Gambling Games and Mathematics

Can the familiarity with mathematics help a gambler to win? It’s possible to often hear the very best piece of advice given by means of a mathematician to your lover of gambling games is an assertion which lies in the fact that the top strategy in gambling games is complete abstention from participation within them. Lots of mathematicians consider that the most which the theory of probability along with the theory of games may give a gambler are the strategies following which he won’t lose too much.

It’s difficult to predict if the American mathematician Edward Thorp shared this perspective, when once spending winter holidays in Las-Vegas, he, having entered a casino, decided to try his fortune in the game of twenty one. As it turned out, “Dame Fortune” was extremely unkind to him. We usually do not know for sure what amount of money this teacher of math of one of American universities lost that winter night by the end of the 50-s – the start of the 60s of the last century, however, judging by these occasions the sum was not small. Otherwise, how can we account for the truth that development of an optimum strategy of this game became for several years an “idte fixe” of our hero. Anyway, the matter wasn’t only in the total amount of money lost by the mathematician.

Besides, he could guess a croupier of dishonesty, since, as he’d detected, cards weren’t shuffled after each game. Though, throughout the match itself it did not make him very uneasy. Nevertheless, subsequently, having seen casinos numerous times, he discovered that as the rules didn’t presuppose obligatory shuffling of cards after each game, so it was difficult to accuse a croupier of anything. Anyway, he managed to develop a successful strategy in the game of twenty one.

This strategy among other things was based on the same very facet which had put a conquered mathematician on his guard – cards were not shuffled too commonly. At that, this, apparently, generally, was done not because of some evil design, but in order to avert, so to say, unnecessary slow downs in the sport. The results of his studies Edward Thorp set forth in a publication published in 1962 (Thorp E.O Defeat the dealer. A winning strategy for the game of twenty one. – New York: Blaisdell,1962.) which made owners of gambling houses in the state of Nevada basically shift the rules of the game of twenty-one. But let’s not ride prior to the hounds.

In accordance 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 dealing croupier. At once out of two cards taken for himself an official of a casino showed one of them (generally the first one) to gamblers. Gamblers value their cards based on the next scale. That gambler was considered a winner who had cards on hand together 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 setting it easier, take a “widow”, any number of cards. But if, because of this, the total number of points following a widow, will exceed 21 points then a gambler must drop from a game having revealed his cards.

Specific rules were created with respect to positions. If, as a result, it turned out that in accordance with all the game rules a casino’s visitor had a “better” number of points on hand than the usual croupier had, he received a gain in the amount of the stake which he had made, otherwise, this gambler lost his stake. In the event of an identical variety of points of a gambler plus a croupier, the game finished in peace, that’s the consequence of the game is considered “harmless” both for a gambler plus a casino.

Let us point out that unlike common gamblers a croupier is not obliged to open his cards in that case in the event the number of points in these cards exceeds 21. Moreover, after each of the gamblers have opened their cards, and therefore, all the stakes go to a casino gamblers cannot practically figure out what was the quantity of points of a croupier, to be able to assemble their game strategy for the next game (whether to risk or to not stand pat, and etc). It goes without saying, it gives a croupier substantial edges. Furthermore, all the gamblers are really aware of this, and, continue to play. Nothing could be carried out about it, who does not take risks, as is understood, does not win.

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