Mathematics Colloquia and Seminars

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Card shuffling is a quintessential part of modern probability. With the theory of Markov chains, an elementary result is that shuffling the deck repeatedly eventually produces a well-mixed deck, where all orderings are roughly equally likely. The question today is about how long this takes; that is, how many shuffles does it take to get "close enough"? This is known as the mixing time of the shuffle. Some shuffles and their results are particularly famous, such as Bayer and Diaconis's result of "seven shuffles are enough" when applying the riffle shuffle to a standard 52-card deck. Other shuffles, however, are not so easy to analyze. I will discuss the Thorp shuffle, which has an easier to understand description compared to the riffle shuffle but whose mixing time remains to be pinned down exactly.

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