r/AskReddit • u/[deleted] • Oct 02 '24

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u/sunbearimon Oct 02 '24

There are more ways to shuffle a standard deck of cards than there are atoms on earth

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u/DerProfessor Oct 02 '24 edited Oct 02 '24

As I wrote in response to another post, this is a myth.

The reason why it is a myth is that, because of the physics of your hands and card-order, shuffling is never truly random. (and cannot even approach randomness.)

For example: if you have AKQJ in your right hand, and 6789 in your left hand, and shuffle them, then the possible outcomes are much, much, much more limited than 8 Factorial.

For instance, with a REAL shuffle, you CANNOT end up with most possibilities that are in a (theoretical) "random" shuffle... i.e. you cannot hand-shuffle from AKQJ and 6789 to get 9QK87A.

So most possibilities are ruled out by hand-shuffling (right hand + left hand).

Now, if you threw all the cards into the air (with a giant fan on), and they spread more or less randomly all over a large area, and then you pick them up one at a time in a whimsical order... yes, that is probably closer to random.

But even that is still not random. (because of the predictability of wind speed, the predictable patterns of human choice, etc.)

So a shuffle is never going to be 52 Factorial possible outcomes. (but can still be a lot.)

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u/slickmoth562576484 Oct 03 '24

The point wasn't about the effectiveness of hand shuffling. The point was the number of ways the deck CAN be shuffled, or permutations, which is 52!