Card shuffles: Difference between revisions

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shuffle: (J♣ 2♠ 4♦ A♦ K♥ 6♦ 5♦ 8♣ 2♦ T♥ 4♠ 3♣ 7♦ 9♠ T♦ J...
shuffle: (J♣ 2♠ 4♦ A♦ K♥ 6♦ 5♦ 8♣ 2♦ T♥ 4♠ 3♣ 7♦ 9♠ T♦ J...
</pre>
</pre>


=={{header|Ruby}}==

Two methods to solve the requirements, and a third one as bonus.

<lang Ruby>
def riffle deck
left, right = deck.partition{rand(10).odd?}
new_deck = []

# the condition below is true when both left and right stacks are empty
until ((left_card=left.pop).to_i + (right_card=right.shift).to_i).zero? do
new_deck << left_card if left_card
new_deck << right_card if right_card
end

new_deck
end

def overhand deck
new_deck = []

until deck.empty? do
stack = deck[-rand(deck.size * 0.2), deck.size]
new_deck += stack
deck -= stack
end

new_deck
end

def bonus deck
deck.sort { |a, b| Time.now.to_i % a <=> Time.now.to_i % b }
end

deck = [*1..20]

puts riffle(deck).inspect
puts overhand(deck).inspect
puts bonus(deck).inspect
</lang>



=={{header|Tcl}}==
=={{header|Tcl}}==

Revision as of 18:39, 2 July 2017

Card shuffles 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.

There are many techniques that people use to shuffle cards for card games. Some are more effective than others.

The task here is to implement the (seemingly) more common techniques of the riffle shuffle and overhand shuffle for n iterations. Implementing playing cards is not necessary if it would be easier to implement these shuffling methods for generic collections. Where possible, compare this to a standard/built-in shuffling procedure.

One iteration of the riffle shuffle is defined as:

  1. Split the deck into two piles
  2. Merge the two piles by alternating taking one card from the top or bottom (the same throughout the whole merge) of each pile
  3. The merged deck is now the new "shuffled" deck

One iteration of the overhand shuffle is defined as:

  1. Take a group of consecutive cards from the top of the deck. For our purposes up to 20% of the deck seems like a good amount.
  2. Place that group on top of a second pile
  3. Repeat these steps until there are no cards remaining in the original deck
  4. The second pile is now the new "shuffled" deck

Bonus: Implement other methods described here. Allow for "human errors" of imperfect cutting and interleaving.

C++

<lang cpp>

  1. include <time.h>
  2. include <algorithm>
  3. include <iostream>
  4. include <string>
  5. include <deque>


class riffle { public: 

   void shuffle( std::deque<int>* v, int tm )
   {
       std::deque<int> tmp;

bool fl; size_t len; std::deque<int>::iterator it;

copyTo( v, &tmp );

for( int t = 0; t < tm; t++ ) { std::deque<int> lHand( rand() % ( tmp.size() / 3 ) + ( tmp.size() >> 1 ) ), rHand( tmp.size() - lHand.size() );

std::copy( tmp.begin(), tmp.begin() + lHand.size(), lHand.begin() ); std::copy( tmp.begin() + lHand.size(), tmp.end(), rHand.begin() ); tmp.clear();

while( lHand.size() && rHand.size() ) { fl = rand() % 10 < 5; if( fl ) 

   		    len = 1 + lHand.size() > 3 ? rand() % 3 + 1 : rand() % ( lHand.size() ) + 1;

else len = 1 + rHand.size() > 3 ? rand() % 3 + 1 : rand() % ( rHand.size() ) + 1;

while( len ) { if( fl ) { tmp.push_front( *lHand.begin() ); lHand.erase( lHand.begin() ); } else { tmp.push_front( *rHand.begin() ); rHand.erase( rHand.begin() ); } len--; } }

if( lHand.size() < 1 ) { for( std::deque<int>::iterator x = rHand.begin(); x != rHand.end(); x++ ) tmp.push_front( *x ); } if( rHand.size() < 1 ) { for( std::deque<int>::iterator x = lHand.begin(); x != lHand.end(); x++ ) tmp.push_front( *x ); } } copyTo( &tmp, v ); 

