand.        IF @found = 1            UPDATE results SET result = 1 WHERE strategy = @strategy AND game = @game;         SET @game = @game + 1;    ENDENDGO CREATE FUNCTION dbo.computeProbability(@strategy VARCHAR(10))RETURNS decimal (18, 2)AS BEGIN    RETURN (        SELECT (SUM(CAST(result AS INT)) * 10000 / COUNT(*)) / 100        FROM results        WHERE strategy = @strategy    );ENDGO -- Simulate several thousand instances of the game:DECLARE @gamesCount INT = 2000; -- ...where the prisoners randomly open drawers.EXECUTE playGame @gamesCount, 'random'; -- ...where the prisoners use the optimal strategy mentioned in the Wikipedia article.EXECUTE playGame @gamesCount, 'optimal'; -- Show and compare the computed probabilities of success for the two strategies.DECLARE @log VARCHAR(max);SET @log = CONCAT('Games count: ', @gamesCount);RAISERROR (@log, 0, 1) WITH NOWAIT;SET @log = CONCAT('Probability of success with "random" strategy: ', dbo.computeProbability('random'));RAISERROR (@log, 0, 1) WITH NOWAIT;SET @log = CONCAT('Probability of success with "optimal" strategy: ', dbo.computeProbability('optimal'));RAISERROR (@log, 0, 1) WITH NOWAIT;GO DROP FUNCTION dbo.computeProbability;DROP PROCEDURE dbo.playGame;DROP PROCEDURE dbo.find;DROP PROCEDURE dbo.shuffleDrawers;DROP TABLE dbo.results;DROP TABLE dbo.drawers;DROP TABLE dbo.numbers;GO`

Output:

```Games count: 2000
Probability of success with "random" strategy: 0.00
Probability of success with "optimal" strategy: 31.00```

## VBA/Visual Basic

`Sub HundredPrisoners()     NumberOfPrisoners = Int(InputBox("Number of Prisoners", "Prisoners", 100))    Tries = Int(InputBox("Numer of Tries", "Tries", 1000))    Selections = Int(InputBox("Number of Selections", "Selections", NumberOfPrisoners / 2))     StartTime = Timer     AllFoundOptimal = 0    AllFoundRandom = 0    AllFoundRandomMem = 0     For i = 1 To Tries        OptimalCount = HundredPrisoners_Optimal(NumberOfPrisoners, Selections)        RandomCount = HundredPrisoners_Random(NumberOfPrisoners, Selections)        RandomMemCount = HundredPrisoners_Random_Mem(NumberOfPrisoners, Selections)         If OptimalCount = NumberOfPrisoners Then            AllFoundOptimal = AllFoundOptimal + 1        End If        If RandomCount = NumberOfPrisoners Then            AllFoundRandom = AllFoundRandom + 1        End If        If RandomMemCount = NumberOfPrisoners Then            AllFoundRandomMem = AllFoundRandomMem + 1        End If    Next i      ResultString = "Optimal: " & AllFoundOptimal & " of " & Tries & ": " & AllFoundOptimal / Tries * 100 & "%"    ResultString = ResultString & Chr(13) & "Random: " & AllFoundRandom & " of " & Tries & ": " & AllFoundRandom / Tries * 100 & "%"    ResultString = ResultString & Chr(13) & "RandomMem: " & AllFoundRandomMem & " of " & Tries & ": " & AllFoundRandomMem / Tries * 100 & "%"     EndTime = Timer     ResultString = ResultString & Chr(13) & "Elapsed Time: " & Round(EndTime - StartTime, 2) & " s"    ResultString = ResultString & Chr(13) & "Trials/sec: " & Tries / Round(EndTime - StartTime, 2)     MsgBox ResultString, vbOKOnly, "Results" End Sub Function HundredPrisoners_Optimal(ByVal NrPrisoners, ByVal NrSelections) As Long    Dim DrawerArray() As Long     ReDim DrawerArray(NrPrisoners - 1)     For Counter = LBound(DrawerArray) To UBound(DrawerArray)        DrawerArray(Counter) = Counter + 1    Next Counter     FisherYates DrawerArray     For i = 1 To NrPrisoners        NumberFromDrawer = DrawerArray(i - 1)        For j = 1 To NrSelections - 1            If NumberFromDrawer = i Then                FoundOwnNumber = FoundOwnNumber + 1                Exit For            End If            NumberFromDrawer = DrawerArray(NumberFromDrawer - 1)        Next j    Next i    HundredPrisoners_Optimal = FoundOwnNumberEnd Function Function HundredPrisoners_Random(ByVal NrPrisoners, ByVal NrSelections) As Long    Dim DrawerArray() As Long    ReDim DrawerArray(NrPrisoners - 1)     FoundOwnNumber = 0     For Counter = LBound(DrawerArray) To UBound(DrawerArray)        DrawerArray(Counter) = Counter + 1    Next Counter     FisherYates DrawerArray      For i = 1 To NrPrisoners        For j = 1 To NrSelections            RandomDrawer = Int(NrPrisoners * Rnd)            NumberFromDrawer = DrawerArray(RandomDrawer)            If NumberFromDrawer = i Then                FoundOwnNumber = FoundOwnNumber + 1                Exit For            End If        Next j    Next i    HundredPrisoners_Random = FoundOwnNumberEnd Function Function HundredPrisoners_Random_Mem(ByVal NrPrisoners, ByVal NrSelections) As Long    Dim DrawerArray() As Long    Dim SelectionArray() As Long    ReDim DrawerArray(NrPrisoners - 1)    ReDim SelectionArray(NrPrisoners - 1)     HundredPrisoners_Random_Mem = 0    FoundOwnNumberMem = 0     For Counter = LBound(DrawerArray) To UBound(DrawerArray)        DrawerArray(Counter) = Counter + 1    Next Counter     For Counter = LBound(SelectionArray) To UBound(SelectionArray)        SelectionArray(Counter) = Counter + 1    Next Counter     FisherYates DrawerArray     For i = 1 To NrPrisoners        FisherYates SelectionArray        For j = 1 To NrSelections            NumberFromDrawer = DrawerArray(SelectionArray(j - 1) - 1)            If NumberFromDrawer = i Then                FoundOwnNumberMem = FoundOwnNumberMem + 1                Exit For            End If        Next j    Next i    HundredPrisoners_Random_Mem = FoundOwnNumberMemEnd Function Sub FisherYates(ByRef InputArray() As Long)     Dim Temp As Long    Dim PosRandom As Long    Dim Counter As Long    Dim Upper As Long    Dim Lower As Long     Lower = LBound(InputArray)    Upper = UBound(InputArray)     Randomize     For Counter = Upper To (Lower + 1) Step -1        PosRandom = CLng(Int((Counter - Lower + 1) * Rnd + Lower))        Temp = InputArray(Counter)        InputArray(Counter) = InputArray(PosRandom)        InputArray(PosRandom) = Temp    Next Counter End Sub`
Output:
```Optimal: 29090 of 100000: 29.09%
Random: 0 of 100000: 0%
RandomMem: 0 of 100000: 0%
Elapsed Time: 388.41 s```

