Card shuffling question.

[guapo337]

Say one started with a deck of cards in perfect order. This deck is then split perfectly into two halves of 26 cards each. These cards are in perfect order. Then, the two halves are shuffled together in a perfect manner, so that the cards are then combined into one deck again, one by one from each deck.

How many times would you have to shuffle perfectly so that the cards would be back into their original order?

 

[Warthog912]

? Good question I have not need for the math that is required for this problem, I wanna know the answer though-

 

[guapo337]

Originally posted by: Warthog912
? Good question I have not need for the math that is required for this problem, I wanna know the answer though-

Myself as well.

 

[Kyteland]

If I remember correctly it is 7. Let me double check.

 

[brunswickite]

i would assume none, if i read the question correctly,

everytime you shuffle a deck of cards it would just be moving one card, so no matter how many times you shuffle the cards teh cards will be in order..

for example 123456789 in cards, when shuffled once would looke like 567891234, when shuffled again, 789123456, again 891234567... when you shuffle the cards the cards remain in some order

 

[shuan24]

what do you mean by "shuffle"? Like, in what way? Like the bridge shuffle?

 

[brunswickite]

Originally posted by: shuan24
what do you mean by "shuffle"? Like, in what way? Like the bridge shuffle?

well in shuffleing i mean spliting the cards in and brining the card all the way on the bottom of the deck into the middle of the deck, and repeating

 

[shimsham]

Originally posted by: Kyteland
If I remember correctly it is 7. Let me double check.

7 is the number for the best shuffle, IIRC. i dont know how many to put them back in order.

 

[Kyteland]

it is 8 or 52 depending on how you do it. Assuming all cards are numbered 1-52 then shuffling them as such:

1-2-3-4-5-6... -> 1-27-2-28-3-29...
goes back in order after 8 shuffles

1-2-3-4-5-6... -> 27-1-28-2-29-3...
goes back in order after 52 shuffles

Edit: I was close with 7. I've figured this out before and knew it was somewhere near that.

 

[gistech1978]

ive heard after seven shuffles its shuffled as much as its going to be.
so there is no need to shuffle more than 7 times.
i dont have proof, just what ive heard.

 

[Thraxen]

for example 123456789 in cards, when shuffled once would looke like 567891234, when shuffled again, 789123456, again 891234567... when you shuffle the cards the cards remain in some order

I don't think that's right. Let's say you have 8 cards numbered 1 through 8. You split the deck so now you have one deck that is 1-4 (top to bottom) and the other is 5-8 (top to bottom). When you shuffle one card from the bottom of one deck falls first, then the bottom card from the other side, and then back to the first deck (etc...). So the resulting order should be 4, 8, 3, 7, 2, 6, 1, and 5 if the 4 from the bottom of one half goes first. This all assumes a perfect shuffle.

 

[guapo337]

When I mean shuffle I mean bridge shuffling. So you shuffle, cut in half, shuffle again.

 

[shimsham]

Originally posted by: gistech1978
ive heard after seven shuffles its shuffled as much as its going to be.
so there is no need to shuffle more than 7 times.
i dont have proof, just what ive heard.

i believe it was an actual study funded by a university. too lazy to google.

 

[SLU MD]

7 shuffles gets you to perfect randomness of the cards, it does NOT get you back to the order you started. I have no idea how many it would be, but its probably a fair amount.

slu md

 

[guapo337]

Originally posted by: xxSLUxxMDxx
7 shuffles gets you to perfect randomness of the cards, it does NOT get you back to the order you started. I have no idea how many it would be, but its probably a fair amount.

slu md

ahh see thats what im wondering.

 

[3point14]

Originally posted by: xxSLUxxMDxx
7 shuffles gets you to perfect randomness of the cards, it does NOT get you back to the order you started. I have no idea how many it would be, but its probably a fair amount.

slu md

I prof I know at Lindenwood said that his old mentor at Yale could do 7 shuffles back and have a perfect deck. I'm too lazy (and busy) to google right now, but I think there are only a dozen people in the world that can get the cards from a straight deck, to completely random, back to completely perfect again in 10 shuffles.

BTW...nice choice on SLU for you MD instead of Wash U. I have always been impressed by the doctors that come from SLU's medical program :beer:

 

[Joker81]

public class Shuffle{

int [] deck = new int[52];
int [] compDeck = new int [52];
int [] topDeck = new int[26];
int [] bottomDeck = new int[26];


public Shuffle(){
//deck = new int[52];

for(int M = 0; M < 52; M++){
deck[M] = M;
compDeck[M] = M;
}
int j = 0;
do{

cut(deck, topDeck, bottomDeck);
deck = shuff(topDeck, bottomDeck);
j++;
System.out.println(j);
}while(deck != compDeck);


}

public void cut(int[] decks, int[] top, int[] bottom){
for(int M= 0; M < 26; M++){
top[M] = decks[M];
bottom[M] = decks[M+26];
}
}

public int [] shuff (int[] top, int[] bottom){
int [] newDeck = new int[52];
for(int M=0; M< 26; M++){
newDeck[2*M]=top[M];
newDeck[2*M+1]=bottom[M];
}
return newDeck;
}

public static void main(String[] args) {
Shuffle e = new Shuffle();

}



Thats some java code that im trying to try. You guys check it because right now its about 4.9 million shuffles with no identical matches yet. does perfect order mean card 1 is on top? becuase thats what my code does. because they could be in order but start with card 1 half way down the deck.

