Two bullet roulette

From Rosetta Code
Revision as of 10:19, 17 February 2021 by rosettacode>Gerard Schildberger (→‎{{header|REXX}}: changed the program to use a simple string (instead of an indexed array) for the cartridge chamber.)
Two bullet roulette is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The following is supposedly a question given to mathematics graduates seeking jobs on Wall Street: 

 A revolver handgun has a revolving cylinder with six chambers for bullets.
   
 It is loaded with the following procedure:
     1. Check the first chamber to the right of the trigger for a bullet.  If a bullet
        is seen, the cylinder is rotated one chamber clockwise and the next chamber
        checked until an empty chamber is found.
     2. A cartridge containing a bullet is placed in the empty chamber.
     3. The cylinder is then rotated one chamber clockwise.
   
 To randomize the cylinder's position, the cylinder is spun, which causes the cylinder to take
 a random position from 1 to 6 chamber rotations clockwise from its starting position.
   
 When the trigger is pulled the gun will fire if there is a bullet in position 0, which is just
 counterclockwise from the loading position.
   
 The gun is unloaded by removing all cartridges from the cylinder.
   
 According to the legend, a suicidal Russian imperial military officer plays a game of Russian
 roulette by putting two bullets in a six-chamber cylinder and pulls the trigger twice.
 If the gun fires with a trigger pull, this is considered a successful suicide.
   
 The cylinder is always spun before the first shot, but it may or may not be spun after putting
 in the first bullet and may or may not be spun after taking the first shot.
   
 Which of the following situations produces the highest probability of suicide?
   
   A. Spinning the cylinder after loading the first bullet, and spinning again after the first shot.
   B. Spinning the cylinder after loading the first bullet only.
   C. Spinning the cylinder after firing the first shot only.
   D. Not spinning the cylinder either after loading the first bullet or after the first shot.
   E. The probability is the same for all cases.


Task
  1. Run a repeated simulation of each of the above scenario, calculating the percentage of suicide with a randomization of the four spinning, loading and firing order scenarios.
  2. Show the results as a percentage of deaths for each type of scenario.
  3. The hand calculated probabilities are 5/9, 7/12, 5/9, and 1/2. A correct program should produce results close enough to those to allow a correct response to the interview question.


Reference

Youtube video on the Russian 1895 Nagant revolver [[1]]

C

Translation of: Go

<lang c>#include <stdbool.h>

  1. include <stdio.h>
  2. include <stdlib.h>
  3. include <string.h>
  4. include <time.h>

static int nextInt(int size) { 

   return rand() % size;

}

static bool cylinder[6];

static void rshift() { 

   bool t = cylinder[5];
   int i;
   for (i = 4; i >= 0; i--) {
       cylinder[i + 1] = cylinder[i];
   }
   cylinder[0] = t;

}

static void unload() { 

   int i;
   for (i = 0; i < 6; i++) {
       cylinder[i] = false;
   }

}

static void load() { 

   while (cylinder[0]) {
       rshift();
   }
   cylinder[0] = true;
   rshift();

}

static void spin() { 

   int lim = nextInt(6) + 1;
   int i;
   for (i = 1; i < lim; i++) {
       rshift();
   }

}

static bool fire() { 

   bool shot = cylinder[0];
   rshift();
   return shot;

}

static int method(const char *s) { 

   unload();
   for (; *s != '\0'; s++) {
       switch (*s) {
       case 'L':
           load();
           break;
       case 'S':
           spin();
           break;
       case 'F':
           if (fire()) {
               return 1;
           }
           break;
       }
   }
   return 0;

}

static void append(char *out, const char *txt) { 

   if (*out != '\0') {
       strcat(out, ", ");
   }
   strcat(out, txt);

}

static void mstring(const char *s, char *out) { 

   for (; *s != '\0'; s++) {
       switch (*s) {
       case 'L':
           append(out, "load");
           break;
       case 'S':
           append(out, "spin");
           break;
       case 'F':
           append(out, "fire");
           break;
       }
   }

}

static void test(char *src) { 

   char buffer[41] = "";
   const int tests = 100000;
   int sum = 0;
   int t;
   double pc;

   for (t = 0; t < tests; t++) {
       sum += method(src);
   }

   mstring(src, buffer);
   pc = 100.0 * sum / tests;

   printf("%-40s produces %6.3f%% deaths.\n", buffer, pc);

}

int main() { 

   srand(time(0));

   test("LSLSFSF");
   test("LSLSFF");
   test("LLSFSF");
   test("LLSFF");

   return 0;

}</lang>

Output:
load, spin, load, spin, fire, spin, fire produces 55.456% deaths.
load, spin, load, spin, fire, fire       produces 58.301% deaths.
load, load, spin, fire, spin, fire       produces 55.487% deaths.
load, load, spin, fire, fire             produces 50.289% deaths.

