One can often hear that the best piece of advice given by a mathematician to a lover of gambling games is an assertion that lies in the fact that the best strategy in gambling games is complete abstention from participation in them. Many mathematicians consider that the most which the theory of probability and the theory of games can give a gambler are the strategies following which he won’t lose too much.

It is difficult to predict whether the American mathematician Edward Thorp shared this view when once spending winter holidays in Las-Vegas, he, having entered a casino, decided to try his luck in the game of twenty-one. As it turned out, “Dame Fortune” was extremely unkind to him. We do not know for sure what amount of money this teacher of mathematics of one of the American universities lost that winter night at the end of the 50-s – the beginning of the 60-s of the last century. However, judging by the following events, the amount was not small. Otherwise, how can we account that the development of this game’s optimal strategy became an “edit fixe” of our hero for several years? Besides, the matter was not only in the quantity of money lost by the mathematician. Perhaps, Thorp was simply an extremely venturesome person, and his pride both of a gambler and an expert-mathematician was hurt. Besides, he could suspect a croupier of dishonesty since, as he had noticed, cards were not shuffled after each game. However, it did not make him very uneasy during the game itself. However, after visiting casinos sometimes, he noticed that as the rules did not presuppose obligatory shuffling of cards after each game, it was difficult to accuse a croupier of anything. Anyway, he managed to develop a winning strategy in the game of twenty-one.

This strategy, among other things, was based on the very same aspect which had put a defeated mathematician on his guard – cards were not shuffled too often. At that, this, apparently, as a rule, was done not because of some evil design but to avoid, so to say, unnecessary slowdowns in the game. The results of his studies Edward Thorp put forth in a book published in 1962 (Thorp E.O Beat the dealer. A winning strategy for the fun of twenty-one. – New York: Blaisdell,1962.) which made owners of gambling houses in the state of Nevada essentially change the rules of the game of twenty-one. But let’s not ride before the hounds.

Following 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 same time, out of two cards taken for himself, an official of a casino like Big Dollar online Casino showed one of them usually the first one to gamblers. Gamblers evaluate their cards according to the following scale. Jacks, queens and kings have a value equal to 10 points; an ace could be assigned either 1 point or 11 points, the value of the rest of the cards coincided with their numerical value eights had 8 points, nines took 9, etc.. That gambler was considered a winner who had cards on hand with the sum of points closest to 21 from the bottom. Having assessed the received cards, every gambler (including a croupier) had a right to take from a pack or, to put it simpler, take a “widow”, any amount of cards. However, if, as a result, the total number of points after a widow exceeds 21 points, then a gambler must drop out of a game having shown his cards.

Special rules were established concerning stakes. Initially, upper and lower bounds were set, and every gambler had a right to choose a specific stake (within these bounds) depending on the evaluation of his position. If, as a result, it turned out that following the game rules, a casino’s visitor had a “better” number of points on hand than a croupier had, he received again in the amount of the stake he had made. Otherwise, this gambler lost his stake. In the case of an equal number of points of a gambler and a croupier, the game ended in peace; the result of the game is considered “harmless” both for a gambler and a casino.