How many shuffles to randomize a deck of cards?

  title={How many shuffles to randomize a deck of cards?},
  author={Lloyd N. Trefethen and Lloyd M. Trefethen},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  pages={2561 - 2568}
  • L. Trefethen, L. Trefethen
  • Published 8 October 2000
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
A celebrated theorem of Aldous, Bayer and Diaconis asserts that it takes ∼3/2 log2 n riffle shuffles to randomize a deck of n cards, asymptotically as n → ∞, and that the randomization occurs abruptly according to a 'cut–off phenomenon'. These results depend upon measuring randomness by a quantity known as the total variation distance. If randomness is measured by uncertainty or entropy in the sense of information theory, the behaviour is different. It takes only ∼log2 n shuffles to reduce the… Expand

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