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search for: home casino games and mathematics. part 1. can the knowledge of mathematics help a gambler to win? one can often hear that the best piece of advice given by a mathematician to a lover of gambling games is an assertion 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 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 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 for the fact that development of an optimal strategy of this game became for a number of years an idte fixe” of our hero. 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. though, during the game itself it did not make him very uneasy. however, afterwards, having visited casinos a number of times, he noticed that as the rules did not presuppose obligatory shuffling of cards after each game, so 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 same very 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 in order 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 game 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. 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 the same time out of two cards taken for himself an official of a 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, and etc). that gambler was considered a winner who had cards on hand with the sum of points closest to 21 from the bottom. at that, having assessed the received cards every gambler (including a croupier) had a right to take from a pack or putting it simpler, take a widow”, any amount of cards. however, if, as a result, the total number of points after a widow, will exceed 21 points then a gambler must drop out of a game having shown his cards. special rules were established with regard to stakes. initially, upper and lower bounds were set, and every gambler had a right of choice of a specific stake (within these bounds) depending on the evaluation of his position. if, as a result, it turned out that in accordance 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 amount of the stake that he had made, otherwise, this gambler lost his stake. in case of an equal number of points of a gambler and a croupier, the game ended in peace, that is the result of the game is considered harmless” both for a gambler and a casino. let’s point out that unlike ordinary gamblers a croupier is not obliged to open his cards in that case if the number of points in these cards exceeds 21. moreover, after all the gamblers have opened their cards, and therefore, all the stakes go to a casino gamblers cannot practically find out what was the number of points of a croupier, in order to build their game strategy for the next game (whether to risk or not to stand pat, and etc). it goes without saying, it gives a croupier considerable advantages. besides, all the gamblers are surely aware of this, and, … continue to play. nothing can be done about it, who does not take risks, as is known, does not win. wins and losses of casino gambling gambling is a form of entertainment that involves the extensive use of money as betting instruments. while it can be entertaining as well as enjoyable, indulging excessively in the game can be dangerous, especially when the money involved is already one’s lifetime savings after years of hard work. this is especially true when the form of gambling that one indulges in is that of casino gambling. needless to say, casino gambling has some good and bad effects on a person. in some countries, especially in those areas where islam is the prevailing religion, casino gambling is strictly prohibited. religious authorities in these countries generally frown upon this game of chance basically because of the perceived social costs that it inevitably brings. however, in a number of countries, especially those which are highly-industrialized, casino gambling is a legal business venture, although certain regulations or limits are often set. this is because the game is a double-edged sword. it gives you the opportunity to double or even triple your money. at the same time, however, when you grab that opportunity, you unwittingly also give the game the chance to take away some,if not all, of your money. the stakes easily become higher in the case of casino gambling. in this form of expensive entertainment, there are usually only two ways to go – either you get to double your money or you lose all of it. this is not just small money, the amount involved usually run in the thousands. casinos operate on the basic premise that it allows you to have a crack at their money, but at the same time they get to have a shot at yours as well. who gets to go home as the winner at the end of the game depends on how you will play the game which will have to include the amount of money that you will be willing to place on the betting floor. this is not to say that casino gambling should be banned altogether. the game as well as its concept has been with us for decades. perhaps the game has gone on even for centuries. another thing, as a form of entertainment, it still has its own share of beneficial effects; relaxation being the prime consideration. the key to successfully playing the game is simply to handle it with the proper attitude. gambling to be an effective means of entertainment should be approached as simply a game and nothing more. of course, the aim is to win if possible. but at the same time, a player should not totally discount the possibility that one could also lose. and losing means giving away only the amount of money that you can afford to lose. this is essentially a good strategy, especially when it comes to the issue of casino gambling, where the betting stakes are higher, in which case a planned betting method is recommended. this will include discipline, which basically means having the ability to control yourself, especially when losses start piling up and the winnings that were accumulated in the early games start dwindling because of your casino g
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