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And I decided to this shuffle by picking two random cards from the 8 decks ans swapping their position, how many iterations would I need to have a properly shuffled 8 decks of cards?
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My guess is that this behaves a lot like the top-in shuffle, which in some sense takes about n log n iterations to randomize a deck with n cards.
However, the best I could find was that about 2 n^2 iterations suffice to randomize the deck. See problems 6 and 7 on
this homework assignment.
More precisely, there is a random (but dependent) stopping time at which the deck is uniformly shuffled so that the expected stopping time is 2n^2. The probability that the stopping time is greater than 2n^2+k decays exponentially in k.
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Is this a good method of shuffling for statistial analysis?
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No. There are fast, effective algorithms. This is not one of them.