Factor

Translation of: Julia
Translation of: Python

<lang factor>USING: accessors assocs circular formatting fry kernel literals math random sequences ; IN: rosetta-code.roulette

CONSTANT: cyl $[ { f f f f f f } <circular> ]

cylinder ( -- seq ) cyl [ drop f ] map! ;
load ( seq -- seq' )
   0 over nth [ dup rotate-circular ] when
   t 0 rot [ set-nth ] [ rotate-circular ] [ ] tri ;
spin ( seq -- seq' ) [ 6 random 1 + + ] change-start ;
fire ( seq -- ? seq' )
   [ 0 swap nth ] [ rotate-circular ] [ ] tri ;
LSLSFSF ( -- ? ) cylinder load spin load spin fire spin fire drop or ;
LSLSFF ( -- ? ) cylinder load spin load spin fire fire drop or ;
LLSFSF ( -- ? ) cylinder load load spin fire spin fire drop or ;
LLSFF ( -- ? ) cylinder load load spin fire fire drop or ;
percent ( ... n quot: ( ... -- ... ? ) -- ... x )
   0 -rot '[ _ call( -- ? ) 1 0 ? + ] [ times ] keepd /f 100 * ; inline
run-test ( description quot -- )
   100,000 swap percent
   "Method <%s> produces %.3f%% deaths.\n" printf ;
main ( -- )
   {
       { "load, spin, load, spin, fire, spin, fire" [ LSLSFSF ] }
       { "load, spin, load, spin, fire, fire" [ LSLSFF ] }
       { "load, load, spin, fire, spin, fire" [ LLSFSF ] }
       { "load, load, spin, fire, fire" [ LLSFF ] }
   } [ run-test ] assoc-each ;

MAIN: main</lang>

Output:
"rosetta-code.roulette" run
Method <load, spin, load, spin, fire, spin, fire> produces 55.598% deaths.
Method <load, spin, load, spin, fire, fire> produces 58.390% deaths.
Method <load, load, spin, fire, spin, fire> produces 55.500% deaths.
Method <load, load, spin, fire, fire> produces 49.841% deaths.

Go

Translation of: Wren

Though procedural rather than OO. <lang go>package main

import ( 

   "fmt"
   "math/rand"
   "strings"
   "time"

)

var cylinder = [6]bool{}

func rshift() { 

   t := cylinder[5]
   for i := 4; i >= 0; i-- {
       cylinder[i+1] = cylinder[i]
   }
   cylinder[0] = t

}

func unload() { 

   for i := 0; i < 6; i++ {
       cylinder[i] = false
   }

}

func load() { 

   for cylinder[0] {
       rshift()
   }
   cylinder[0] = true
   rshift()

}

func spin() { 

   var lim = 1 + rand.Intn(6)
   for i := 1; i < lim; i++ {
       rshift()
   }

}

func fire() bool { 

   shot := cylinder[0]
   rshift()
   return shot

}

func method(s string) int { 

   unload()
   for _, c := range s {
       switch c {
       case 'L':
           load()
       case 'S':
           spin()
       case 'F':
           if fire() {
               return 1
           }
       }
   }
   return 0

}

func mstring(s string) string { 

   var l []string
   for _, c := range s {
       switch c {
       case 'L':
           l = append(l, "load")
       case 'S':
           l = append(l, "spin")
       case 'F':
           l = append(l, "fire")
       }
   }
   return strings.Join(l, ", ")

}

func main() { 

   rand.Seed(time.Now().UnixNano())
   tests := 100000
   for _, m := range []string{"LSLSFSF", "LSLSFF", "LLSFSF", "LLSFF"} {
       sum := 0
       for t := 1; t <= tests; t++ {
           sum += method(m)
       }
       pc := float64(sum) * 100 / float64(tests)
       fmt.Printf("%-40s produces %6.3f%% deaths.\n", mstring(m), pc)
   }

}</lang>

Output:

Sample run: 

load, spin, load, spin, fire, spin, fire produces 55.267% deaths.
load, spin, load, spin, fire, fire       produces 58.110% deaths.
load, load, spin, fire, spin, fire       produces 55.405% deaths.
load, load, spin, fire, fire             produces 49.889% deaths.

