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Trailing the Dovetail Shuffle to its Lair

Dave Bayer and Persi Diaconis
The Annals of Applied Probability
Vol. 2, No. 2 (May, 1992), pp. 294-313
Stable URL: http://www.jstor.org/stable/2959752
Page Count: 20
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Trailing the Dovetail Shuffle to its Lair
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Abstract

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: 3/2 log2 n + θ 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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