|
You've assumed that shuffles produce random distributions. They do not. Picture a deck with the 7 of Spades as the top card. You split the deck in half, and shuffle the cards together.
There are not 52 possible locations for the 7S to appear, post shuffle. Given a standard shuffle (small groups of cards falling together at a time), the 7S will always appear in the top 5 or 10 cards. This last number is a conjecture, but it will certainly not appear much deeper than that, and will not appear in the bottom half of the deck at all, unless the shuffler simply "cuts" instead of shuffles.
So, the distribution is not random. Each card will only move by a few positions in a well-ordered shuffle (relative to other shuffles). Assume that a large number of people regularly open brand new decks, which have the same starting order, and then give one shuffle. There is a much more limited (relatively) set of possible distributions for that first shuffle, that first permutation.
|