Do you think the shuffle of the cards do not matter? Think again. How many times must a pack of perfectly ordered playing cards be shuffled until its order is close to random? That depends on what shuffling method you use. Professor Persi Diaconis of Stanford University, a professional magician who changed career and became a mathematician and statistician, made a thorough study of shuffling. He found that, if you use the riffle shuffle (the usual way card players shuffle cards: cut off about half the pack and riffle the two packets together), it takes just 7 times! If you use the overhand shuffle (another popular method) it takes 2500 times!

In Las Vegas, cards are shuffled from four to seven times, at the discretion of the casino owners, said Richard Ingram, a Las Vegas enforcement agent for the state gambling control board. Dr. Diaconis said he almost never sees a dealer shuffle seven times. He said his research also shows that when dealers shuffle several decks at once, they need to shuffle more. Two decks should be shuffled nine times, he said, and six decks should be shuffled 12 times, which is unheard of in the casinos.

I have never seen them do that in any casino. According to Dr. Diaconis it takes 5 to 12 shuffles to perfectly mix a deck. But, said Dr. Diaconis, ''nobody in practice shuffles 12 times.'' In the meantime, he also worked on ''perfect shuffles,'' those that exactly interlace the cards. Almost no one except a magician can do perfect shuffles every time. Dr. Diaconis showedl years ago that if a person actually does perfect shuffles, the cards would never be thoroughly mixed. He derived a mathematical proof showing that if a deck is perfectly shuffled eight times, the cards will be in the same order as they were before the shuffling.

Magicicans have long taken advantage of the non-randomnesss of most card shuffling, Dr. Diaconis said. In fact, he said, Charles T. Jordan, a magician, chicken farmer and professional contest entrant from Petaluma, Calif., made a fair amount of money around the turn of the century by selling a card trick exploiting the fact Dr. Diaconis said he first began to think about the shuffling problem 20 years ago after a visit to A.T.&T Bell Laboratories in Murray Hill, N.J. Mathematicians there told him about the problem but said they had given up trying to solve it in 1955 because there were so many ways to arrange a deck.

As you can see there is math in shuffling.

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