The Mixing Time of the Thorp Shuffle

  • Authors:

  • Ben Morris

  • Affiliations:

  • morris@math.ucdavis.edu

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2008

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Abstract

The Thorp shuffle is defined as follows. Cut a deck of cards into two equal piles. Drop the first card from the left pile or the right pile according to the outcome of a fair coin flip, then drop from the other pile. Continue this way until both piles are empty. We show that the mixing time for the Thorp shuffle with $2^d$ cards is polynomial in $d$.