I58,753,000,000 to 1

158,753,000,000 to 1

Toward the end of a long, uneventful evening at contract bridge, North stretches, gapes, makes off to the kitchen to mix another round. East whispers something to South and West who nod and chuckle. Then East quickly sorts the 13 spades from the deck, stacks it so that every fourth card is a spade. North returns with the drinks to find East just beginning to deal. When North, gasping, has bid his grand slam, laid down his 13 spades and scored 3,240 points (vulnerable, redoubled), East leaps to the telephone, gets the local newspaper on the wire. . .

Something of that sort must by mathematical necessity be back of at least 90% of the newsstories which every few months tell of someone in the U. S. holding a 13-trump bridge hand. Such is the conclusion of Louis Frank Woodruff, assistant professor of electrical power transmission, at M. I. T., who has worked out some remarkable card facts by means of algebraic permutations & combinations. In the current issue of M. I. T.'s Technology Review Professor Woodruff's figures show that the chance of any honestly dealt hand's consisting of an entire suit are 1 in 158,753,000.000. This means that if each of the 10,000,000 U. S. bridge players played 15 hands every day, year in & year out, a solid-suit hand would occur under the law of averages only once every three years.

Of more immediate interest to bridge enthusiasts are the figures on distribution expectancy. Run-of-the-mine players who feel "safer" in a suit bid than at no-trump, like to pick up hands containing long suits studded with honors, short or void suits representing ability to ruff. If the cards are shuffled so that a truly random arrangement results, a player should get a 6-card suit every six hands, a 7-card suit every 28 hands, a singleton every three hands, a void suit every 20 hands.

Most players enjoy these holdings less frequently than they should. They cheat themselves out of juicy hands by hasty or unskillful shuffling which does not produce true random distribution. After a hand of play the pack is composed of 13 tricks the great majority of which contain three or four cards of like suit. If the deal is made from this unshuffled pack, each player will get one card from each trick, and the result will be a number of 3-and 4-card suits typical of weak hands. Poor shuffling does not correct this tendency. After examining hundreds of hands dealt after one, two, three and four shuffles, Mr. Woodruff shows that it takes at least four good shuffles to produce the proper quota of uneven distribution. With the help of an M. I. T. colleague, he has invented a machine controlled by a 52-lobe irregular cam which is designed to deal a pack into hands of the ideal random type in four seconds.

Professor Woodruffs showiest figure is the number of ways in which a pack of 52 cards may be arranged: 80,660,000,000,000,000,000.000,000,000,000,000,000, 000,000,000,000,000, 000, 000,000,000,000.

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