## Visual Basic .NET

Translation of: C#
`Module Module1     Function PlayOptimal() As Boolean        Dim secrets = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList         For p = 1 To 100            Dim success = False             Dim choice = p - 1            For i = 1 To 50                If secrets(choice) = p - 1 Then                    success = True                    Exit For                End If                choice = secrets(choice)            Next             If Not success Then                Return False            End If        Next         Return True    End Function     Function PlayRandom() As Boolean        Dim secrets = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList         For p = 1 To 100            Dim choices = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList             Dim success = False            For i = 1 To 50                If choices(i - 1) = p Then                    success = True                    Exit For                End If            Next             If Not success Then                Return False            End If        Next         Return True    End Function     Function Exec(n As UInteger, play As Func(Of Boolean))        Dim success As UInteger = 0        For i As UInteger = 1 To n            If play() Then                success += 1            End If        Next        Return 100.0 * success / n    End Function     Sub Main()        Dim N = 1_000_000        Console.WriteLine("# of executions: {0}", N)        Console.WriteLine("Optimal play success rate: {0:0.00000000000}%", Exec(N, AddressOf PlayOptimal))        Console.WriteLine(" Random play success rate: {0:0.00000000000}%", Exec(N, AddressOf PlayRandom))    End Sub End Module`
Output:
```# of executions: 1000000
Optimal play success rate: 31.12990000000%
Random play success rate: 0.00000000000%```

## VBScript

` option explicitconst npris=100const ntries=50const ntests=1000.dim drawer(100),opened(100),ifor i=1 to npris: drawer(i)=i:nextshuffle drawerwscript.echo rf(tests(false)/ntests*100,10," ")  &" % success for random"wscript.echo rf(tests(true) /ntests*100,10," ")  &" % success for optimal strategy" function rf(v,n,s) rf=right(string(n,s)& v,n):end function  sub shuffle(d) 'knut's shuffledim i,j,trandomize timerfor i=1 to npris   j=int(rnd()*i+1)   t=d(i):d(i)=d(j):d(j)=tnextend sub function tests(strat)dim cntp,i,jtests=0for i=1 to ntests  shuffle drawer  cntp=0  if strat then      for j=1 to npris	if not trystrat(j) then exit for      next  else		     for j=1 to npris       if not tryrand(j) then exit for     next        end if  if j>=npris then tests=tests+1nextend function  function tryrand(pris)  dim i,r 	erase opened  for i=1 to ntries    do       r=int(rnd*npris+1)    loop until opened(r)=false    opened(r)=true    if drawer(r)= pris then tryrand=true : exit function  next  tryrand=falseend function    function trystrat(pris)  dim i,r  r=pris  for i=1 to ntries    if drawer(r)= pris then trystrat=true	:exit function    r=drawer(r)  next  trystrat=falseend function	 `

Output:

