Shuffling large decks of cards and the Bernoulli-Laplace urn model
Shuffling large decks of cards and the Bernoulli-Laplace urn model
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Evita Nestoridi , Princeton University
In boardgames, in Casino games with multiple decks and in cryptography, one is sometimes faced with the practical听problem: how can a human (as opposed to the computer) shuffle a big deck of cards. One natural procedure (used听by casino鈥檚) is to break the deck into several reasonable size piles, shuffle each throughly, assemble, do some simple听deterministic thing (like a cut) and repeat. G. White and I introduce variations of the classical Bernoulli-Laplace urn听model (the first Markov Chain!) involving swaps of big groups of balls. Now, a coupling argument and spherical function听theory allow the original problem to be solved.1