Card shuffles
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.
- Task
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:
- Split the deck into two piles
- Merge the two piles by taking one card from the top of either pile in proportion to the number of cards remaining in the pile. To start with the probability for both piles will be 26/52 (50-50), then 25/51-26/51 etc etc as the riffle progresses.
- The merged deck is now the new "shuffled" deck
One iteration of the overhand shuffle is defined as:
- 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.
- Place that group on top of a second pile
- Repeat these steps until there are no cards remaining in the original deck
- The second pile is now the new "shuffled" deck
- Bonus
Implement other methods described in the Wikipedia article: card shuffling.
Allow for "human errors" of imperfect cutting and interleaving.
Related tasks:
APL
If we generate a deck by
deck ← ⊂[1](52⍴'A23456789TJQK'),[0.5](13⍴'S'),(13⍴'H'),(13⍴'D'),(13⍴'C')
Then a generated deck looks like
AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC
Sorting a deck merely requires generating 52 unique random nunmbers from 1 to 52.
deck[52?52]
JD 8C TH 8D KH QH 6S AH 4D JS 5S AD 6H 3H 3D 5C 9C 7C 7S 4C JC 3S KD 9H 3C 4H 2D TD KS TS 7D JH 9D 8H 6D 7H 2H 4S QC AC KC 9S AS QS TC 2C 8S 5D 2S 6C 5H QD
C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
void init() {
srand((unsigned int)time(NULL));
}
int random(int low, int high) {
int diff, val;
diff = high - low;
if (diff == 0) {
return low;
}
val = rand() % diff;
return val + low;
}
void initDeck(int *deck, const int size) {
int i;
for (i = 0; i < size; ++i) {
*deck++ = i + 1;
}
}
void writeDeck(const int *deck, const int size) {
int i;
printf("[");
if (size > 0) {
printf("%d", *deck++);
}
for (i = 1; i < size; ++i) {
printf(", %d", *deck++);
}
printf("]");
}
void riffleShuffle(int * const deck, const int size, int flips) {
int n, cutPoint, nlp, lp, rp, bound;
int *nl;
nl = (int *)malloc(size * sizeof(int));
for (n = 0; n < flips; ++n) {
cutPoint = size / 2;
if (random(0, 2) > 0) {
cutPoint = cutPoint + random(0, size / 10);
} else {
cutPoint = cutPoint - random(0, size / 10);
}
nlp = 0;
lp = 0;
rp = cutPoint;
while (lp < cutPoint && rp < size) {
/* Allow for an imperfect riffling so that more than one card
can come from the same side in a row biased towards the side
with more cards. Remove the IF statement for perfect riffling.
*/
bound = (cutPoint - lp) * 50 / (size - rp);
if (random(0, 50) >= bound) {
nl[nlp++] = deck[rp++];
} else {
nl[nlp++] = deck[lp++];
}
}
while (lp < cutPoint) {
nl[nlp++] = deck[lp++];
}
while (rp < size) {
nl[nlp++] = deck[rp++];
}
memcpy(deck, nl, size * sizeof(int));
}
free(nl);
}
void overhandShuffle(int * const mainHand, const int size, int passes) {
int n, cutSize, mp, op, tp, i;
int *otherHand, *temp;
otherHand = (int *)malloc(size * sizeof(int));
temp = (int *)malloc(size * sizeof(int));
for (n = 0; n < passes; ++n) {
mp = 0;
op = 0;
tp = 0;
while (mp < size) {
cutSize = random(0, size / 5) + 1;
/* grab the next cut up to the end of the cards left in the main hand */
for (i = 0; i < cutSize && mp < size; ++i) {
temp[tp++] = mainHand[mp++];
}
/* add them to the cards in the other hand,
sometimes to the front sometimes to the back */
if (random(0, 10) >= 1) {
/* front most of the time */
/* move the elements of other hand forward to make room for temp */
for (i = op - 1; i >= 0; --i) {
otherHand[i + tp] = otherHand[i];
}
/* copy temp to the front of other hand */
memcpy(otherHand, temp, tp * sizeof(int));
op += tp;
tp = 0;
} else {
/* end sometimes */
for (i = 0; i < tp; ++i, ++op) {
otherHand[op] = temp[i];
}
tp = 0;
}
}
/* move the cards back to the main hand */
memcpy(mainHand, otherHand, size * sizeof(int));
}
free(otherHand);
free(temp);
}
#define SIZE 20
int main() {
int deck[SIZE];
init();
printf("Riffle shuffle\n");
initDeck(deck, SIZE);
writeDeck(deck, SIZE);
printf("\n");
riffleShuffle(deck, SIZE, 10);
writeDeck(deck, SIZE);
printf("\n\n");
printf("Riffle shuffle\n");
initDeck(deck, SIZE);
writeDeck(deck, SIZE);
printf("\n");
riffleShuffle(deck, SIZE, 1);
writeDeck(deck, SIZE);
printf("\n\n");
printf("Overhand shuffle\n");
initDeck(deck, SIZE);
writeDeck(deck, SIZE);
printf("\n");
overhandShuffle(deck, SIZE, 10);
writeDeck(deck, SIZE);
printf("\n\n");
printf("Overhand shuffle\n");
initDeck(deck, SIZE);
writeDeck(deck, SIZE);
printf("\n");
overhandShuffle(deck, SIZE, 1);
writeDeck(deck, SIZE);
printf("\n\n");
return 0;
}
- Output:
Riffle shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [1, 15, 6, 2, 11, 18, 9, 5, 3, 4, 7, 16, 13, 8, 10, 14, 19, 12, 17, 20] Riffle shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [1, 2, 11, 3, 4, 5, 12, 13, 6, 7, 14, 8, 15, 16, 9, 17, 10, 18, 19, 20] Overhand shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [2, 19, 4, 10, 11, 8, 12, 7, 6, 3, 16, 14, 18, 1, 5, 13, 9, 15, 17, 20] Overhand shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [20, 17, 18, 19, 14, 15, 16, 10, 11, 12, 13, 9, 8, 7, 5, 6, 1, 2, 3, 4]
C#
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace CardShuffles {
public static class Helper {
public static string AsString<T>(this ICollection<T> c) {
StringBuilder sb = new StringBuilder("[");
sb.Append(string.Join(", ", c));
return sb.Append("]").ToString();
}
}
class Program {
private static Random rand = new Random();
public static List<T> riffleShuffle<T>(ICollection<T> list, int flips) {
List<T> newList = new List<T>(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.Count / 2
+ (rand.Next(0, 2) == 0 ? -1 : 1) * rand.Next((int)(newList.Count * 0.1));
//split the deck
List<T> left = new List<T>(newList.Take(cutPoint));
List<T> right = new List<T>(newList.Skip(cutPoint));
newList.Clear();
while (left.Count > 0 && right.Count > 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.Count / right.Count) / 2) {
newList.Add(right.First());
right.RemoveAt(0);
}
else {
newList.Add(left.First());
left.RemoveAt(0);
}
}
//if either hand is out of cards then flip all of the other hand to the shuffled deck
if (left.Count > 0) newList.AddRange(left);
if (right.Count > 0) newList.AddRange(right);
}
return newList;
}
public static List<T> overhandShuffle<T>(List<T> list, int passes) {
List<T> mainHand = new List<T>(list);
for (int n = 0; n < passes; n++) {
List<T> otherHand = new List<T>();
while (mainHand.Count>0) {
//cut at up to 20% of the way through the deck
int cutSize = rand.Next((int)(list.Count * 0.2)) + 1;
List<T> temp = new List<T>();
//grab the next cut up to the end of the cards left in the main hand
for (int i = 0; i < cutSize && mainHand.Count > 0; i++) {
temp.Add(mainHand.First());
mainHand.RemoveAt(0);
}
//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
temp.AddRange(otherHand);
otherHand = temp;
}
else {
//end sometimes
otherHand.AddRange(temp);
}
}
//move the cards back to the main hand
mainHand = otherHand;
}
return mainHand;
}
static void Main(string[] args) {
List<int> list = new List<int>() { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 };
