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Gambling Games and Mathematics

Can the familiarity with mathematics help a gambler to win? One can often learn pokergod the best bit of advice given by means of a mathematician into a lover of gambling games is an affirmation which lies in the fact that the best strategy in gambling games is complete abstention from participation in them. A lot of mathematicians consider that the most which the theory of probability and also the theory of games can give a gambler are the strategies following which he will not lose too much.

It is tough to predict whether the American mathematician Edward Thorp shared this viewpoint, when once spending winter vacations in Las-Vegas, he, having entered a casino, determined to try his fortune in the game of twenty one. As it turned out, "Dame Fortune" was exceptionally unkind to him. We don't know for sure what amount of money this teacher of math of one of American universities lost that winter night at the end of the 50s - the start of the 60s of the last century, however, judging by these events the sum wasn't little. Otherwise, how can we account for the truth that development of an optimum strategy of this game became for a number of years an "idte fixe" of our hero. Besides, the issue was not only in the volume of money lost by the mathematician.

Moreover, he could suspect a croupier of dishonesty, since, as he'd detected, cards were not shuffled after every match. Though, through the game itself it failed to make him very uneasy. However, afterward, having seen casinos numerous times, he discovered 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 managed to build up a successful strategy in the game of twenty-one.

This strategy among other things was centered on the same very facet which had place a defeated mathematician on his guard - cards weren't shuffled too commonly. At that, this, seemingly, usually, was done not because of some evil design, but to be able to avert, so to say, unnecessary slow downs in the sport. The outcomes of his studies Edward Thorp set forth in a book published in 1962 (Thorp E.O Defeat the dealer. A winning strategy for the game of twenty one. - But let us not ride before the hounds.

In compliance with all 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 the exact same time out of two cards taken for himself an official of a casino revealed one of them (normally the first one) to gamblers. Gamblers evaluate their cards based on the following scale. Jacks, queens and kings have a value equivalent to 10 points, an ace may be assigned either 1 point or 11 points, the worth of the rest 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 together with the total of points closest to 21 from the bottom. At that, having evaluated the received cards every gambler (including a croupier) had a right to take from a pack or placing it simpler, take a "widow", any number of cards. However, if, as a result, the total amount 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 together with the game rules a casino's visitor had a "better" number of points on hand than a croupier had, he received a gain in the sum of the stake which he had made, otherwise, this gambler lost his stake. In the event of an identical quantity of points of a gambler as well as a croupier, the game finished in peace, this is the end result of the game is considered "harmless" both for a gambler and also a casino.

Furthermore, after most of the gamblers have opened their cards, and so, all of the stakes go to a casino gamblers cannot virtually find out what was the quantity of points of a croupier, as a way to create their game strategy for the next match (whether to risk or to not stand pat, and etc). It goes without saying, it supplies a croupier considerable edges. Besides, all the gamblers are really aware of this, and, continue to play. Nothing could be done about it, who doesn't take threats, as is understood, will not win.

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