 

[tikwanleap]

I was bored here.... so here's the brute force way...

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

 

[tikwanleap]

Originally posted by: Joker81
public class Shuffle{

int [] deck = new int[52];
int [] compDeck = new int [52];
int [] topDeck = new int[26];
int [] bottomDeck = new int[26];


public Shuffle(){
//deck = new int[52];

for(int M = 0; M < 52; M++){
deck[M] = M;
compDeck[M] = M;
}
int j = 0;
do{

cut(deck, topDeck, bottomDeck);
deck = shuff(topDeck, bottomDeck);
j++;
System.out.println(j);
}while(deck != compDeck);


}

public void cut(int[] decks, int[] top, int[] bottom){
for(int M= 0; M < 26; M++){
top[M] = decks[M];
bottom[M] = decks[M+26];
}
}

public int [] shuff (int[] top, int[] bottom){
int [] newDeck = new int[52];
for(int M=0; M< 26; M++){
newDeck[2*M]=top[M];
newDeck[2*M+1]=bottom[M];
}
return newDeck;
}

public static void main(String[] args) {
Shuffle e = new Shuffle();

}



Thats some java code that im trying to try. You guys check it because right now its about 4.9 million shuffles with no identical matches yet. does perfect order mean card 1 is on top? becuase thats what my code does. because they could be in order but start with card 1 half way down the deck.

}while(deck != compDeck); <-- this line may be causing the problem. Not sure if java is smart enough to compare the 52 integers or if it just compares if the array pointer is pointing to the same memory location. (like in c)

 

[DrPizza]

Originally posted by: tikwanleap
I was bored here.... so here's the brute force way...

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

Answer was already given, thanks for providing the proof.

btw, if someone is shuffling in this manner, then it's not "totally random" as someone suggested above. It may look random to someone though. Also, any good magician can pick out a card that doesn't fit the order, even after 2 or 3 "random" shuffles.

 

[Joker81]

}while(deck != compDeck); <-- this line may be causing the problem. Not sure if java is smart enough to compare the 52 integers or if it just compares if the array pointer is pointing to the same memory location. (like in c)[/quote]

thanks you were right i fixed it. Just replace the Shuffle() function with this portion. It will work. and it turns out to be 8.




public Shuffle(){
//deck = new int[52];
int comp = 0;
for(int m= 0; m< 52; i++){
deck[m] = m;
compDeck[m] = m;
}
int j = 0;

do{
comp = 0;
cut(deck, topDeck, bottomDeck);
deck = shuff(topDeck, bottomDeck);
j++;
for(int d=0; d < 52; d++){
if(deck[d]==compDeck[d]){
comp ++;
}
}

}while(comp < 52);
System.out.println(j);

}

 

[notfred]

My program that i wrote takes 52 tries to shuffle the deck back to it's original position.

Here's the code:

#!/usr/bin/perl

# cards.pl
use strict;

# initialize deck
my @cards;
foreach my $ii(1..52){
push @cards, $ii;
}

# print deck order
print "------\n@cards\n------\n";

# make a copy of @cards;
my @original = @cards;

# split @cards

my @top;
my @bot;
for my $ii(1..26){
push @top, (shift @cards);
}
for my $ii(1..26){
push @bot, (shift @cards);
}

print "TOP: @top\n\nBOTTOM: @bot\n";

# combine again
for my $ii(1..26){
unshift @cards, (pop @top);
unshift @cards, (pop @bot);
}

my $shuffles = 1;
# After 1 shuffle, show the card order
print "1 Shuffle: ------\n@cards\n------\n";

until (&compare){
for my $ii(1..26){
push @top, (shift @cards);
}
for my $ii(1..26){
push @bot, (shift @cards);
}

# combine again
for my $ii(1..26){
unshift @cards, (pop @top);
unshift @cards, (pop @bot);
}

$shuffles++;
print "\n$shuffles Shuffles:\n@cards\n\n";
}


sub compare{
for (my $ii = 0; $ii <52; $ii++){
if ($original[$ii] != $cards[$ii]){
return 0;
}
}
return 1;
}


And here's the order of the cards after each shuffle:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

52 Shuffles:
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

 

[Joker81]

I think notfred ways as someone said before is you take the bottom half deck and add that card before the top half deck card. Thats why it was 52

 

[guapo337]

this is crazy

 

[bootymac]

go fish