Quote:
Originally Posted by Flint
I'm not calculating this scenario based on professional magicians doing elaborate card tricks. I'm talking about people playing a hand of cards, and then shuffling a few times, and then playing another hand. And, maybe they drop them on the floor, or one of the cards get bent, etc.
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Right. I believe I addressed that in the second sentence. You are never guaranteed to match any particular shuffle (including the initial order), no matter how many times you shuffle.
The perfect shuffle thing was an amusing aside.
Quote:
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If one card gets out of order in your series of "perfect" shuffles, you've started down the long road of 8.06581751709439 e+67 permutations.
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Worse than that. If you make one mistake, and then continue a series of perfect shuffles, you will
never get the original order back. You'll cycle through a sequence of eight incorrect shuffles until you make another mistake.
edit:
Another aside- out-shuffles have a cycle of eight, and in-shuffles have a cycle of 52.