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
Jadwin Hall 111

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