   }

private: 

   void copyTo( std::deque<int>* a, std::deque<int>* b )
   {

for( std::deque<int>::iterator x = a->begin(); x != a->end(); x++ ) b->push_back( *x ); a->clear(); 

   }

};

class overhand { public: 

   void shuffle( std::deque<int>* v, int tm )
   {

std::deque<int> tmp; bool top; for( int t = 0; t < tm; t++ ) { while( v->size() ) { size_t len = rand() % ( v->size() ) + 1; top = rand() % 10 < 5; while( len ) { if( top ) tmp.push_back( *v->begin() ); else tmp.push_front( *v->begin() ); v->erase( v->begin() ); len--; } } for( std::deque<int>::iterator x = tmp.begin(); x != tmp.end(); x++ ) v->push_back( *x );

tmp.clear(); } 

   }

};

// global - just to make things simpler --------------------------------------------------- std::deque<int> cards;

void fill() { 

   cards.clear();
   for( int x = 0; x < 20; x++ )

cards.push_back( x + 1 ); }

void display( std::string t ) { 

   std::cout << t << "\n";
   for( std::deque<int>::iterator x = cards.begin(); x != cards.end(); x++ )

std::cout << *x << " "; 

   std::cout << "\n\n";

}

int main( int argc, char* argv[] ) { 

   srand( static_cast<unsigned>( time( NULL ) ) );
   riffle r; overhand o;	

   fill(); r.shuffle( &cards, 10 ); display( "RIFFLE" );
   fill(); o.shuffle( &cards, 10 ); display( "OVERHAND" );
   fill(); std::random_shuffle( cards.begin(), cards.end() ); display( "STD SHUFFLE" );

   return 0;

} </lang>

Output:
RIFFLE
18 9 17 20 3 4 16 8 7 10 5 14 12 1 13 19 2 11 15 6

OVERHAND
2 13 12 11 10 9 18 17 6 5 4 3 7 20 19 15 8 14 16 1

STD SHUFFLE
14 4 17 3 12 5 19 6 20 2 16 11 8 15 7 13 10 18 9 1

J

Generally, this task should be accomplished in J using ({~ ?~@#). Here we take an approach that's more comparable with the other examples on this page.

<lang J>NB. overhand cut overhand=: (\: [: +/\ %@%:@# > # ?@# 0:)@]^:[

NB. Gilbert–Shannon–Reeds model riffle=: (({.~+/)`(I.@])`(-.@]#inv (}.~+/))} ?@(#&2)@#)@]^:[</lang>

The probability of a cut occurring between each pair of cards in this overhand shuffle is proportional to the reciprocal of the square root of the number of cards in the deck.

In other words, overhand cut breaks the deck into some number of pieces and reverses the order of those pieces.

Here are some examples of the underlying selection mechanism in action for a deck of 10 cards:

<lang J> ([: +/\ %@%:@# > # ?@# 0:) i.10 0 0 0 0 0 0 0 0 1 1 

  ([: +/\ %@%:@# > # ?@# 0:) i.10

1 1 2 2 2 3 3 3 3 3 

  ([: +/\ %@%:@# > # ?@# 0:) i.10

0 1 1 2 3 3 3 3 4 5 

  ([: +/\ %@%:@# > # ?@# 0:) i.10

0 1 1 1 1 2 2 3 3 3</lang>

The final step of a cut is to sort the deck in descending order based on the numbers we compute this way.

The left argument says how many of these cuts to perform.