```         0 % success for random
32.9 % success for optimal strategy
```

## Vlang

Translation of: Wren
`import randimport rand.seed// Uses 0-based numbering rather than 1-based numbering throughout.fn do_trials(trials int, np int, strategy string) {    mut pardoned := 0    for _ in 0..trials {        mut drawers := []int{len: 100, init: it}        rand.shuffle<int>(mut drawers) or {panic('shuffle failed')}        mut next_trial := false        for p in 0..np {            mut next_prisoner := false            if strategy == "optimal" {                mut prev := p                for _ in 0..50 {                    this := drawers[prev]                    if this == p {                        next_prisoner = true                        break                    }                    prev = this                }            } else {                // Assumes a prisoner remembers previous drawers (s)he opened                // and chooses at random from the others.                mut opened := bool{}                for _ in 0..50 {                    mut n := 0                    for {                        n = rand.intn(100) or {0}                        if !opened[n] {                            opened[n] = true                            break                        }                    }                    if drawers[n] == p {                        next_prisoner = true                        break                    }                }            }            if !next_prisoner {                next_trial = true                break            }        }        if !next_trial {            pardoned++        }    }    rf := f64(pardoned) / f64(trials) * 100    println("  strategy = \${strategy:-7}  pardoned = \${pardoned:-6} relative frequency = \${rf:-5.2f}%\n")} fn main() {    rand.seed(seed.time_seed_array(2))    trials := 100000    for np in [10, 100] {        println("Results from \$trials trials with \$np prisoners:\n")        for strategy in ["random", "optimal"] {            do_trials(trials, np, strategy)        }    }}`
Output:

Sample run:

```Results from 100000 trials with 10 prisoners:

strategy = random   pardoned = 91     relative frequency = 0.09 %

strategy = optimal  pardoned = 31321  relative frequency = 31.32%

Results from 100000 trials with 100 prisoners:

strategy = random   pardoned = 0      relative frequency = 0.00 %

strategy = optimal  pardoned = 31318  relative frequency = 31.32%
```

## Wren

Translation of: Go
Library: Wren-fmt
`import "random" for Randomimport "/fmt" for Fmt var rand = Random.new() var doTrials = Fn.new{ |trials, np, strategy|    var pardoned = 0    for (t in 0...trials) {        var drawers = List.filled(100, 0)        for (i in 0..99) drawers[i] = i        rand.shuffle(drawers)        var nextTrial = false        for (p in 0...np) {            var nextPrisoner = false            if (strategy == "optimal") {                var prev = p                for (d in 0..49) {                    var curr = drawers[prev]                    if (curr == p) {                        nextPrisoner = true                        break                    }                    prev = curr                }            } else {                var opened = List.filled(100, false)                for (d in 0..49) {                    var n                    while (true) {                        n = rand.int(100)                        if (!opened[n]) {                            opened[n] = true                            break                        }                    }                    if (drawers[n] == p) {                        nextPrisoner = true                        break                    }                }            }            if (!nextPrisoner) {               nextTrial = true               break            }        }        if (!nextTrial) pardoned = pardoned + 1    }    var rf = pardoned/trials * 100    Fmt.print("  strategy = \$-7s  pardoned = \$,6d relative frequency = \$5.2f\%\n", strategy, pardoned, rf)} var trials = 1e5for (np in [10, 100]) {    Fmt.print("Results from \$,d trials with \$d prisoners:\n", trials, np)    for (strategy in ["random", "optimal"]) doTrials.call(trials, np, strategy)}`
Output:

Sample run:

