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How Many Times Should You Shuffle a Deck of Cards?

Brad Mann

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| ©1994 by COMAP, Inc. | The UMAP Journal 15.4 | 30 pages

How many times do you have to shuffle a deck of cards in order to mix them reasonably well? The answer is about seven times for a deck of 52 cards, according to Persi Diaconis. This somewhat surprising result made the New York Times a few years ago [Kolata 19901. Why it is so can be seen by an intriguing and yet understandable analysis of the process of shuffling. This paper is an exposition of such an analysis in Bayer and Diaconis [1992], though many people have done work on shuffling. These have included E. Gilbert [I9551 and Claude Shannon at Bell Labs in the 1950s, and, more recently, Jim Reeds [1981] and David Aldous.