Console.WriteLine(list.AsString());
list = riffleShuffle(list, 10);
Console.WriteLine(list.AsString());
Console.WriteLine();
list = new List<int>() { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 };
Console.WriteLine(list.AsString());
list = riffleShuffle(list, 1);
Console.WriteLine(list.AsString());
Console.WriteLine();
list = new List<int>() { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 };
Console.WriteLine(list.AsString());
list = overhandShuffle(list, 10);
Console.WriteLine(list.AsString());
Console.WriteLine();
list = new List<int>() { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 };
Console.WriteLine(list.AsString());
list = overhandShuffle(list, 1);
Console.WriteLine(list.AsString());
Console.WriteLine();
}
}
}
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [9, 2, 8, 3, 20, 15, 1, 13, 7, 18, 5, 16, 4, 19, 10, 6, 12, 14, 11, 17] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [12, 1, 2, 3, 4, 13, 14, 5, 15, 16, 6, 7, 17, 8, 18, 19, 9, 10, 20, 11] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [13, 18, 12, 17, 10, 9, 19, 11, 16, 15, 6, 8, 14, 1, 3, 2, 5, 4, 7, 20] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [20, 17, 18, 19, 15, 16, 11, 12, 13, 14, 10, 7, 8, 9, 5, 6, 2, 3, 4, 1]
C++
#include <time.h>
#include <algorithm>
#include <iostream>
#include <string>
#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;
}
- 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
D
import std.container.array;
import std.random;
import std.range;
import std.stdio;
auto riffleShuffle(T)(T[] list, int flips) {
auto newList = Array!T(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.length / 2
+ choice([-1, 1]) * uniform!"[]"(0, newList.length / 10);
//split the deck
auto left = newList[0..cutPoint];
auto right = newList[cutPoint..$];
newList.clear();
while (left.length > 0 && right.length > 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 (uniform01() >= (cast(real) left.length / right.length) / 2) {
newList.insertAfter(newList[], right.front);
right.popFront();
} else {
newList.insertAfter(newList[], left.front);
left.popFront();
}
}
//if either hand is out of cards then flip all of the other hand to the shuffled deck
if (!left.empty) newList ~= left;
if (!right.empty) newList ~= right;
}
return newList.array;
}
auto overhandShuffle(T)(T[] list, int passes) {
auto mainHand = Array!T(list);
for (int n=0; n<passes; n++) {
Array!T otherHand;
while (mainHand.length > 0) {
//cut at up to 20% of the way through the deck
int cutSize = uniform!"[]"(0, list.length / 5) + 1;
Array!T temp;
//grab the next cut up to the end of the cards left in the main hand
for (int i=0; i<cutSize && mainHand.length>0; i++) {
temp ~= mainHand[0];
mainHand.linearRemove(mainHand[0..1]);
}
//add them to the cards in the other hand, sometimes to the front sometimes to the back
if (uniform01() >= 0.1) {
//front most of the time
otherHand = temp ~ otherHand;
} else {
//end sometimes
otherHand ~= temp;
}
}
//move the cards back to the main hand
mainHand = otherHand;
}
return mainHand.array;
}
void main() {
auto list = iota(1,21).array;
writeln(list);
list = riffleShuffle(list, 10);
writeln(list);
writeln();
list = iota(1,21).array;
writeln(list);
list = riffleShuffle(list, 1);
writeln(list);
writeln();
list = iota(1,21).array;
writeln(list);
list = overhandShuffle(list, 10);
writeln(list);
writeln();
list = iota(1,21).array;
writeln(list);
list = overhandShuffle(list, 1);
writeln(list);
writeln();
list = iota(1,21).array;
writeln(list);
list.randomShuffle();
writeln(list);
}
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [7, 2, 4, 13, 19, 12, 9, 20, 6, 5, 17, 18, 1, 16, 3, 10, 14, 11, 8, 15] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [11, 12, 1, 2, 3, 4, 13, 5, 14, 15, 16, 6, 7, 17, 18, 8, 9, 19, 10, 20] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [20, 4, 1, 19, 13, 8, 17, 10, 15, 12, 6, 7, 2, 11, 9, 16, 18, 3, 5, 14] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [18, 19, 20, 16, 17, 11, 12, 13, 14, 15, 7, 8, 9, 10, 4, 5, 6, 1, 2, 3] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [10, 17, 19, 13, 5, 12, 1, 2, 14, 4, 9, 16, 7, 3, 15, 20, 8, 11, 6, 18]
FreeBASIC
Sub Riffle(s() As Integer, res() As Integer)
Dim As Integer l, r, i
l = Ubound(s) + 1
r = Int(Rnd * l)
Redim res(-1)
For i = 1 To l
If r + i <= l Then
Redim Preserve res(Ubound(res) + 1)
res(Ubound(res)) = s(r + i - 1)
End If
If i <= r Then
Redim Preserve res(Ubound(res) + 1)
res(Ubound(res)) = s(i - 1)
End If
Next
End Sub
Sub Overhand(s() As Integer, res() As Integer)
Dim As Integer i, l, r
l = Ubound(s) + 1
Redim res(-1)
Dim temp() As Integer
Dim newRes() As Integer
Dim newS() As Integer
While l > 0
r = Int(Rnd * (l * 0.2))
If r > l Or r = 0 Then r = l
Redim temp(r - 1)
For i = 0 To r - 1
temp(i) = s(i)
Next
Redim newRes(Ubound(temp) + Ubound(res) + 1)
For i = 0 To Ubound(temp)
newRes(i) = temp(i)
Next
For i = 0 To Ubound(res)
newRes(Ubound(temp) + 1 + i) = res(i)
Next
Redim res(Ubound(newRes))
For i = 0 To Ubound(newRes)
res(i) = newRes(i)
Next
Redim newS(l - r - 1)
For i = r To l - 1
newS(i - r) = s(i)
Next
Redim s(Ubound(newS))
For i = 0 To Ubound(newS)
s(i) = newS(i)
Next
l = Ubound(s) + 1
Wend
End Sub
Const DECKSIZE = 52 - 24
Sub ShowDeck(s() As Integer)
Dim As Integer i, c
For i = 1 To DECKSIZE
c = s(i - 1) - 1
Print Mid("89TJQKA", (c Mod 7) + 1, 1) & Mid("HCDS", Int(c / 7) + 1, 1); " ";
Next
Print
End Sub
Sub Tagset(size As Integer, s() As Integer)
Redim s(size - 1)
For i As Integer = 0 To size - 1
s(i) = i + 1
Next
End Sub
Randomize Timer
Dim deck() As Integer
Dim res() As Integer
Print "Riffle shuffle:"
Tagset(DECKSIZE, deck())
Riffle(deck(), res())
ShowDeck(res())
Print !"\nOverhand shuffle:"
Tagset(DECKSIZE, deck())
Overhand(deck(), res())
ShowDeck(res())
Sleep
- Output:
Riffle shuffle: AH 8H 8C 9H 9C TH TC JH JC QH QC KH KC AC 8D 9D TD JD QD KD AD 8S 9S TS JS QS KS AS Overhand shuffle: 8C 9C TC JC QC KC AC 8D 9D TD JD QD KD AD 8S 9S TS JS QS KS AS KH AH 8H 9H TH JH QH
Go
package main
import (
"fmt"
"math/rand"
"time"
)
func reverse(s []int) {
for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
s[i], s[j] = s[j], s[i]
}
}
func riffle(deck []int, iterations int) []int {
le := len(deck)
pile := make([]int, le)
copy(pile, deck)
for i := 0; i < iterations; i++ {
mid := le / 2
tenpc := mid / 10
// choose a random number within 10% of midpoint
cut := mid - tenpc + rand.Intn(2*tenpc+1)
// split deck into two at cut point
deck1 := make([]int, cut)
deck2 := make([]int, le-cut)
copy(deck1, pile[:cut])
copy(deck2, pile[cut:])
pile = pile[:0]
fromTop := rand.Intn(2) // choose to draw from top (1) or bottom (0)
for len(deck1) > 0 && len(deck2) > 0 {
if fromTop == 1 {
el1 := deck1[0]
deck1 = deck1[1:]
el2 := deck2[0]
deck2 = deck2[1:]
pile = append(pile, el1, el2)
} else {
el1 := deck1[len(deck1)-1]
deck1 = deck1[:len(deck1)-1]
el2 := deck2[len(deck2)-1]
deck2 = deck2[:len(deck2)-1]
pile = append(pile, el1, el2)
}
}
// add any remaining cards to the pile and reverse it
if len(deck1) > 0 {
pile = append(pile, deck1...)
