Open Access
May, 1992 Trailing the Dovetail Shuffle to its Lair
Dave Bayer, Persi Diaconis
Ann. Appl. Probab. 2(2): 294-313 (May, 1992). DOI: 10.1214/aoap/1177005705


We analyze the most commonly used method for shuffling cards. The main result is a simple expression for the chance of any arrangement after any number of shuffles. This is used to give sharp bounds on the approach to randomness: $\frac{3}{2} \log_2 n + \theta$ shuffles are necessary and sufficient to mix up $n$ cards. Key ingredients are the analysis of a card trick and the determination of the idempotents of a natural commutative subalgebra in the symmetric group algebra.


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Dave Bayer. Persi Diaconis. "Trailing the Dovetail Shuffle to its Lair." Ann. Appl. Probab. 2 (2) 294 - 313, May, 1992.


Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0757.60003
MathSciNet: MR1161056
Digital Object Identifier: 10.1214/aoap/1177005705

Primary: 20B30
Secondary: 60B15 , 60C05 , 60F99

Keywords: card shuffling , symmetric group algebra , total variation distance

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 2 • May, 1992
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