Julia

Translation of: Python

<lang julia>const cyl = zeros(Bool, 6)

function load() 

   while cyl[1]
       cyl .= circshift(cyl, 1)
   end
   cyl[1] = true
   cyl .= circshift(cyl, 1)

end

spin() = (cyl .= circshift(cyl, rand(1:6)))

fire() = (shot = cyl[1]; cyl .= circshift(cyl, 1); shot)

function LSLSFSF() 

   cyl .= 0
   load(); spin(); load(); spin()
   fire() && return true
   spin(); return fire()

end

function LSLSFF() 

   cyl .= 0
   load(); spin(); load(); spin()
   fire() && return true
   return fire()

end

function LLSFSF() 

   cyl .= 0
   load(); load(); spin()
   fire() && return true
   spin(); return fire()

end

function LLSFF() 

   cyl .= 0
   load(); load(); spin()
   fire() && return true
   return fire()

end

function testmethods(N = 10000000) 

   for (name, method) in [("load, spin, load, spin, fire, spin, fire", LSLSFSF),
                          ("load, spin, load, spin, fire, fire", LSLSFF),
                          ("load, load, spin, fire, spin, fire", LLSFSF),
                          ("load, load, spin, fire, fire", LLSFF)]
       percentage = 100 * sum([method() for _ in 1:N]) / N
       println("Method $name produces $percentage per cent deaths.")
   end

end

testmethods()

</lang>

Output:
Method load, spin, load, spin, fire, spin, fire produces 55.54253 per cent deaths.
Method load, spin, load, spin, fire, fire produces 58.32598 per cent deaths.
Method load, load, spin, fire, spin, fire produces 55.54244 per cent deaths.
Method load, load, spin, fire, fire produces 50.02247 per cent deaths.

Kotlin

Translation of: C

<lang scala>import kotlin.random.Random

val cylinder = Array(6) { false }

fun rShift() { 

   val t = cylinder[cylinder.size - 1]
   for (i in (0 until cylinder.size - 1).reversed()) {
       cylinder[i + 1] = cylinder[i]
   }
   cylinder[0] = t

}

fun unload() { 

   for (i in cylinder.indices) {
       cylinder[i] = false
   }

}

fun load() { 

   while (cylinder[0]) {
       rShift()
   }
   cylinder[0] = true
   rShift()

}

fun spin() { 

   val lim = Random.nextInt(0, 6) + 1
   for (i in 1..lim) {
       rShift()
   }

}

fun fire(): Boolean { 

   val shot = cylinder[0]
   rShift()
   return shot

}

fun method(s: String): Int { 

   unload()
   for (c in s) {
       when (c) {
           'L' -> {
               load()
           }
           'S' -> {
               spin()
           }
           'F' -> {
               if (fire()) {
                   return 1
               }
           }
       }
   }
   return 0

}

fun mString(s: String): String { 

   val buf = StringBuilder()
   fun append(txt: String) {
       if (buf.isNotEmpty()) {
           buf.append(", ")
       }
       buf.append(txt)
   }
   for (c in s) {
       when (c) {
           'L' -> {
               append("load")
           }
           'S' -> {
               append("spin")
           }
           'F' -> {
               append("fire")
           }
       }
   }
   return buf.toString()

}

fun test(src: String) { 

   val tests = 100000
   var sum = 0

   for (t in 0..tests) {
       sum += method(src)
   }

   val str = mString(src)
   val pc = 100.0 * sum / tests
   println("%-40s produces %6.3f%% deaths.".format(str, pc))

}

fun main() { 

   test("LSLSFSF");
   test("LSLSFF");
   test("LLSFSF");
   test("LLSFF");

}</lang>

Output:
load, spin, load, spin, fire, spin, fire produces 55.638% deaths.
load, spin, load, spin, fire, fire       produces 58.140% deaths.
load, load, spin, fire, spin, fire       produces 55.725% deaths.
load, load, spin, fire, fire             produces 49.875% deaths.