} else if len(deck2) > 0 {
pile = append(pile, deck2...)
}
reverse(pile) // as pile is upside down
}
return pile
}
func overhand(deck []int, iterations int) []int {
le := len(deck)
pile := make([]int, le)
copy(pile, deck)
pile2 := make([]int, 0)
twentypc := le / 5
for i := 0; i < iterations; i++ {
for len(pile) > 0 {
cards := 1 + rand.Intn(twentypc)
if cards > len(pile) {
cards = len(pile)
}
temp := make([]int, cards)
copy(temp, pile[:cards])
pile2 = append(temp, pile2...)
pile = pile[cards:]
}
pile = append(pile, pile2...)
pile2 = pile2[:0]
}
return pile
}
func main() {
rand.Seed(time.Now().UnixNano())
fmt.Println("Starting deck:")
deck := make([]int, 20)
for i := 0; i < 20; i++ {
deck[i] = i + 1
}
fmt.Println(deck)
const iterations = 10
fmt.Println("\nRiffle shuffle with", iterations, "iterations:")
fmt.Println(riffle(deck, iterations))
fmt.Println("\nOverhand shuffle with", iterations, "iterations:")
fmt.Println(overhand(deck, iterations))
fmt.Println("\nStandard library shuffle with 1 iteration:")
rand.Shuffle(len(deck), func(i, j int) {
deck[i], deck[j] = deck[j], deck[i] // shuffles deck in place
})
fmt.Println(deck)
}
- Output:
Sample output:
Starting deck: [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20] Riffle shuffle with 10 iterations: [19 12 4 7 15 3 13 11 2 8 18 9 10 16 17 14 20 6 1 5] Overhand shuffle with 10 iterations: [5 7 9 4 13 3 15 11 2 8 18 12 1 17 16 6 14 19 10 20] Standard library shuffle with 1 iteration: [15 16 10 4 7 2 6 18 14 13 17 1 12 3 11 8 19 20 5 9]
Groovy
class CardShuffles {
private static final Random rand = new Random()
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().intdiv(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
}
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
}
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)
println(list)
list = riffleShuffle(list, 10)
println(list)
println()
list = Arrays.asList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
println(list)
list = riffleShuffle(list, 1)
println(list)
println()
list = Arrays.asList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
println(list)
list = overhandShuffle(list, 10)
println(list)
println()
list = Arrays.asList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
println(list)
list = overhandShuffle(list, 1)
println(list)
println()
list = Arrays.asList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
println(list)
Collections.shuffle(list)
println(list)
}
}
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [3, 2, 9, 4, 7, 13, 18, 10, 12, 16, 20, 11, 19, 8, 14, 5, 17, 15, 6, 1] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [12, 13, 1, 14, 2, 15, 16, 3, 4, 5, 6, 7, 17, 8, 18, 9, 10, 19, 11, 20] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [3, 8, 14, 10, 9, 6, 12, 15, 2, 16, 19, 17, 20, 18, 13, 11, 1, 5, 7, 4] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [18, 19, 20, 15, 16, 17, 13, 14, 11, 12, 9, 10, 3, 4, 1, 2, 5, 6, 7, 8] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [18, 17, 20, 5, 8, 11, 2, 4, 3, 7, 19, 10, 15, 14, 12, 13, 16, 9, 1, 6]
J
NB. overhand cut
overhand=: (\: [: +/\ %@%:@# > # ?@# 0:)@]^:[
NB. Gilbert–Shannon–Reeds model
riffle=: (({.~+/)`(I.@])`(-.@]#inv (}.~+/))} ?@(#&2)@#)@]^:[
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:
([: +/\ %@%:@# > # ?@# 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
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:
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
Java
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");
}
}
- 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]
jq
Adapted from Wren
Works with gojq, the Go implementation of jq
jq currently does not have a built-in PRNG, so this entry will use an external source of entropy, and specifically /dev/urandom. So a suitable invocation of jq or gojq would look like this:
< /dev/urandom tr -cd '0-9' | fold -w 1 | jq -MRnrc -f card-shuffles.jq
### Preliminaries
# Output: a prn in range(0;$n) where $n is `.`
def prn:
if . == 1 then 0
else . as $n
| ([1, (($n-1)|tostring|length)]|max) 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;
### Riffle
# input: deck
def riffle(iterations):
((length / 2)|floor) as $mid
| {pile: .}
| reduce range(0; iterations) as $i (.;
(($mid / 10)|floor) as $tenpc
# choose a random number within 10% of midpoint
| ($mid - $tenpc + ((2 * $tenpc + 1)|prn)) as $cut
# split deck into two at cut point
| .deck1 = .pile[0:$cut]
| .deck2 = .pile[$cut:]
| .pile = []
# choose to draw from top or bottom
| ((2|prn) == 1) as $fromTop
| until( (.deck1|length) == 0 or (.deck2|length) == 0;
if $fromTop
then .deck1[0] as $card
| .deck1 |= .[1:]
| .pile += [$card]
| .deck2[0] as $card
| .deck2 |= .[1:]
| .pile += [$card]
else .deck1[-1] as $card
| .deck1 |= .[:-1]
| .pile += [$card]
| .deck2[-1] as $card
| .deck2 |= .[:-1]
| .pile += [$card]
end )
# add any remaining cards to the pile and reverse it
| if (.deck1|length > 0)
then .pile += .deck1
elif (.deck2|length > 0)
then .pile += .deck2
else .