Task examples:

<lang J> 1 riffle i.20 0 1 2 3 4 5 6 7 8 13 14 9 15 16 17 10 18 11 12 19 

  10 riffle i.20

6 10 13 8 2 14 15 9 19 3 18 16 11 1 12 17 5 4 0 7 

  1 overhand i.20

17 18 19 13 14 15 16 4 5 6 7 8 9 10 11 12 0 1 2 3 

  10 overhand i.20

15 11 2 4 5 12 16 10 17 19 9 8 6 13 3 18 7 1 0 14</lang>

Java

Works with: Java version 1.5+

<lang java5>import java.util.Arrays; import java.util.Collections; import java.util.LinkedList; import java.util.List; import java.util.Random;

public class CardShuffles{

private static final Random rand = new Random();

public static <T> LinkedList<T> riffleShuffle(List<T> list, int flips){ LinkedList<T> newList = new LinkedList<T>();

newList.addAll(list);

for(int n = 0; n < flips; n++){ //cut the deck at the middle +/- 10%, remove the second line of the formula for perfect cutting int cutPoint = newList.size() / 2 + (rand.nextBoolean() ? -1 : 1 ) * rand.nextInt((int)(newList.size() * 0.1));

//split the deck List<T> left = new LinkedList<T>(); left.addAll(newList.subList(0, cutPoint)); List<T> right = new LinkedList<T>(); right.addAll(newList.subList(cutPoint, newList.size()));

newList.clear();

while(left.size() > 0 && right.size() > 0){ //allow for imperfect riffling so that more than one card can come form the same side in a row //biased towards the side with more cards //remove the if and else and brackets for perfect riffling if(rand.nextDouble() >= ((double)left.size() / right.size()) / 2){ newList.add(right.remove(0)); }else{ newList.add(left.remove(0)); } }

//if either hand is out of cards then flip all of the other hand to the shuffled deck if(left.size() > 0) newList.addAll(left); if(right.size() > 0) newList.addAll(right); } return newList; }

public static <T> LinkedList<T> overhandShuffle(List<T> list, int passes){ LinkedList<T> mainHand = new LinkedList<T>();

mainHand.addAll(list); for(int n = 0; n < passes; n++){ LinkedList<T> otherHand = new LinkedList<T>();

while(mainHand.size() > 0){ //cut at up to 20% of the way through the deck int cutSize = rand.nextInt((int)(list.size() * 0.2)) + 1;

LinkedList<T> temp = new LinkedList<T>();

//grab the next cut up to the end of the cards left in the main hand for(int i = 0; i < cutSize && mainHand.size() > 0; i++){ temp.add(mainHand.remove()); }

//add them to the cards in the other hand, sometimes to the front sometimes to the back if(rand.nextDouble() >= 0.1){ //front most of the time otherHand.addAll(0, temp); }else{ //end sometimes otherHand.addAll(temp); } }

//move the cards back to the main hand mainHand = otherHand; } return mainHand; }

public static void main(String[] args){ List<Integer> list = Arrays.asList(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20); System.out.println(list); list = riffleShuffle(list, 10); System.out.println(list + "\n"); 

               list = Arrays.asList(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20);

System.out.println(list); list = riffleShuffle(list, 1); System.out.println(list + "\n");

list = Arrays.asList(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20); System.out.println(list); list = overhandShuffle(list, 10); System.out.println(list + "\n"); 

               list = Arrays.asList(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20);

System.out.println(list); list = overhandShuffle(list, 1); System.out.println(list + "\n");

list = Arrays.asList(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20); System.out.println(list); Collections.shuffle(list); System.out.println(list + "\n"); } }</lang>

Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[20, 11, 1, 9, 15, 4, 19, 16, 8, 13, 7, 2, 14, 12, 10, 3, 17, 18, 6, 5]

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[1, 12, 2, 3, 4, 5, 13, 14, 15, 6, 16, 7, 8, 9, 17, 18, 10, 19, 20, 11]

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[20, 3, 10, 4, 2, 8, 1, 18, 13, 19, 14, 6, 9, 12, 16, 15, 5, 7, 11, 17]

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[18, 19, 20, 17, 13, 14, 15, 16, 9, 10, 11, 12, 8, 6, 7, 3, 4, 5, 1, 2]

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[18, 12, 13, 14, 2, 3, 15, 5, 9, 19, 7, 11, 1, 6, 4, 20, 16, 17, 10, 8]

