The Annals of Applied Probability

A rule of thumb for riffle shuffling

Sami Assaf, Persi Diaconis, and K. Soundararajan

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We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, for example, suits disregarded or only the colors of interest. For these features the number of shuffles drops from (3/2) log2n to log2n. We derive closed formulae and an asymptotic “rule of thumb” formula which is remarkably accurate.

Article information

Ann. Appl. Probab. Volume 21, Number 3 (2011), 843-875.

First available in Project Euclid: 2 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 60C05: Combinatorial probability

Card shuffling cutoff phenomenon lumping of Markov chains Poisson summation


Assaf, Sami; Diaconis, Persi; Soundararajan, K. A rule of thumb for riffle shuffling. Ann. Appl. Probab. 21 (2011), no. 3, 843--875. doi:10.1214/10-AAP701.

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