end
| .pile |= reverse # as pile is upside down
)
| .pile;
### Overhand
# input: deck
def overhand(iterations):
((length / 5)|floor) as $twentypc
| { pile: .,
pile2: [] }
| reduce range(0; iterations) as $i (.;
until (.pile|length == 0;
([(.pile|length), (1 + ($twentypc|prn))] | min) as $cards
| .pile2 = .pile[0:$cards] + .pile2
| .pile |= .[$cards:]
| .pile += .pile2
| .pile2 = [] )
| .pile ;
### Example
def deck: [range(1;21)];
def iterations: 10;
deck
| "Starting deck:",
"Riffle shuffle with \(iterations) iterations:",
riffle(iterations),
"\nOverhand shuffle with \(iterations) iterations:",
overhand(iterations),
"\nStandard library shuffle with 1 iteration:",
knuthShuffle- Output:
Starting deck: Riffle shuffle with 10 iterations: [1,18,17,13,12,16,15,11,19,14,10,8,4,6,7,3,2,20,5,9] Overhand shuffle with 10 iterations: [2,6,1,10,14,3,4,5,8,7,9,19,11,12,17,16,18,20,13,15] Standard library shuffle with 1 iteration: [6,9,15,17,19,11,10,7,2,14,18,13,16,8,12,3,5,20,1,4]
Julia
function riffleshuffle!(list::Vector, flips::Integer)
len = length(list)
# pre-allocate the left and right part for efficiency
llist = similar(list, len÷2 + fld(len, 10))
rlist = similar(list, len÷2 + fld(len, 10))
for _ in Base.OneTo(flips)
# cut the deck at the middle +/- 10%,
# remove the second line of the formula for perfect cutting
cut = len ÷ 2 + rand(-1:2:1) * rand(0:fld(len, 10))
# split the deck and copy it to left and right
copy!(llist, 1, list, 1, cut)
copy!(rlist, 1, list, cut + 1, len - cut)
ind, indl, indr = len, cut, len - cut
while indl ≥ 1 && indr ≥ 1
if rand() < indl / 2indr
list[ind] = llist[indl]
indl -= 1
else
list[ind] = rlist[indr]
indr -= 1
end
ind -= 1
end
copy!(list, 1, rlist, 1, indr)
copy!(list, 1, llist, 1, indl)
end
return list
end
function overhandshuffle!(list::Vector, passes::Integer)
len = length(list)
otherhand = similar(list)
for _ in Base.OneTo(passes)
ind = 1
while ind ≤ endof(list)
chklen = min(rand(1:cld(len, 5)), len - ind + 1)
copy!(otherhand, ind, list, len - ind - chklen + 2, chklen)
ind += chklen
end
list .= otherhand
end
return list
end
v = collect(1:20)
println("# Riffle shuffle (1):\n", v)
println(" -> ", riffleshuffle!(v, 1), "\n")
v = collect(1:20)
println("# Riffle shuffle (10):\n", v)
println(" -> ", riffleshuffle!(v, 10), "\n")
v = collect(1:20)
println("# Overhand shuffle (1):\n", v)
println(" -> ", overhandshuffle!(v, 1), "\n")
v = collect(1:20)
println("# Overhand shuffle (10):\n", v)
println(" -> ", overhandshuffle!(v, 10), "\n")
v = collect(1:20)
println("# Default shuffle:\n", v)
println(" -> ", shuffle!(v), "\n")
- Output:
# Riffle shuffle (1): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] -> [11, 1, 12, 2, 3, 13, 14, 4, 5, 15, 6, 16, 17, 7, 8, 18, 9, 10, 19, 20] # Riffle shuffle (10): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] -> [13, 11, 7, 2, 12, 1, 3, 16, 19, 5, 4, 14, 9, 10, 18, 15, 6, 17, 8, 20] # Overhand shuffle (1): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] -> [19, 20, 17, 18, 15, 16, 14, 13, 10, 11, 12, 6, 7, 8, 9, 2, 3, 4, 5, 1] # Overhand shuffle (10): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] -> [2, 8, 12, 4, 1, 5, 7, 11, 17, 6, 14, 19, 3, 9, 10, 15, 18, 13, 16, 20] # Default shuffle: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] -> [3, 11, 18, 14, 2, 12, 13, 4, 10, 19, 8, 16, 20, 5, 1, 6, 9, 15, 17, 7]
Kotlin
// version 1.1.51
import java.util.Random
import java.util.Collections.shuffle
val r = Random()
fun riffle(deck: List<Int>, iterations: Int): List<Int> {
val pile = deck.toMutableList()
repeat(iterations) {
val mid = deck.size / 2
val tenpc = mid / 10
// choose a random number within 10% of midpoint
val cut = mid - tenpc + r.nextInt(2 * tenpc + 1)
// split deck into two at cut point
val deck1 = pile.take(cut).toMutableList()
val deck2 = pile.drop(cut).toMutableList()
pile.clear()
val fromTop = r.nextBoolean() // choose to draw from top or bottom
while (deck1.size > 0 && deck2.size > 0) {
if (fromTop) {
pile.add(deck1.removeAt(0))
pile.add(deck2.removeAt(0))
}
else {
pile.add(deck1.removeAt(deck1.lastIndex))
pile.add(deck2.removeAt(deck2.lastIndex))
}
}
// add any remaining cards to the pile and reverse it
if (deck1.size > 0) pile.addAll(deck1)
else if (deck2.size > 0) pile.addAll(deck2)
pile.reverse() // as pile is upside down
}
return pile
}
fun overhand(deck: List<Int>, iterations: Int): List<Int> {
val pile = deck.toMutableList()
val pile2 = mutableListOf<Int>()
val twentypc = deck.size / 5
repeat(iterations) {
while (pile.size > 0) {
val cards = minOf(pile.size, 1 + r.nextInt(twentypc))
pile2.addAll(0, pile.take(cards))
repeat(cards) { pile.removeAt(0) }
}
pile.addAll(pile2)
pile2.clear()
}
return pile
}
fun main(args: Array<String>) {
println("Starting deck:")
var deck = List<Int>(20) { it + 1 }
println(deck)
val iterations = 10
println("\nRiffle shuffle with $iterations iterations:")
println(riffle(deck, iterations))
println("\nOverhand shuffle with $iterations iterations:")
println(overhand(deck, iterations))
println("\nStandard library shuffle with 1 iteration:")
shuffle(deck) // shuffles deck in place
println(deck)
}
Sample output:
Starting deck: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] Riffle shuffle with 10 iterations: [5, 18, 3, 12, 15, 6, 8, 16, 2, 20, 17, 11, 13, 1, 9, 14, 19, 7, 10, 4] Overhand shuffle with 10 iterations: [2, 8, 1, 4, 11, 7, 3, 5, 17, 12, 10, 9, 6, 18, 20, 14, 19, 13, 15, 16] Standard library shuffle with 1 iteration: [17, 9, 12, 15, 7, 13, 18, 8, 2, 20, 5, 10, 16, 6, 14, 4, 19, 3, 11, 1]
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)
- 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
Modula-2
MODULE CardShuffles;
FROM FormatString IMPORT FormatString;
FROM RandomNumbers IMPORT Random;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteCard(c : CARDINAL);
