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

Author

Listed:
  • Evita Nestoridi

    (Princeton University)

  • Graham White

    (Stanford University)

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.

Suggested Citation

  • Evita Nestoridi & Graham White, 2019. "Shuffling Large Decks of Cards and the Bernoulli–Laplace Urn Model," Journal of Theoretical Probability, Springer, vol. 32(1), pages 417-446, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-018-0807-3
    DOI: 10.1007/s10959-018-0807-3
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