The identity is the most likely exchange shuffle for large n

Daniel Goldstein; David Moews

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The identity is the most likely exchange shuffle for large n

Daniel Goldstein·David Moews

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Abstract

Let a deck of n cards be shuffled by successively exchanging the cards in positions 1, 2, ..., n with cards in randomly chosen positions. We show that for n equal to 18 or greater, the identity permutation is the most likely. We prove a surprising symmetry of the resulting distribution on permutations. We also obtain the limiting distribution of the number of fixed points as n goes to infinity.

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Daniel Goldstein, David Moews. 2000-10-06. The identity is the most likely exchange shuffle for large n. https://arxiv.org/abs/math/0010066

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