VAR buf : ARRAY[0..15] OF CHAR;
BEGIN
FormatString("%c", buf, c);
WriteString(buf)
END WriteCard;
PROCEDURE WriteInteger(i : INTEGER);
VAR buf : ARRAY[0..15] OF CHAR;
BEGIN
FormatString("%02i", buf, i);
WriteString(buf)
END WriteInteger;
PROCEDURE WriteIntArray(array : ARRAY OF INTEGER);
VAR i : CARDINAL;
BEGIN
WriteString("[");
FOR i:=0 TO HIGH(array) DO
IF i>0 THEN
WriteString(", ");
END;
WriteInteger(array[i]);
END;
WriteString("]")
END WriteIntArray;
(*---------------------------------------*)
TYPE Deck_t = ARRAY[0..20] OF INTEGER;
PROCEDURE InitDeck(VAR deck : ARRAY OF INTEGER);
VAR i : CARDINAL;
BEGIN
FOR i:=0 TO HIGH(deck) DO
deck[i] := i + 1
END
END InitDeck;
PROCEDURE RiffleShuffle(VAR deck : Deck_t; flips : CARDINAL);
VAR
n,cutPoint,nlp,lp,rp,bound : CARDINAL;
nl : Deck_t;
BEGIN
FOR n:=1 TO flips DO
cutPoint := HIGH(deck) / 2;
IF Random(0, 2) > 0 THEN
cutPoint := cutPoint + Random(0, HIGH(deck) / 10);
ELSE
cutPoint := cutPoint - Random(0, HIGH(deck) / 10);
END;
nlp := 0;
lp := 0;
rp := cutPoint;
WHILE (lp <= cutPoint) AND (rp < HIGH(deck)) DO
(* Allow for an imperfect riffling so that more than one card can come from the same side in a row
biased towards the side with more cards. Remove the IF statement for perfect riffling. *)
bound := (cutPoint - lp) * 50 / (HIGH(deck) - rp);
IF Random(0, 50)>= bound THEN
nl[nlp] := deck[rp];
INC(nlp);
INC(rp);
ELSE
nl[nlp] := deck[lp];
INC(nlp);
INC(lp);
END
END;
WHILE lp <= cutPoint DO
nl[nlp] := deck[lp];
INC(nlp);
INC(lp);
END;
WHILE rp < HIGH(deck) DO
nl[nlp] := deck[rp];
INC(nlp);
INC(rp);
END;
deck := nl
END
END RiffleShuffle;
PROCEDURE OverhandShuffle(VAR mainHand : Deck_t; passes : CARDINAL);
VAR
n,cutSize,mp,op,tp,i : CARDINAL;
otherHand,temp : Deck_t;
BEGIN
FOR n:=1 TO passes DO
mp := 0;
op := 0;
FOR i:=0 TO HIGH(otherHand) DO
otherHand[i] := 9999
END;
WHILE mp < HIGH(mainHand) DO
(* Cut at up to 20% of the way through the deck *)
cutSize := Random(0, HIGH(mainHand) / 5) + 1;
tp := 0;
(* Grab the next cut up to the end of the cards left in the main hand *)
i:=0;
WHILE (i < cutSize) AND (mp < HIGH(mainHand)) DO
temp[tp] := mainHand[mp];
INC(tp);
INC(mp);
INC(i);
IF mp = HIGH(mainHand) THEN
temp[tp] := mainHand[mp];
INC(tp);
INC(mp);
END
END;
(* Add them to the cards in the other hand, sometimes to the front and sometimes to the back *)
IF Random(0, 10) >= 1 THEN
(* otherHand = temp + otherHand *)
(* copy other hand elements up by temp spaces *)
i := op;
WHILE (i > 0) AND (op > 0) DO
otherHand[tp + i] := otherHand[i];
DEC(i)
END;
IF op > 0 THEN
otherHand[tp] := otherHand[0]
END;
(* copy the elements of temp into the front of other hand *)
FOR i:=0 TO tp-1 DO
otherHand[i] := temp[i]
END
ELSE
(* otherHand = otherHand + temp *)
FOR i:=0 TO tp DO
otherHand[op+i] := temp[i]
END
END;
op := op + tp
END;
(* Move the cards back to the main hand *)
mainHand := otherHand
END
END OverhandShuffle;
(* Main *)
VAR deck : Deck_t;
BEGIN
WriteString("Riffle shuffle");
WriteLn;
InitDeck(deck);
WriteIntArray(deck);
WriteLn;
RiffleShuffle(deck, 10);
WriteIntArray(deck);
WriteLn;
WriteLn;
WriteString("Riffle shuffle");
WriteLn;
InitDeck(deck);
WriteIntArray(deck);
WriteLn;
RiffleShuffle(deck, 1);
WriteIntArray(deck);
WriteLn;
WriteLn;
WriteString("Overhand shuffle");
WriteLn;
InitDeck(deck);
WriteIntArray(deck);
WriteLn;
OverhandShuffle(deck, 10);
WriteIntArray(deck);
WriteLn;
WriteLn;
WriteString("Overhand shuffle");
WriteLn;
InitDeck(deck);
WriteIntArray(deck);
WriteLn;
OverhandShuffle(deck, 1);
WriteIntArray(deck);
WriteLn;
ReadChar;
END CardShuffles.
Nim
import algorithm, deques, random, sequtils, strutils
proc riffle(deck: seq[int]; iterations: Positive): seq[int] =
result = deck
for _ in 1..iterations:
let mid = deck.len div 2
let tenPc = mid div 10
# Choose a random number within 10% of midpoint.
let cut = mid - tenPc + rand(2 * tenPc)
# Split deck into two at cut point.
var deck1 = result[0..<cut].toDeque
var deck2 = result[cut..^1].toDeque
result.setLen(0)
let fromTop = bool(rand(1)) # Choose to draw from top or bottom.
while deck1.len > 0 and deck2.len > 0:
if fromTop:
result.add deck1.popFirst
result.add deck2.popFirst
else:
result.add deck1.popLast
result.add deck2.popLast
# Add any remaining cards to the pile and reverse it.
if deck1.len > 0: result.add deck1.toSeq
elif deck2.len > 0: result.add deck2.toSeq
result.reverse()
proc overhand(deck: seq[int]; iterations: Positive): seq[int] =
result = deck
var pile: seq[int]
let twentyPc = deck.len div 5
for _ in 1..iterations:
while result.len > 0:
let cards = min(result.len, rand(1..twentyPc))
pile.insert result[0..<cards]
result.delete(0, cards - 1)
result = move(pile)
when isMainModule:
randomize()
echo "Starting deck:"
var deck = toSeq(1..20)
echo deck.join(" ")
let iterations = 10
echo "\nRiffle shuffle with $# iterations:".format(iterations)
echo riffle(deck, iterations).join(" ")
echo "\nOverhand shuffle with $# iterations:".format(iterations)
echo overhand(deck, iterations).join(" ")
echo "\nStandard library shuffle with one iteration:"
deck.shuffle() # Shuffles deck in place.
echo deck.join(" ")
- Output:
Starting deck: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Riffle shuffle with 10 iterations: 7 13 18 10 17 5 16 6 20 2 9 12 14 8 19 4 11 1 15 3 Overhand shuffle with 10 iterations: 2 9 10 4 6 5 14 12 11 17 19 1 13 16 8 3 7 18 20 15 Standard library shuffle with one iteration: 7 9 15 10 1 19 5 14 6 8 4 3 18 17 16 12 13 20 2 11
PARI/GP
Riffle shuffle:
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.");Overhand shuffle:
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.");Usage:
riffle([1..52])
overhand([1..52])- 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
Follows the Raku implementation for the overhand shuffle, but uses classic one-liner for riffle.
