Can the familiarity with math help a gambler to win? It’s possible to frequently learn that the finest bit of advice given by a mathematician to some lover of gambling games is an affirmation which lies in the fact that the most effective strategy in gambling games is complete abstention from participation within them. Plenty of mathematicians consider the most which the theory of probability as well as the theory of games can give a gambler are the strategies following which he will not lose too much.
It is tough to forecast whether the American mathematician Edward Thorp shared this view, when once spending winter vacations in Las Vegas, he, having entered a casino, decided to try his chance in the sport of twenty one. As it turned out, “Dame Fortune” was exceptionally unkind to him. We usually do not know for sure what amount of money this teacher of mathematics of one of American universities lost that winter night by the end of the 50s – the start of the 60-s of the last century, yet, judging by these occasions the sum wasn’t modest. Otherwise, how do we account for the truth that development of an optimum strategy of this game became to get a number of years an “idte fixe” of our hero. Anyway, the issue was not only in the number of money lost by the mathematician.
Besides, he could suspect a croupier of dishonesty, since, as he’d detected, cards are not shuffled after every game. Though, throughout the game itself it didn’t make him very uneasy. Yet, afterwards, having visited casinos several times, he noticed that as the rules did not presuppose obligatory shuffling of cards after each game, so it was tricky to accuse a croupier of anything. Anyway, he was able to build up a successful strategy in the game of twenty-one.
This strategy among other things was based on the same very aspect which had put a defeated mathematician on his guard – cards were not shuffled too frequently. At that, this, apparently, generally, was done not because of some bad design, but so that you can prevent, thus to say, unnecessary slow downs in the game. The results of his studies Edward Thorp put forth in a publication published in 1962 (Thorp E.O Conquer the dealer. A successful strategy for the game of twenty one. – New York: Blaisdell,1962.) But let’s not ride before the hounds.
In compliance with the game rules of twenty-one of that time one croupier dealt gamblers two cards each out of a thoroughly shuffled pack consisting of 52 cards. Gamblers themselves did not show their cards to a coping croupier. In precisely the same time out of two cards chosen for himself an official of a casino showed one of them (usually the first one) to gamblers. Gamblers value their cards according to the next scale. Jacks, queens and kings have a value equivalent to 10 points, an ace may be assigned either 1 point or 11 points, the value of the remainder of the cards coincided with their numerical value (eights had 8 points, nines chose 9, and etc). That gambler was considered a victor who had cards on hand with the sum of points closest to 21 from the bottom. At that, having evaluated the received cards every gambler (including a croupier) had a right to choose from a pack or putting it easier, take a “widow”, any amount of cards. However, if, as a result, the total quantity of points following a widow, will surpass 21 points then a gambler must drop out of a game having revealed his cards.
Special rules were established with respect to positions. Initially, upper and lower bounds were set, and every gambler had a right of choice of a particular stake (within these bounds) depending on the assessment of his place. If, as a result, it turned out that in accordance with all the game rules a casino’s visitor had a “better” amount of points on hand than the usual croupier had, he received a gain in the quantity of the stake which he had made, otherwise, this gambler lost his stake. In case of an equivalent amount of points of a gambler along with a croupier, the game ended in peace, that is the end result of the match is considered “benign” both for a gambler as well as a casino.
Let’s point out that unlike normal gamblers a croupier isn’t obliged to open his cards in that case if the number of points in these cards exceeds 21. Furthermore, after most of the gamblers have opened their cards, and therefore, all the stakes visit a casino gamblers cannot practically figure out what was the number of points of a croupier, as a way to assemble their game strategy for another game (whether to risk or to not stand pat, and etc). It goes without saying, it supplies a croupier significant advantages. Moreover, all the gamblers are undoubtedly aware of this, and, continue to play. Nothing could be done about it, who does not take risks, as is known, will not win.