Perl

Translation of: Raku

<lang perl>use strict; use warnings; use feature 'say';

my @cyl; my $shots = 6;

sub load { 

   push @cyl, shift @cyl while $cyl[1];
   $cyl[1] = 1;
   push @cyl, shift @cyl

}

sub spin { push @cyl, shift @cyl for 0 .. int rand @cyl } sub fire { push @cyl, shift @cyl; $cyl[0] }

sub LSLSFSF { 

   @cyl = (0) x $shots;
   load, spin, load, spin;
   return 1 if fire;
   spin;
   fire

}

sub LSLSFF { 

   @cyl = (0) x $shots;
   load, spin, load, spin;
   fire or fire

}

sub LLSFSF { 

   @cyl = (0) x $shots;
   load, load, spin;
   return 1 if fire;
   spin;
   fire

}

sub LLSFF { 

   @cyl = (0) x $shots;
   load, load, spin;
   fire or fire

}

my $trials = 10000;

for my $ref (<LSLSFSF LSLSFF LLSFSF LLSFF>) { 

   no strict 'refs';
   my $total = 0;
   $total += &$ref for 1..$trials;
   printf "%7s %.2f%%\n", $ref, $total / $trials * 100;

}</lang>

Output:
LSLSFSF 55.04%
 LSLSFF 58.77%
 LLSFSF 55.09%
  LLSFF 50.13%

Phix

<lang Phix>function spin(sequence revolver, integer count) 

   while count do
       revolver = revolver[$]&revolver[1..$-1]
       count -= 1
   end while
   return revolver

end function

function load(sequence revolver) 

   while revolver[1] do
       revolver = spin(revolver,1) 
   end while
   revolver[1] = true
   revolver = spin(revolver,1) 
   return revolver

end function

bool dead = false function fire(sequence revolver) 

   if revolver[1] then dead = true end if
   revolver = spin(revolver,1) 
   return revolver

end function

procedure test(string method) 

   integer deaths = 0,
           limit = 100000
   for n=1 to limit do
       sequence revolver = repeat(false,6)
       dead = false
       for i=1 to length(method) do
           integer ch = method[i]
           switch ch
             case 'L': revolver = load(revolver)
             case 'S': revolver = spin(revolver,rand(6))
             case 'F': revolver = fire(revolver)
           end switch 
       end for
       deaths += dead
   end for
   printf(1,"%s: %5.2f\n",{method,100*deaths/limit})

end procedure

printf(1,"Load/Spin/Fire method percentage fatalities:\n") papply({"LSLSFSF","LSLSFF","LLSFSF","LLSFF"},test)</lang>

Output:
Load/Spin/Fire method percentage fatalities:
LSLSFSF: 55.66
LSLSFF: 58.55
LLSFSF: 55.76
LLSFF: 49.97

Python

<lang python>""" Russian roulette problem """ import numpy as np

class Revolver: 

   """ simulates 6-shot revolving cylinger pistol """

   def __init__(self):
       """ start unloaded """
       self.cylinder = np.array([False] * 6)

   def unload(self):
       """ empty all chambers of cylinder """
       self.cylinder[:] = False

   def load(self):
       """ load a chamber (advance til empty if full already), then advance once """
       while self.cylinder[1]:
           self.cylinder[:] = np.roll(self.cylinder, 1)
       self.cylinder[1] = True

   def spin(self):
       """ spin cylinder, randomizing position of chamber to be fired """
       self.cylinder[:] = np.roll(self.cylinder, np.random.randint(1, high=7))

   def fire(self):
       """ pull trigger of revolver, return True if fired, False if did not fire """
       shot = self.cylinder[0]
       self.cylinder[:] = np.roll(self.cylinder, 1)
       return shot

   def LSLSFSF(self):
       """ load, spin, load, spin, fire, spin, fire """
       self.unload()
       self.load()
       self.spin()
       self.load()
       self.spin()
       if self.fire():
           return True
       self.spin()
       if self.fire():
           return True
       return False