sub overhand {
our @cards; local *cards = shift;
my(@splits,@shuffle);
my $x = int +@cards / 5;
push @splits, (1..$x)[int rand $x] for 1..+@cards;
while (@cards) {
push @shuffle, [splice @cards, 0, shift @splits];
}
@cards = flatten(reverse @shuffle);
}
sub flatten { map { ref $_ eq 'ARRAY' ? @$_ : $_ } @_ }
sub riffle {
our @cards; local *cards = shift;
splice @cards, @cards/2 - $_, 0, pop @cards for 0 .. (@cards/2)-1;
}
@cards = 1..20;
overhand(\@cards) for 1..10;
print join ' ', @cards, "\n";
@cards = 1..20;
riffle(\@cards) for 1..10;
print join ' ', @cards, "\n";
- Output:
9 11 5 2 4 14 1 3 8 6 15 13 16 12 19 20 7 18 10 17 1 10 19 9 18 8 17 7 16 6 15 5 14 4 13 3 12 2 11 20
Phix
function riffle(sequence s) sequence res = {} integer l = length(s), r = rand(l) for i=1 to l do if r+i<=l then res &= s[r+i] end if if i<=r then res &= s[i] end if end for return res end function function overhand(sequence s) sequence res = {} integer l = length(s) while length(s) do integer r = rand(l*0.2) if r>length(s) then r = length(s) end if res = s[1..r]&res s = s[r+1..$] 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)))
- 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
PicoLisp
(load "@lib/simul.l")
(de riffle (Lst)
(let N (/ (setq @@ (length Lst)) 2)
(conc
(mapcan list (head N Lst) (tail (- N) Lst))
(and (bit? 1 @@) (tail 1 Lst)) ) ) )
(de overhand (Lst)
(let N (/ (* (length Lst) 20) 100)
(make
(while (flip (cut N 'Lst))
(for I @
(yoke I) ) ) ) ) )
(println 'riffle (riffle (range 1 19)) )
(println 'overhand (overhand (range 1 19)) )
(println 'shuffle (shuffle (range 1 19)) )- Output:
riffle (1 10 2 11 3 12 4 13 5 14 6 15 7 16 8 17 9 18 19) overhand (19 16 17 18 13 14 15 10 11 12 7 8 9 4 5 6 1 2 3) shuffle (5 3 13 15 17 12 14 11 2 1 19 7 6 9 18 8 10 4 16)
Python
import random
def riffleShuffle(va, flips):
nl = va
for n in range(flips):
#cut the deck at the middle +/- 10%, remove the second line of the formula for perfect cutting
cutPoint = len(nl)/2 + random.choice([-1, 1]) * random.randint(0, len(va)/10)
# split the deck
left = nl[0:cutPoint]
right = nl[cutPoint:]
del nl[:]
while (len(left) > 0 and len(right) > 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 (random.uniform(0, 1) >= len(left) / len(right) / 2):
nl.append(right.pop(0))
else:
nl.append(left.pop(0))
if (len(left) > 0):
nl = nl + left
if (len(right) > 0):
nl = nl + right
return nl
def overhandShuffle(va, passes):
mainHand = va
for n in range(passes):
otherHand = []
while (len(mainHand) > 0):
#cut at up to 20% of the way through the deck
cutSize = random.randint(0, len(va) / 5) + 1
temp = []
#grab the next cut up to the end of the cards left in the main hand
i=0
while (i<cutSize and len(mainHand) > 0):
temp.append(mainHand.pop(0))
i = i + 1
#add them to the cards in the other hand, sometimes to the front sometimes to the back
if (random.uniform(0, 1) >= 0.1):
#front most of the time
otherHand = temp + otherHand
else:
otherHand = otherHand + temp
#move the cards back to the main hand
mainHand = otherHand
return mainHand
print "Riffle shuffle"
nums = [x+1 for x in range(21)]
print nums
print riffleShuffle(nums, 10)
print
print "Riffle shuffle"
nums = [x+1 for x in range(21)]
print nums
print riffleShuffle(nums, 1)
print
print "Overhand shuffle"
nums = [x+1 for x in range(21)]
print nums
print overhandShuffle(nums, 10)
print
print "Overhand shuffle"
nums = [x+1 for x in range(21)]
print nums
print overhandShuffle(nums, 1)
print
print "Library shuffle"
nums = [x+1 for x in range(21)]
print nums
random.shuffle(nums)
print nums
print
- Output:
Riffle shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] [4, 16, 5, 19, 3, 14, 2, 9, 20, 13, 17, 10, 6, 7, 1, 18, 12, 11, 8, 21, 15] Riffle shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] [13, 14, 15, 1, 16, 2, 3, 17, 4, 5, 18, 6, 7, 19, 8, 9, 20, 10, 11, 21, 12] Overhand shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] [21, 12, 5, 16, 7, 2, 15, 14, 20, 6, 8, 11, 13, 1, 4, 17, 19, 9, 3, 18, 10] Overhand shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] [21, 20, 19, 18, 16, 17, 14, 15, 11, 12, 13, 4, 5, 6, 7, 1, 2, 3, 8, 9, 10] Library shuffle [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] [14, 12, 2, 17, 18, 21, 8, 4, 15, 9, 11, 10, 3, 1, 7, 19, 20, 6, 5, 16, 13]
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 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)))
- 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...
Raku
(formerly Perl 6)
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(*);
REXX
A little extra effort was put into the create subroutine to build any sort of deck, even a multiple deck as in canasta and samba (with/without jokers). Adding options for short decks, pinochle, schmear, six-handed 500, and the like would be prohibitive and muddy up the code and be distracting.
