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.
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