   def LSLSFF(self):
       """ load, spin, load, spin, fire, fire """
       self.unload()
       self.load()
       self.spin()
       self.load()
       self.spin()
       if self.fire():
           return True
       if self.fire():
           return True
       return False

   def LLSFSF(self):
       """ load, load, spin, fire, spin, fire """
       self.unload()
       self.load()
       self.load()
       self.spin()
       if self.fire():
           return True
       self.spin()
       if self.fire():
           return True
       return False

   def LLSFF(self):
       """ load, load, spin, fire, fire """
       self.unload()
       self.load()
       self.load()
       self.spin()
       if self.fire():
           return True
       if self.fire():
           return True
       return False


if __name__ == '__main__': 

   REV = Revolver()
   TESTCOUNT = 100000
   for (name, method) in [['load, spin, load, spin, fire, spin, fire', REV.LSLSFSF],
                          ['load, spin, load, spin, fire, fire', REV.LSLSFF],
                          ['load, load, spin, fire, spin, fire', REV.LLSFSF],
                          ['load, load, spin, fire, fire', REV.LLSFF]]:

       percentage = 100 * sum([method() for _ in range(TESTCOUNT)]) / TESTCOUNT
       print("Method", name, "produces", percentage, "per cent deaths.")

</lang>

Output:
Method load, spin, load, spin, fire, spin, fire produces 55.652 per cent deaths.
Method load, spin, load, spin, fire, fire produces 58.239 per cent deaths.
Method load, load, spin, fire, spin, fire produces 55.774 per cent deaths.
Method load, load, spin, fire, fire produces 50.071 per cent deaths.

Raku

<lang perl6>unit sub MAIN ($shots = 6);

my @cyl;

sub load () { 

   @cyl.=rotate(-1) while @cyl[1];
   @cyl[1] = 1;
   @cyl.=rotate(-1);

}

sub spin () { @cyl.=rotate: (^@cyl).pick }

sub fire () { @cyl.=rotate; @cyl[0] }

sub LSLSFSF { 

   @cyl = 0 xx $shots;
   load, spin, load, spin;
   return 1 if fire;
   spin;
   fire

}

sub LSLSFF { 

   @cyl = 0 xx $shots;
   load, spin, load, spin;
   fire() || fire

}

sub LLSFSF { 

   @cyl = 0 xx $shots;
   load, load, spin;
   return 1 if fire;
   spin;
   fire

}

sub LLSFF { 

   @cyl = 0 xx $shots;
   load, load, spin;
   fire() || fire

}

my %revolver; my $trials = 100000;

for ^$trials { 

   %revolver<LSLSFSF> += LSLSFSF;
   %revolver<LSLSFF>  += LSLSFF;
   %revolver<LLSFSF>  += LLSFSF;
   %revolver<LLSFF>   += LLSFF;

}

say "{.fmt('%7s')}: %{(%revolver{$_} / $trials × 100).fmt('%.2f')}" 

 for <LSLSFSF LSLSFF LLSFSF LLSFF></lang>
Sample output (default; 6 shooter):
LSLSFSF: %55.37
 LSLSFF: %58.30
 LLSFSF: %55.42
  LLSFF: %50.29

Though if you go and look at the Wikipedia article for the 1895 Nagant revolver mentioned in the task reference section, you'll see it is actually a 7 shot revolver... so, run again with 7 chambers:

raku roulette.raku 7

Sample output (7 shooter):
LSLSFSF: %49.29
 LSLSFF: %51.14
 LLSFSF: %48.74
  LLSFF: %43.08

Or, how about a Ruger GP100 10 round revolver?

raku roulette.raku 10

Sample output (10 shooter):
LSLSFSF: %36.00
 LSLSFF: %37.00
 LLSFSF: %36.13
  LLSFF: %29.77

Doesn't change the answers, B (LSLSFF) is definitely the worst most likely choice in all cases.

REXX

Translation of: GO


This REXX version eliminates the spinning of the bullet chamber if the random number for a spin is   6   (which would
normally just spin the bullet chamber around to its initial position,   thereby saving some busywork by the program).