Six-handed 500 has additional cards of: ♣11 ♣12 ♠11 ♠12 ♦11 ♦12 ♦13 ♦11 ♦12 ♦13
/*REXX program simulates various types of shuffling a deck of cards (any kind of deck).*/
call create; call show 'new deck' /*build and display a new card deck. */
call create; call riffle 1 /*invoke a riffle shuffle (N times). */
call show 'riffle shuffle' /*display the results from last shuffle*/
call create; call overhand 1/5 /*invoke overhand shuffle with 20% cuts*/
call show 'overhand shuffle' /*display the results from last shuffle*/
call create; call barnYard 13 /*also called a washing machine shuffle*/
call show 'barn yard shuffle' /*display the results from last shuffle*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
create: if 9=='f9'x then suit= "cdhs" /*EBCDIC? Then use letters for suits.*/
else suit= "♣♦♥♠" /* ASCII? " " symbols " " */
jokers= 0 /*number of jokers in the card deck. */
wild= copies("jH jL", jokers) /*a large # of high jokers, low jokers.*/
rank= 'A23456789tJQK' /*t in the rank represents a ten (10).*/
decks= 1 /*the number of decks, building a shoe?*/
$= /*the initial (null) card deck (string)*/
do s=1 for length(suit) /*process each of the card deck suits. */
_= substr(suit, s, 1) /*extract a single suit to build + pips*/
do r=1 for length(rank) /*process each of the card deck pips. */
$= $ _ || substr(rank, r, 1) /*build a card, then append it to deck.*/
end /*r*/ /*Note: some decks have more pips, >13.*/
end /*s*/ /* " " " " " suits, >4.*/
$= space($ subword(wild, 1, jokers) ) /*keep a new card deck for each shuffle*/
$= copies($, decks) /*maybe build multiple decks for a shoe*/
#= words($) /*set the number of cards in the deck. */
/*another entry point for this function*/
build: @.=; do j=1 for words($) /*build an array for the card deck. */
@.j= word($, j) /*construct an card from the deck list.*/
end /*j*/
return $ /*elide the leading blank in the deck. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
?: return random(1, word( arg(1) #, 1) ) /*gen a random number from 1 ──► arg. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
barnYard: do j=1 for arg(1); x=?();
do until y\==x | #<2; y=?()
end /*until*/
parse value @.x @.y with @.y @.x
end /*j*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
riffle: $A= subword($, 1, #%2); $B= subword($, #%2 + 1); $= /*split deck in half*/
do j=1 for max( words($A), words($B) ); $= $ word($A, j) word($B, j)
end /*j*/
$= space($); call build; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
overhand: parse arg pc .; if pc=='' then pc= 1/5; chunk= # * pc % 1; $B=
do while words($)\==0; $B= $B subword($, 1, chunk); $= subword($, chunk +1)
end /*while*/
$= space($B); call build; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: _=@.1; do j=2 for #-1; _=_ @.j; end /*j*/; L = length(_)
say center( arg(1), L, '═'); say _; say; return /*show deck*/
- output:
═════════════════════════════════════════════════════════════════════════new deck══════════════════════════════════════════════════════════════════════════ ♣A ♣2 ♣3 ♣4 ♣5 ♣6 ♣7 ♣8 ♣9 ♣t ♣J ♣Q ♣K ♦A ♦2 ♦3 ♦4 ♦5 ♦6 ♦7 ♦8 ♦9 ♦t ♦J ♦Q ♦K ♥A ♥2 ♥3 ♥4 ♥5 ♥6 ♥7 ♥8 ♥9 ♥t ♥J ♥Q ♥K ♠A ♠2 ♠3 ♠4 ♠5 ♠6 ♠7 ♠8 ♠9 ♠t ♠J ♠Q ♠K ══════════════════════════════════════════════════════════════════════riffle shuffle═══════════════════════════════════════════════════════════════════════ ♣A ♥A ♣2 ♥2 ♣3 ♥3 ♣4 ♥4 ♣5 ♥5 ♣6 ♥6 ♣7 ♥7 ♣8 ♥8 ♣9 ♥9 ♣t ♥t ♣J ♥J ♣Q ♥Q ♣K ♥K ♦A ♠A ♦2 ♠2 ♦3 ♠3 ♦4 ♠4 ♦5 ♠5 ♦6 ♠6 ♦7 ♠7 ♦8 ♠8 ♦9 ♠9 ♦t ♠t ♦J ♠J ♦Q ♠Q ♦K ♠K ═════════════════════════════════════════════════════════════════════overhand shuffle══════════════════════════════════════════════════════════════════════ ♣A ♣2 ♣3 ♣4 ♣5 ♣6 ♣7 ♣8 ♣9 ♣t ♣J ♣Q ♣K ♦A ♦2 ♦3 ♦4 ♦5 ♦6 ♦7 ♦8 ♦9 ♦t ♦J ♦Q ♦K ♥A ♥2 ♥3 ♥4 ♥5 ♥6 ♥7 ♥8 ♥9 ♥t ♥J ♥Q ♥K ♠A ♠2 ♠3 ♠4 ♠5 ♠6 ♠7 ♠8 ♠9 ♠t ♠J ♠Q ♠K ═════════════════════════════════════════════════════════════════════barn yard shuffle═════════════════════════════════════════════════════════════════════ ♣A ♣2 ♣3 ♠2 ♥6 ♣6 ♣7 ♣8 ♦8 ♥8 ♣J ♣Q ♣K ♦A ♦2 ♦3 ♦4 ♥t ♦6 ♦7 ♠A ♦9 ♦t ♦J ♦Q ♠t ♥A ♥2 ♣t ♥4 ♠5 ♣5 ♦K ♥Q ♥9 ♦5 ♥J ♥3 ♥K ♣9 ♣4 ♠3 ♠4 ♠K ♠6 ♥7 ♠8 ♠9 ♠7 ♠J ♠Q ♥5
Ruby
Two methods to solve the requirements, and a third one as bonus.
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
deck, new_deck = deck.dup, []
s = deck.size
new_deck += deck.pop(rand(s * 0.2)) until deck.empty?
new_deck
end
def bonus deck
deck.sort { |a, b| Time.now.to_i % a <=> Time.now.to_i % b }
end
deck = [*1..20]
p riffle(deck)
p overhand(deck)
p bonus(deck)
Scala
import scala.collection.mutable.ListBuffer
import scala.util.Random
object CardShuffles {
val rand = new Random()
def riffleShuffle[T](source: List[T], flips: Int): List[T] = {
val list = source.to[ListBuffer]
for (_ <- 1 to flips) {
//cut the deck at the middle +/- 10%, remove the second line of the formula for perfect cutting
val cutPoint = list.size / 2 + (if (rand.nextBoolean()) -1 else 1) * rand.nextInt((list.size * 0.1).toInt)
//split the deck
val left = list.slice(0, cutPoint)
val right = list.slice(cutPoint, list.size)
list.clear()
while (left.nonEmpty && right.nonEmpty) {
//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() >= (1.0 * left.size / right.size) / 2.0) {
list.append(right.remove(0))
} else {
list.append(left.remove(0))
}
}
//if either hand is out of cards then flip all of the other hand to the shuffled deck
if (left.nonEmpty) list.appendAll(left)
if (right.nonEmpty) list.appendAll(right)
}
list.toList
}
def overhandShuffle[T](source: List[T], passes: Int): List[T] = {
var mainHand = source.to[ListBuffer]
for (_ <- 1 to passes) {
val otherHand = new ListBuffer[T]
while (mainHand.nonEmpty) {
//cut at up to 20% of the way through the deck
val cutSize = rand.nextInt((source.size * 0.2).toInt) + 1
val temp = new ListBuffer[T]
//grab the next cut up to the end of the cards left in the main hand
var i = 0
while (i < cutSize && mainHand.nonEmpty) {
temp.append(mainHand.remove(0))
i = i + 1
}
//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.insertAll(0, temp)
} else {
//end sometimes
otherHand.appendAll(temp)
}
}
//move the cards back to the main hand
mainHand = otherHand
}
mainHand.toList
}
def main(args: Array[String]): Unit = {
// riffle shuffle
var lst = (1 to 20).toList
println(lst)
var sorted = riffleShuffle(lst, 10)
println(sorted)
println()
lst = (1 to 20).toList
println(lst)
sorted = riffleShuffle(lst, 1)
println(sorted)
println()
// overhand shuffle
lst = (1 to 20).toList
println(lst)
sorted = overhandShuffle(lst, 10)
println(sorted)
println()
lst = (1 to 20).toList
println(lst)
