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

Evita Nestoridi () and Graham White ()
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Evita Nestoridi: Princeton University
Graham White: Stanford University

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 417-446

Abstract: 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.

Keywords: Bernoulli–Laplace urn model; Shuffling large decks; Mixing times; Path coupling; Spherical functions; Dual Hahn polynomials; Gelfand pairs; 60C05; 60J10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0807-3

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