Lua

<lang lua>-- Return a table respresenting a standard deck of cards in order function newDeck () 

   local cards, suits = {}, {"C", "D", "H", "S"}
   for _, suit in pairs(suits) do
       for value = 2, 14 do
           if value == 10 then value = "T" end
           if value == 11 then value = "J" end
           if value == 12 then value = "Q" end
           if value == 13 then value = "K" end
           if value == 14 then value = "A" end
           table.insert(cards, value .. suit)
       end
   end
   return cards

end

-- Display all cards (strings) in a given deck (table) function show (deck) 

   for _, card in pairs(deck) do io.write(card .. " ") end
   print("\n")

end

-- Perform a riffle shuffle on deck and return it as a new table function riffle (deck) 

   local pile1, pile2, pos = {}, {}, 1
   for i, card in ipairs(deck) do
       if i < math.ceil(#deck / 2) + 1 then
           table.insert(pile1, card)
       else
           table.insert(pile2, card)
       end
   end
   deck = {}
   while pile2[pos] do
       table.insert(deck, pile1[pos])
       table.insert(deck, pile2[pos])
       pos = pos + 1
   end
   return deck

end

-- Perform an overhand shuffle on a deck and return it as a new table function overhand (deck) 

   local newDeck, twentyPercent, groupSize, pos = {}, math.floor(#deck / 5)
   repeat
       repeat
           groupSize = math.random(twentyPercent)
       until groupSize <= #deck
       for pos = #deck - groupSize, #deck do
           table.insert(newDeck, deck[pos])
           deck[pos] = nil
       end
   until #deck == 0
   return newDeck

end

-- Main procedure math.randomseed(os.time()) local deck1, deck2 = newDeck(), newDeck() deck1 = riffle(deck1) print("Sorted deck after one riffle shuffle:") show(deck1) deck2 = overhand(deck2) print("Sorted deck after one overhand shuffle:") show(deck2)</lang>

Output:
Sorted deck after one riffle shuffle:
2C 2H 3C 3H 4C 4H 5C 5H 6C 6H 7C 7H 8C 8H 9C 9H TC TH JC JH QC QH KC KH AC AH 2D
 2S 3D 3S 4D 4S 5D 5S 6D 6S 7D 7S 8D 8S 9D 9S TD TS JD JS QD QS KD KS AD AS

Sorted deck after one overhand shuffle:
QS KS AS 3S 4S 5S 6S 7S 8S 9S TS JS JH QH KH AH 2S 4H 5H 6H 7H 8H 9H TH 2H 3H 4D
 5D 6D 7D 8D 9D TD JD QD KD AD QC KC AC 2D 3D 4C 5C 6C 7C 8C 9C TC JC 2C 3C

PARI/GP

Riffle shuffle: <lang parigp>riffle(v)= { 

 my(n=#v,k,t,deck=vector(n),left,right);
 t=random(2^n);
 for(i=0,n,
   t -= binomial(n,i);
   if(t<0, k=i; break)
 );
 if(k==0||k==n, return(v));
 left=k;
 right=n-k;
 deck=vector(n,i,
   t=random(n+1-i);
   v[if(t<left, k-left--, n-right--)]
 );
 vecextract(v, deck);

} addhelp(riffle, "riffle(v): Riffle shuffles the vector v, following the Gilbert-Shannon-Reeds model.");</lang>

Overhand shuffle: <lang parigp>overhand(v)= { 

 my(u=[],t,n=2*#v\5);
 while(#v,
   t=min(random(n)+1,#v);
   u=concat(v[1..t],u);
   v=if(t<#v,v[t+1..#v],[]);
 );
 u;