Changing the cartridge chamber from an index array to a simple string made the program around   200%   faster. <lang rexx>/*REXX pgm simulates scenarios for a two─bullet Russian roulette game with a 6 cyl. gun.*/ parse arg cyls tests seed . /*obtain optional arguments from the CL*/ if cyls== | cyls=="," then cyls= 6 /*Not specified? Then use the default.*/ if tests== | tests=="," then tests= 100000 /* " " " " " " */ if datatype(seed, 'W') then call random ,,seed /* " " " " " " */ cyls_ = cyls - 1 /*shortcut placeholder for cylinders-1 */ scenarios= 'LsLsFsF LsLsFF LLsFsF LLsFF' /*the list of scenarios to be tested. */

  1. = words(scenarios) /*the number of actions in a scenario. */
      do m=1  for #;   q= word(scenarios, m)    /*test each of the scenarios specified.*/
      sum = 0
                  do t=1  for tests;   sum= sum + method(q)
                  end   /*t*/

      say action(q)      '  produces  '      left( (sum*100/tests)"%", 7)      ' deaths.'
      end   /*m*/

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fire:  != left(@, 1); call next; return ! load: if left(@, 1) then call next; @= 1 || right(@, cyls_); return next: @= right(@, cyls_)left(@, 1); return spin:  ?= random(1, cyls); if ?\==6 then do ?; call next; end; return /*──────────────────────────────────────────────────────────────────────────────────────*/ method: arg scenario; @= copies(0, cyls) /*start with an empty cartridge chamber*/ 

                              do a=1  for length(scenario);   act= substr(scenario, a, 1)
                              if act=='L'  then call load
                              if act=='S'  then call spin
                              if act=='F'  then if fire()  then return 1
                              end   /*a*/;                                       return 0

/*──────────────────────────────────────────────────────────────────────────────────────*/ action: arg scenario,$; do a=1 for length(scenario); act= substr(scenario, a, 1) 

                              if act=='L'  then $= $", load"
                              if act=='S'  then $= $", spin"
                              if act=='F'  then $= $", fire"
                              end   /*j*/;    return right( strip( strip($, , ",") ), 50)</lang>
output   when using the default inputs:
          load, spin, load, spin, fire, spin, fire   produces   55.44%   deaths.
                load, spin, load, spin, fire, fire   produces   58.487%  deaths.
                load, load, spin, fire, spin, fire   produces   55.82%   deaths.
                      load, load, spin, fire, fire   produces   50.021%  deaths.

Wren

Library: Wren-fmt

<lang ecmascript>import "random" for Random import "/fmt" for Fmt

var Rand = Random.new()

class Revolver { 

   construct new() { 
       _cylinder = List.filled(6, false)
   }

   rshift() {
       var t = _cylinder[-1]
       for (i in 4..0) _cylinder[i+1] = _cylinder[i]
       _cylinder[0] = t
   }

   unload() {
       for (i in 0..5) _cylinder[i] = false
   }

   load() {
       while (_cylinder[0]) rshift()
       _cylinder[0] = true
       rshift()
   }

   spin() {
       for (i in 1..Rand.int(1, 7)) rshift()
   }

   fire() {
       var shot = _cylinder[0]
       rshift()
       return shot
   }

   method(s) {
       unload()
       for (c in s) {
           if (c == "L") {
               load()
           } else if (c == "S") {
               spin()
           } else if (c == "F") {
               if (fire()) return 1
           }
       }
       return 0
   }

   static mstring(s) {
       var l = []
       for (c in s) {
           if (c == "L") {
               l.add("load")
           } else if (c == "S") {
               l.add("spin")
           } else if (c == "F") {
               l.add("fire")
           }
       }
       return l.join(", ")
   }

}

var rev = Revolver.new() var tests = 100000 for (m in ["LSLSFSF", "LSLSFF", "LLSFSF", "LLSFF"]) { 

   var sum = 0
   for (t in 1..tests) sum = sum + rev.method(m)
   Fmt.print("$-40s produces $6.3f\% deaths.", Revolver.mstring(m), sum * 100 / tests)

}</lang>

Output:

Sample run: 

load, spin, load, spin, fire, spin, fire produces 55.500% deaths.
load, spin, load, spin, fire, fire       produces 58.162% deaths.
load, load, spin, fire, spin, fire       produces 55.512% deaths.
load, load, spin, fire, fire             produces 50.013% deaths.
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