[Condensed from San Diego Union, p. D-1, 15-Jan-90]

 It takes just seven ordinary, imperfect shuffles to mix a deck of cards
 thoroughly, researchers have found.  Fewer are not enough, and more do
 not significantly improve the mixing.

 The mathematical proof, discovered after studies of results from elaborate
 computer calculations and careful observation of card games, confirms the
 intuition of many gamblers, bridge enthusiasts, and casual players that
 most shuffling is inadequate.

 The usual shuffling done by people produces a card order that is "far from
 random," Diaconis, the author of the discovery, said.  "Most people shuffle
 cards three or four times.  Five is considered excessive."

 The realization that most shuffled decks are not actually random allows
 gamblers to improve their odds of winning.  "There are people who go to
 casinos and make money on this," Diaconis said.  "I know people who are out
 there doing that now."  Diaconis said he almost never sees a dealer shuffle
 seven times.

 Bridge players usually shuffle about four times, except in some tournaments
 where a computer randomly mixes the cards, said Edgar Kaplan, who is editor
 and publisher of Bridge World magazine.

 By saying that the deck is completely mixed after seven shuffles, Diaconis
 and Bayer mean that every arrangement of the 52 cards is equally likely, or
 that any card is as likely to be in one place as in another.

 The cards do get more and more randomly mixed if a person keeps on shuffling
 more than seven times, but seven shuffles is a transition point, the first
 time that randomness is close.  Additional shuffles do not appreciably
 alter things.