} addhelp(overhand, "overhand(v): Overhand shuffles the vector v.");</lang>

Usage: <lang parigp>riffle([1..52]) overhand([1..52])</lang>

Output:
%1 = [1, 2, 3, 21, 4, 22, 23, 5, 24, 25, 26, 6, 27, 28, 29, 30, 7, 31, 32, 33, 34, 35, 36, 8, 37, 38, 39, 40, 9, 10, 11, 12, 41, 42, 43, 13, 44, 45, 14, 46, 47, 48, 15, 16, 17, 49, 50, 18, 51, 19, 20, 52]
%2 = [44, 45, 46, 47, 48, 49, 50, 51, 52, 43, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 23, 24, 25, 26, 27, 28, 29, 30, 31, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1, 2, 3, 4]

Perl 6

<lang perl6>use v6;

sub overhand ( @cards ) { 

   my @splits = roll 10, ^( @cards.elems div 5 )+1;
   @cards.rotor( @splits  ,:partial ).reverse.flat

}

sub riffle ( @pile is copy ) { 

   my @pile2 = @pile.splice: @pile.elems div 2 ;

   roundrobin(
       @pile.rotor(  (1 .. 3).roll(7), :partial ),
       @pile2.rotor( (1 .. 3).roll(9), :partial ),
   ).flat

}

my @cards = ^20; @cards.=&overhand for ^10; say @cards;

my @cards2 = ^20; @cards2.=&riffle for ^10; say @cards2;

say (^20).pick(*); </lang>

Phix

<lang Phix>function riffle(sequence s) sequence res = {} integer l = length(s) integer r = rand(l) 

   for i=1 to l do
       if r+i<=l then
           res &= s[r+i]
       end if
       if i<=r then
           res &= s[i]
       end if
   end for
   return res

end function

function overhand(sequence s) sequence res = {} integer l = length(s) 

   while length(s) do
       integer r = rand(l*0.2)
       if r>length(s) then
           r = length(s)
       end if
       res = s[1..r]&res
       s = s[r+1..$]
   end while
   return res

end function

-- to shorten the output, all 2..7 have been removed from the deck constant DECKSIZE=52-24

procedure show_deck(sequence s) 

   for i=1 to DECKSIZE do
       integer c = s[i]-1

-- puts(1,"23456789TJQKA"[remainder(c,13)+1]&"HCDS"[floor(c/13)+1]&" ") 

       puts(1,"89TJQKA"[remainder(c,7)+1]&"HCDS"[floor(c/7)+1]&" ")
   end for
   puts(1,"\n")

end procedure

show_deck(riffle(tagset(DECKSIZE))) show_deck(overhand(tagset(DECKSIZE))) show_deck(shuffle(tagset(DECKSIZE)))</lang>

Output:
TC 8H JC 9H QC TH KC JH AC QH 8D KH 9D AH TD 8C JD 9C QD KD AD 8S 9S TS JS QS KS AS
KS AS JS QS TS AD 8S 9S 9D TD JD QD KD QC KC AC 8D AH 8C 9C TC JC JH QH KH TH 8H 9H
KH TH AH QH 8D JC QC 8C JH 8H 9D KS TD AS KD 8S TC AD TS AC 9C KC 9H QD JD JS 9S QS

Racket

These implementations are in typed/racket, which means that additional annotations are needed which looks like hard work.

On the bright side, if you want to add a new Cutter or Riffler, DrRacket will let you know immediately if you're consuming lists of lists of lists at the right depth and in the right quantities.

Racket has a built in shuffle function. Frankly, I'd go with that in your own code!

<lang racket>#lang typed/racket

---------------------------------------------------------------------------------------------------
Types and shuffle builder
A cutter separates the deck into more than one sub-decks -- the last one of these is "left in the
hand", as per the overhand shuffle (since it is the last strip to be stripped). The riffler
indicates this in its second (non-null) return value

(define-type (Cutter A) (-> (Listof A) (Pair (Listof A) (Listof (Listof A)))))

A riffler takes taking hand and the cut deck parts. returns a newly merged deck in the "taking"
hand and the deck left in the "giving" hand. The shuffler will keep taking,
until there is nothing to give

(define-type (Riffler A) ((Listof A) (Listof A) (Listof A) * -> (Values (Listof A) (Listof A))))

"The shuffler will keep taking until there is nothing to give"... and will do this
the number of times specified by its second argument

