Information Loss in Riffle Shuffling

  • Authors:

  • Dudley Stark;A. Ganesh;Neil O’connell

  • Affiliations:

  • Queen Mary, University of London, Mile End Road, London E1 4NS, UK (e-mail: D.S.Stark@maths.qmw.ac.uk);Microsoft Research, St. George House, 1 Guildhall Street, Cambridge CB2 3NH, UK (e-mail: ajg@microsoft.com);BRIMS, Hewlett-Packard Laboratories, Filton Road, Bristol BS34 8QZ, UK (e-mail: noc@hplb.hpl.hp.com)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2002

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Abstract

We study the asymptotic behaviour of the relative entropy (to stationarity) for a commonly used model for riffle shuffling a deck of n cards m times. Our results establish and were motivated by a prediction in a recent numerical study of Trefethen and Trefethen. Loosely speaking, the relative entropy decays approximately linearly (in m) for m 2 n, and approximately exponentially for m log2 n. The deck becomes random in this information-theoretic sense after m = 3/2 log2 n shuffles.