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June 2011 A rule of thumb for riffle shuffling
Sami Assaf, Persi Diaconis, K. Soundararajan
Ann. Appl. Probab. 21(3): 843-875 (June 2011). DOI: 10.1214/10-AAP701

Abstract

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.

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Sami Assaf. Persi Diaconis. K. Soundararajan. "A rule of thumb for riffle shuffling." Ann. Appl. Probab. 21 (3) 843 - 875, June 2011. https://doi.org/10.1214/10-AAP701

Information

Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1226.60005
MathSciNet: MR2830606
Digital Object Identifier: 10.1214/10-AAP701

Subjects:
Primary: 60B15
Secondary: 60C05

Keywords: card shuffling , Cutoff phenomenon , lumping of Markov chains , Poisson summation

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 3 • June 2011
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