(define-type (Shuffler A) ((Listof A) Natural -> (Listof A)))

makes a shuffler from the cutter and the riffler

(: shuffler-composer (All (A) (Cutter A) (Riffler A) -> (Shuffler A))) (define ((shuffler-composer cut riffle) deck n) 

 (: one-shuffle : (Listof A) -> (Listof A))
 (define (one-shuffle g)
   (let: shuff ((t : (Listof A) null) (g : (Listof A) g))
     (let-values (((t+ g-) (apply riffle t (cut g))))
       (if (null? g-) t+ (shuff t+ g-)))))
 (for/fold : (Listof A) ((d deck)) ((i (in-range n)))
   (one-shuffle d)))
convenient wrapper around the above (otherwise we'd need the inst every time we
wanted to compose a cut and a riffle

(define-syntax-rule (define-composed-shuffler s (c r)) 

 (define: (A) (s [x : (Listof A)] [n : Natural]) : (Listof A)
   ((#{shuffler-composer @ A} c r) x n)))
---------------------------------------------------------------------------------------------------
Overhand (and, as far as I can tell, Indian)

(: overhand-cutter (All (A) (Cutter A))) (: overhand-riffler (All (A) (Riffler A)))

(define (overhand-cutter l) 

 (define spl (match (length l) [0 0] [1 1] [len (add1 (random (sub1 len)))]))
 (list (take l spl) (drop l spl)))

(define (overhand-riffler t p1 . rest) 

 (values (append p1 t) (append* rest)))

(define-composed-shuffler overhand-shuffle (overhand-cutter overhand-riffler))

---------------------------------------------------------------------------------------------------
Riffle (with optional "drop" where two cards are riffled

(: half-deck-cutter (All (A) (Cutter A))) (: mk-riffle-riffler (All (A) ((#:p-drop Nonnegative-Real) -> (Riffler A))))

(define (half-deck-cutter l) 

 (define spl (quotient (length l) 2))
 (list (take l spl) (drop l spl)))
All the "reverse"ing is to emulate a physical shuffle... it's not
necessary for the "randomising" effect (which there isn't really on
a pure riffle anyway)
Additional complexity added by ability to drop cards on both taking
and giving hand

(define ((mk-riffle-riffler #:p-drop (p-drop 0)) t p1 . rest) 

 (define g-/rev
   (let R : (Listof A)
     ((r1 : (Listof A) p1)
      (r2 : (Listof A) (append* rest))
      (rv : (Listof A) t)) ; although t should normaly be null
     (define drop-t? (< (random) p-drop))
     (define drop-g? (< (random) p-drop))
     (match* (r1 r2 drop-t? drop-g?)
       [((list) (app reverse 2r) _ _) (append 2r rv)]
       [((app reverse 1r) (list) _ _) (append 1r rv)]
       [((list a1.1 a1.2 d1 ...) (list a2.1 a2.2 d2 ...) #t #t)
        (R d1 d2 (list* a2.2 a2.1 a1.2 a1.1 rv))]
       [((list a1.1 a1.2 d1 ...) (list a2.1 d2 ...) #t _)
        (R d1 d2 (list* a2.1 a1.2 a1.1 rv))]
       [((list a1.1 d1 ...) (list a2.1 a2.2 d2 ...) _ #t)
        (R d1 d2 (list* a2.2 a2.1 a1.1 rv))]
       [((list a1.1 d1 ...) (list a2.1 d2 ...) _ _)
        (R d1 d2 (list* a2.1 a1.1 rv))])))
 (values (reverse g-/rev) null))

(define-composed-shuffler pure-riffle-shuffle (half-deck-cutter (mk-riffle-riffler))) (define-composed-shuffler klutz-riffle-shuffle (half-deck-cutter (mk-riffle-riffler #:p-drop 0.5)))

---------------------------------------------------------------------------------------------------
Pile Shuffle
Also Wash Shuffle, if pile-height=1 and random-gather=#t