```Results from 100,000 trials with 10 prisoners:

strategy = random   pardoned =     98 relative frequency =  0.10%

strategy = optimal  pardoned = 31,212 relative frequency = 31.21%

Results from 100,000 trials with 100 prisoners:

strategy = random   pardoned =      0 relative frequency =  0.00%

strategy = optimal  pardoned = 31,139 relative frequency = 31.14%
```

## XPL0

`int     Drawer(100); proc KShuffle;          \Randomly rearrange the cards in the drawers\(Woe unto thee if Stattolo shuffle is used instead of Knuth shuffle.)int  I, J, T;[for I:= 100-1 downto 1 do    [J:= Ran(I+1);      \range [0..I]    T:= Drawer(I);  Drawer(I):= Drawer(J);  Drawer(J):= T;    ];]; func Stategy2;          \Return 'true' if stragegy succeedsint  Prisoner, Card, Try;[for Prisoner:= 1 to 100 do   [Card:= Drawer(Prisoner-1);   Try:= 1;   loop [if Card = Prisoner then quit;        if Try >= 50 then return false;        Card:= Drawer(Card-1);        Try:= Try+1;        ];    ];return true;]; func Stategy1;          \Return 'true' if stragegy succeedsint  Prisoner, I, D(100);[for Prisoner:= 1 to 100 do   loop [for I:= 0 to 100-1 do D(I):= I+1;        KShuffle;        for I:= 1 to 50 do            if Drawer(D(I-1)) = Prisoner then quit;        return false;        ];return true;]; proc Strategy(S);int  S, I, Sample;real Successes;[Successes:= 0.;for Sample:= 1 to 100_000 do    [for I:= 0 to 100-1 do Drawer(I):= I+1;    KShuffle;    case S of     1: if Stategy1 then Successes:= Successes + 1.;     2: if Stategy2 then Successes:= Successes + 1.    other [];    ];RlOut(0, Successes/100_000.*100.);  Text(0, "%^m^j");]; [Format(3, 12);Text(0, "Random strategy success rate:  ");Strategy(1);Text(0, "Optimal strategy success rate: ");Strategy(2);]`
Output:
```Random strategy success rate:    0.000000000000%
Optimal strategy success rate:  31.085000000000%
```

## Yabasic

Translation of: Phix
`// Rosetta Code problem: http://rosettacode.org/wiki/100_prisoners// by Galileo, 05/2022 sub play(prisoners, iterations, optimal)    local prisoner, pardoned, found, drawer, drawers(prisoners), i, j, k, p, x     for i = 1 to prisoners : drawers(i) = i : next     for i = 1 to iterations        for k = 1 to prisoners : x = ran(prisoners) + 1 : p = drawers(x) : drawers(x) = drawers(k) : drawers(k) = p : next        for prisoner = 1 to prisoners            found = false            if optimal then drawer = prisoner else drawer = ran(prisoners) + 1 end if            for j = 1 to prisoners / 2                drawer = drawers(drawer)                if drawer = prisoner found = true : break                if not optimal drawer = ran(prisoners) + 1            next            if not found break        next        pardoned = pardoned + found    next     return 100 * pardoned / iterationsend sub iterations = 10000print "Simulation count: ", iterationsfor prisoners = 10 to 100 step 90    random = play(prisoners, iterations, false)    optimal = play(prisoners, iterations, true)    print "Prisoners: ", prisoners, ", random: ", random, ", optimal: ", optimalnext`
Output:
```Simulation count: 10000
Prisoners: 10, random: 0.01, optimal: 35.83
Prisoners: 100, random: 0, optimal: 31.2
---Program done, press RETURN---```

## zkl

`const SLOTS=100, PRISONERS=100, TRIES=50, N=10_000;fcn oneHundredJDI{	// just do it strategy   cupboard,picks := [0..SLOTS-1].walk().shuffle(), cupboard.copy();   // if this prisoner can't find their number in TRIES, all fail   foreach p in (PRISONERS){ if(picks.shuffle().find(p)>=TRIES) return(False); }   True		// all found their number}fcn oneHundredO{	// Optimal strategy   cupboard := [0..SLOTS-1].walk().shuffle();   foreach p in (PRISONERS){      d:=p;      do(TRIES){ if((d=cupboard[d]) == p) continue(2) }  // found my number      return(False);  // this prisoner failed to find their number, all fail   }   True		// all found their number}`
`s:=N.pump(Ref(0).incN,oneHundredJDI).value.toFloat()/N*100;println("Just do it strategy (%,d simulatations): %.2f%%".fmt(N,s)); s:=N.pump(Ref(0).incN,oneHundredO).value.toFloat()/N*100;println("Optimal strategy    (%,d simulatations): %.2f%%".fmt(N,s));`
Output:
```Just do it strategy (10,000 simulatations): 0.00%
Optimal strategy    (10,000 simulatations): 31.16%
```

And a sanity check (from the Raku entry):

`const SLOTS=100, PRISONERS=10, TRIES=50, N=100_000;`
Output:
```Just do it strategy (100,000 simulatations): 0.09%
Optimal strategy    (100,000 simulatations): 31.13%
```