# Games: Beating the Dealer

The omnicompetent computer, whose attention often seems to be concentrated on the welfare of moon travelers and submariners, may at last have produced a palpable boon for the common run of mankind: a system for winning money in a gambling house.

A 30-year-old mathematics professor named Edward O. Thorp claims to have made this important breakthrough by feeding the equivalent of 10,000 man-years of desk-calculator computations into an IBM 704 computer and arriving at a set of discoveries about the way the odds fluctuate in the game of blackjack, or twenty-one. This system enables the initiate to bet heavily when the odds are with him, lightly when they are against him. What's more, the cost of the system—including a set of palm-sized, sweat-resistant charts to take to the casino—is only \$4.95, which happens to be the cost of Thorp's book, Beat the Dealer (Blaisdell).

Hard Hands & Soft. Thorp's system is based on the fact that blackjack is not what mathematicians call an "independent trials process," in which, as in craps or roulette, each play is uninfluenced by the preceding plays. As each card is played in blackjack, it changes the possibilities for both player and dealer by diminishing the number and the variety of cards that may be dealt.

Hence the basic blackjack strategy, according to Thorp's computer, is that the fewer cards valued at two to eight that are left in the pack, the greater advantage to the player. On the other hand a shortage of nines, tens and aces gives the dealer an advantage. A scarcity of fives, Thorp's figures indicate, is more advantageous to the player than a shortage of any other card; when all four fives have been played, the player has an edge of 3.29% or, as expressed roughly in odds, 52-48 in the player's favor. Thorp has devised a series of charts to show when to split a pair ("always split aces and eights, never split fives and tens"),* when to double and when to stand.

Knowing when to stand and when to ask for another card is, of course, the heart of the game. Thorp's chart for this differentiates between what he calls "soft" hands—hands that contain an ace and are therefore less likely to go over 21 (aces count as either 1 or 11)—and "hard" hands, which contain no ace. For example, when the dealer is showing a nine or ten, a soft hand should draw, even on 19, because the ace in it can be taken as 1 if necessary (reducing the 19 to 9), whereas in the same circumstances a hard hand should stand at 17. And when the dealer shows a four, five or six, a hard hand should stand at 12 (because with a four, five or six in his hand the dealer runs a considerable risk of going bust), whereas a soft hand is advised to draw another card up to 18.

This is Thorp's basic strategy; his full-dress system involves a much more complex technique of betting in terms of the number of tens, aces and fives remaining in the deck in relation to the number of cards left in the pack before the next shuffle.

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