(: mk-pile-cutter (All (A) (#:pile-height Positive-Integer -> (Cutter A)))) (: mk-pile-riffler (All (A) ((#:random-gather? Boolean) -> (Riffler A))))

(define ((mk-pile-cutter #:pile-height pile-height) l) 

 (define len-l (length l))
 (define n-piles (add1 (quotient (sub1 len-l) pile-height)))
 (: make-pile (Integer -> (Listof A)))
 (define (make-pile n)
   (for/list : (Listof A) ((i (in-range n len-l n-piles)))
     (list-ref l i)))
 (define pile-0 (make-pile 0))
 (define piles-ns (for/list : (Listof (Listof A)) ((n (in-range 1 n-piles))) (make-pile n)))
 (list* pile-0 piles-ns))

(define ((mk-pile-riffler #:random-gather? (random-gather? #f)) t p1 . rest) 

 (: piles (Listof (Listof A)))
 (define piles (cons p1 rest))
 (define gather (if random-gather? (shuffle piles) piles))
 (values (append* (cons t (if random-gather? (shuffle piles) piles))) null))

(define-composed-shuffler 4-high-pile-shuffle ((mk-pile-cutter #:pile-height 4) (mk-pile-riffler))) (define-composed-shuffler wash-pile-shuffle 

 ((mk-pile-cutter #:pile-height 1) (mk-pile-riffler #:random-gather? #t)))
---------------------------------------------------------------------------------------------------

(define unshuffled-pack 

 (for*/list : (Listof String)
   ((s '(♥ ♦ ♣ ♠))
    (f '(2 3 4 5 6 7 8 9 T J Q K A)))
   (format "~a~a" f s)))
---------------------------------------------------------------------------------------------------
TEST/OUTPUT

(module+ test 

 (require typed/rackunit)  
 (check-equal? (overhand-shuffle null 1) null)
 (check-equal? (overhand-shuffle '(a) 1) '(a))
 (check-equal? (overhand-shuffle '(a b) 1) '(b a))  
 (check-equal? (pure-riffle-shuffle '(1 2 3 4) 1) '(1 3 2 4))
 (error-print-width 80))

(module+ main 

 (printf "deck (original order):          ~.a~%" unshuffled-pack)
 (printf "overhand-shuffle (2 passes):    ~.a~%" (overhand-shuffle unshuffled-pack 2))
 (printf "overhand-shuffle (1300 passes): ~.a~%" (overhand-shuffle unshuffled-pack 1300))
 (printf "riffle: pure                    ~.a~%" (pure-riffle-shuffle unshuffled-pack 1))
 (printf "riffle: klutz                   ~.a~%" (klutz-riffle-shuffle unshuffled-pack 1))
 (printf "4-high piles:                   ~.a~%" (4-high-pile-shuffle unshuffled-pack 1))
 (printf "4-high piles (7 passes):        ~.a~%" (4-high-pile-shuffle unshuffled-pack 7))
 (printf "4-high piles (7 passes again):  ~.a~%" (4-high-pile-shuffle unshuffled-pack 7))
 (printf "wash piles:                     ~.a~%" (wash-pile-shuffle unshuffled-pack 1))
 ;; Or there is always the built-in shuffle:
 (printf "shuffle:                        ~.a~%" (shuffle unshuffled-pack)))</lang>
Output:

You see no output from the tests... that's a good thing, they're all passing.

Output is truncated by the ~.a format in printf. However, this should give you some idea of what's going on. 

