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Shuffling Large Decks of Cards and the Bernoulli-Laplace Urn Model

Author(s): Nestoridi, Evita; White, Graham

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Abstract: In card games, in casino games with multiple decks of cards and in cryptography, one is sometimes faced with the following problem: How can a human (as opposed to a computer) shuffle a large deck of cards? The procedure we study is to break the deck into several reasonably sized piles, shuffle each thoroughly, recombine the piles, perform a simple deterministic operation, for instance a cut, and repeat. This process can also be seen as a generalised Bernoulli-Laplace urn model. We use coupling arguments and spherical function theory to derive upper and lower bounds on the mixing times of these Markov chains.
Publication Date: Mar-2019
Electronic Publication Date: 25-Jan-2018
Citation: Nestoridi, Evita, White, Graham. (2019). Shuffling Large Decks of Cards and the Bernoulli-Laplace Urn Model. JOURNAL OF THEORETICAL PROBABILITY, 32 (417 - 446. doi:10.1007/s10959-018-0807-3
DOI: doi:10.1007/s10959-018-0807-3
ISSN: 0894-9840
EISSN: 1572-9230
Pages: 417 - 446
Language: English
Type of Material: Journal Article
Version: Author's manuscript

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