The large and very incorrect assumption there is that a shuffle of a deck of cards is a random process. It’s not, and it’s not even close. If you cut, then smoothly re-mesh the two stacks of 52, each card will only be moved out of the original order in a very limited fashion. Since many millions of decks have arrived at their first shuffle in exactly the same order, it’s statistically certain that the same combination has been arrived upon, at a minimum, thousands of times. Many, many possible combinations are also deliberately avoided, such as taking a single card [or two, or any number less than 26] out of the original order and then placing it elsewhere in the deck without otherwise reordering the greater or lesser portion. This excludes a lot of the possibilities. The product of actual human [or human-designed] shuffling is nowhere near factorial 52.

The large and very incorrect assumption there is that a shuffle of a deck of cards is a random process. It’s not, and it’s not even close. If you cut, then smoothly re-mesh the two stacks of 52, each card will only be moved out of the original order in a very limited fashion. Since many millions of decks have arrived at their first shuffle in exactly the same order, it’s statistically certain that the same combination has been arrived upon, at a minimum, thousands of times. Many, many possible combinations are also deliberately avoided, such as taking a single card [or two, or any number less than 26] out of the original order and then placing it elsewhere in the deck without otherwise reordering the greater or lesser portion. This excludes a lot of the possibilities. The product of actual human [or human-designed] shuffling is nowhere near factorial 52.

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