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Math Trek

Shuffling the cards: Math does the trick

When to stop shuffling depends on the game

By
3:42pm, November 7, 2008

Here’s the rule: To assure cards get sufficiently mixed up, shuffle a deck about seven times. Mathematician, magician and card shark Persi Diaconis of Stanford University, along with David Bayer of Columbia University, created shock waves in Las Vegas when he figured that out back in 1992. Most dealers had been shuffling much less.

But now Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough. The reason for the lower number is that many games require randomness for only a few specific aspects of the cards, not all. In blackjack, for example, suits don’t matter. Diaconis and his collaborators extended the earlier analysis

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