deck (original order):          (2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ T♥ J♥ Q♥ K♥ A♥ 2♦ 3♦ 4...
overhand-shuffle (2 passes):    (2♥ 6♠ 5♠ J♦ Q♦ K♦ A♦ 2♣ 3♣ 4♣ 5♣ 6♣ 7♣ 8♣ 9♣ T...
overhand-shuffle (1300 passes): (J♦ J♥ J♠ A♥ K♦ 5♥ J♣ 8♣ 2♥ 4♠ 9♥ A♠ K♣ Q♥ 4♥ 7...
riffle: pure                    (2♥ 2♣ 3♥ 3♣ 4♥ 4♣ 5♥ 5♣ 6♥ 6♣ 7♥ 7♣ 8♥ 8♣ 9♥ 9...
riffle: klutz                   (2♥ 2♣ 3♥ 3♣ 4♥ 4♣ 5♣ 5♥ 6♥ 6♣ 7♥ 7♣ 8♥ 8♣ 9♥ 9...
4-high piles:                   (2♥ 2♦ 2♣ 2♠ 3♥ 3♦ 3♣ 3♠ 4♥ 4♦ 4♣ 4♠ 5♥ 5♦ 5♣ 5...
4-high piles (7 passes):        (2♥ 6♥ T♥ A♥ 5♦ 9♦ K♦ 4♣ 8♣ Q♣ 3♠ 7♠ J♠ 3♥ 7♥ J...
4-high piles (7 passes again):  (2♥ 6♥ T♥ A♥ 5♦ 9♦ K♦ 4♣ 8♣ Q♣ 3♠ 7♠ J♠ 3♥ 7♥ J...
wash piles:                     (4♣ K♠ 4♠ Q♥ J♣ A♣ 6♦ 6♥ 7♥ A♠ T♠ T♥ Q♣ 8♠ 3♣ J...
shuffle:                        (J♣ 2♠ 4♦ A♦ K♥ 6♦ 5♦ 8♣ 2♦ T♥ 4♠ 3♣ 7♦ 9♠ T♦ J...


Ruby

Two methods to solve the requirements, and a third one as bonus.

<lang Ruby> def riffle deck 

 left, right = deck.partition{rand(10).odd?}
 new_deck    = []

 # the condition below is true when both left and right stacks are empty
 until ((left_card=left.pop).to_i + (right_card=right.shift).to_i).zero? do
   new_deck << left_card  if left_card
   new_deck << right_card if right_card
 end

 new_deck

end

def overhand deck 

 new_deck = []

 until deck.empty? do
   stack = deck[-rand(deck.size * 0.2), deck.size]
   new_deck += stack
   deck     -= stack
 end

 new_deck

end

def bonus deck 

 deck.sort { |a, b| Time.now.to_i % a <=> Time.now.to_i % b }

end

deck = [*1..20]

puts riffle(deck).inspect puts overhand(deck).inspect puts bonus(deck).inspect </lang>


Tcl

<lang Tcl> proc riffle deck { set length [llength $deck] for {set i 0} {$i < $length/2} { incr i} { lappend temp [lindex $deck $i] [lindex $deck [expr {$length/2+$i}]]} set temp} proc overhand deck { set cut [expr {[llength $deck] /5}] for {set i $cut} {$i >-1} {incr i -1} { lappend temp [lrange $deck [expr {$i *$cut}] [expr {($i+1) *$cut -1}] ]} concat {*}$temp} puts [riffle [list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52]] puts [overhand [list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52]] </lang>

zkl

A much better shuffle is List's shuffle method. <lang zkl>fcn riffle(deck){ 

  len,N:=deck.len(),len/2;
  newDeck:=N.pump(List,'wrap(n){ return(Void.Write,deck[n],deck[N+n]) });
  if(len.isOdd) return(newDeck.append(deck[-1]));
  newDeck

} fcn overHand(deck){ 

  len,N,piles:=deck.len(),(0.2*len).toInt(),(len.toFloat()/N).ceil().toInt();
  piles.pump(List,'wrap(n){ deck[n*N,N] }).reverse().flatten()

}</lang> <lang zkl>riffle( [1..19].walk()).println(); overHand([1..19].walk()).println(); [1..19].walk().shuffle().println();</lang>

Output:
L(1,10,2,11,3,12,4,13,5,14,6,15,7,16,8,17,9,18,19)
L(19,16,17,18,13,14,15,10,11,12,7,8,9,4,5,6,1,2,3)
L(9,11,12,6,17,18,5,10,8,19,2,15,4,3,13,1,7,14,16)
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