sorted = overhandShuffle(lst, 1)
println(sorted)
println()
// builtin
lst = (1 to 20).toList
println(lst)
sorted = Random.shuffle(lst)
println(sorted)
println()
}
}
- Output:
List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) List(13, 10, 7, 14, 6, 17, 9, 18, 5, 2, 11, 12, 8, 3, 20, 19, 15, 16, 1, 4) List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) List(10, 11, 12, 1, 2, 3, 4, 5, 13, 6, 14, 15, 16, 17, 18, 7, 19, 8, 20, 9) List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) List(5, 20, 16, 8, 1, 13, 2, 10, 17, 12, 15, 4, 19, 7, 18, 14, 11, 3, 6, 9) List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) List(20, 18, 19, 14, 15, 16, 17, 10, 11, 12, 13, 8, 9, 5, 6, 7, 1, 2, 3, 4) List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) List(1, 14, 12, 8, 15, 19, 4, 18, 11, 16, 13, 3, 2, 17, 10, 5, 9, 7, 6, 20)
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]]
Visual Basic .NET
Imports System.Runtime.CompilerServices
Imports System.Text
Module Module1
<Extension()>
Function AsString(Of T)(c As ICollection(Of T)) As String
Dim sb = New StringBuilder("[")
sb.Append(String.Join(", ", c))
Return sb.Append("]").ToString()
End Function
Private rand As New Random()
Function RiffleShuffle(Of T)(list As ICollection(Of T), flips As Integer) As List(Of T)
Dim newList As New List(Of T)(list)
For n = 1 To flips
'cut the deck at the middle +/- 10%, remove the second line of the formula for perfect cutting
Dim cutPoint As Integer = newList.Count / 2 + If(rand.Next(0, 2) = 0, -1, 1) * rand.Next(newList.Count * 0.1)
'split the deck
Dim left As New List(Of T)(newList.Take(cutPoint))
Dim right As New List(Of T)(newList.Skip(cutPoint))
newList.Clear()
While left.Count > 0 AndAlso right.Count > 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() >= left.Count / right.Count / 2 Then
newList.Add(right.First())
right.RemoveAt(0)
Else
newList.Add(left.First())
left.RemoveAt(0)
End If
End While
'if either hand is out of cards then flip all of the other hand to the shuffled deck
If left.Count > 0 Then
newList.AddRange(left)
End If
If right.Count > 0 Then
newList.AddRange(right)
End If
Next
Return newList
End Function
Function OverhandShuffle(Of T)(list As ICollection(Of T), passes As Integer) As List(Of T)
Dim mainHand As New List(Of T)(list)
For n = 1 To passes
Dim otherhand = New List(Of T)
While mainHand.Count > 0
'cut at up to 20% of the way through the deck
Dim cutSize = rand.Next(list.Count * 0.2) + 1
Dim temp = New List(Of T)
'grab the next cut up to the end of the cards left in the main hand
Dim i = 0
While i < cutSize AndAlso mainHand.Count > 0
temp.Add(mainHand.First())
mainHand.RemoveAt(0)
i = i + 1
End While
'add them to the cards in the other hand, sometimes to the front sometimes to the back
If rand.NextDouble() >= 0.1 Then
'front most of the time
temp.AddRange(otherhand)
otherhand = temp
Else
'end sometimes
otherhand.AddRange(temp)
End If
End While
'move the cards back to the main hand
mainHand = otherhand
Next
Return mainHand
End Function
Sub Main()
Dim list = New List(Of Integer)(Enumerable.Range(1, 20))
Console.WriteLine(list.AsString())
list = RiffleShuffle(list, 10)
Console.WriteLine(list.AsString())
Console.WriteLine()
list = New List(Of Integer)(Enumerable.Range(1, 20))
Console.WriteLine(list.AsString())
list = RiffleShuffle(list, 1)
Console.WriteLine(list.AsString())
Console.WriteLine()
list = New List(Of Integer)(Enumerable.Range(1, 20))
Console.WriteLine(list.AsString())
list = OverhandShuffle(list, 10)
Console.WriteLine(list.AsString())
Console.WriteLine()
list = New List(Of Integer)(Enumerable.Range(1, 20))
Console.WriteLine(list.AsString())
list = OverhandShuffle(list, 1)
Console.WriteLine(list.AsString())
Console.WriteLine()
End Sub
End Module
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [1, 5, 15, 8, 3, 7, 17, 12, 14, 6, 19, 18, 13, 16, 2, 20, 11, 10, 4, 9] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [1, 2, 12, 13, 14, 3, 15, 4, 5, 16, 17, 6, 7, 8, 9, 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] [15, 16, 20, 14, 17, 9, 10, 5, 6, 3, 12, 18, 11, 4, 1, 2, 8, 13, 19, 7] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] [19, 20, 15, 16, 17, 18, 13, 14, 10, 11, 12, 7, 8, 9, 4, 5, 6, 1, 2, 3]
Wren
import "random" for Random
var r = Random.new()
var riffle = Fn.new { |deck, iterations|
var pile = deck.toList
for (i in 0...iterations) {
var mid = (deck.count / 2).floor
var tenpc = (mid / 10).floor
// choose a random number within 10% of midpoint
var cut = mid - tenpc + r.int(2 * tenpc + 1)
// split deck into two at cut point
var deck1 = pile.take(cut).toList
var deck2 = pile.skip(cut).toList
pile.clear()
var fromTop = r.int(2) == 1 // choose to draw from top or bottom
while (deck1.count > 0 && deck2.count > 0) {
if (fromTop) {
pile.add(deck1.removeAt(0))
pile.add(deck2.removeAt(0))
} else {
pile.add(deck1.removeAt(-1))
pile.add(deck2.removeAt(-1))
}
}
// add any remaining cards to the pile and reverse it
if (deck1.count > 0) {
pile.addAll(deck1)
} else if (deck2.count > 0) {
pile.addAll(deck2)
}
pile = pile[-1..0] // as pile is upside down
}
return pile
}
var overhand = Fn.new { |deck, iterations|
var pile = deck.toList
var pile2 = []
var twentypc = (deck.count / 5).floor
for (i in 0...iterations) {
while (pile.count > 0) {
var cards = pile.count.min(1 + r.int(twentypc))
pile2 = pile[0...cards] + pile2
pile = pile[cards..-1]
}
pile.addAll(pile2)
pile2.clear()
}
return pile
}
System.print("Starting deck:")
var deck = (1..20).toList
System.print(deck)
var iterations = 10
System.print("\nRiffle shuffle with %(iterations) iterations:")
System.print(riffle.call(deck, iterations))
System.print("\nOverhand shuffle with %(iterations) iterations:")
System.print(overhand.call(deck, iterations))
System.print("\nStandard library shuffle with 1 iteration:")
r.shuffle(deck) // shuffles deck in place
System.print(deck)
- Output:
Sample run:
Starting deck: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] Riffle shuffle with 10 iterations: [7, 17, 13, 8, 16, 3, 9, 6, 18, 2, 4, 14, 19, 11, 12, 20, 10, 1, 15, 5] Overhand shuffle with 10 iterations: [11, 1, 5, 7, 9, 20, 19, 10, 2, 3, 4, 6, 8, 12, 13, 18, 16, 15, 14, 17] Standard library shuffle with 1 iteration: [9, 16, 2, 12, 8, 20, 13, 5, 4, 18, 17, 6, 11, 19, 1, 3, 14, 7, 10, 15]
zkl
A much better shuffle is List's shuffle method.
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()
}riffle( [1..19].walk()).println();
overHand([1..19].walk()).println();
[1..19].walk().shuffle().println();- 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)