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search for: home casino games and mathematics. part 2. thorp managed to find out that owners of gambling houses gave their officials rather strict directions with regard to the strategies which they should stick to in the game with visitors. control over fulfillment of these directions had its initial aim to prevent from a frame-up of a croupier with the rest of the gamblers, a chance of which could not be excluded. assigned for a croupier strict rules determining his game strategy really substantially reduced a probability of such a frame-up, but on the other hand, allowed an advanced” gambler to rather adequately reveal the essence of this strategy and effectively oppose it. for unlike a croupier a gambler needn’t show the first of the received cards, as well as isn’t enchained by any strict rules as regards his strategy, that is why flexibly changing his behavior he can confuse a croupier. for example, thorp found out that practically in all gambling houses of nevada state croupiers were strictly ordered to keep away from a widow in case the amount of points in his cards exceeded or was equal to 17, and a player, from our mathematician’s point of view did not have to miss an opportunity to make use of the knowledge of even some aspects of a croupier’s strategy for achievement of his aims. thus, those advantages which had an official of a gambling house from the start (as we already know, he is not obliged to open his cards at the end of the game), can be compensated to a certain degree for the knowledge of a player about the strategic “tunnel vision” of a croupier. besides, as has been mentioned, thorp, while building his strategy presumed that cards were not often shuffled, in particular, if after finishing of a regular game there were still cards left in a pack, a croupier did not collect the thrown-away by the gamblers cards but dealt them anew (and the next game was played), and only after complete exhaustion of a pack, an official of a gambling house collected all the cards, thoroughly shuffled them and a new cycle” began. naturally, if a gambler had a good memory he could change his strategy depending on the knowledge of the cards which had gone out of the game, and what cards could still be counted upon. it is important to remember that a croupier himself who was to strictly follow the directions of the casino’s owners practically without changing his strategy! thorp set himself a task to formulate the rules which would allow him to calculate probabilities of taking out one or another card out of an incomplete pack. knowing these probabilities a gambler could already with reasonable assurance draw cards from the widow without being too much afraid of a pip out”, and besides, on the basis of the knowledge of some aspects of a croupier’s strategy to make suppositions about those cards which he had, and other gamblers as well. naturally, as a gambler was to make a decision with regard to a widow very quickly, the sought rules for calculation of probabilities were to be rather simple for a gambler to be able to use them in mind” with the help of neither a calculator, nor a pen and paper (even if we suppose that a gambler will be given a chance to do calculation on paper, it will certainly arise suspicion). edward thorp managed to solve this mathematical problem having created rather simple algorithms for calculation of probabilities of taking out of one or another card from a pack, and using them to build a strategy of the game of twenty-one which would not be very complicated, allowing a gambler to considerably increase his chances of winning! as the hungarian mathematician a.reni states after a few days of presenting his report on the obtained results at the meeting of the american maths society in 1960 in washington thorp received from a businessman a letter with a check for 1 thousand dollars intended for checking of a winning strategy in practice. thorp accepted the check and having learnt the formulated by him rules left for nevada to try his discovery. the trial went well: less than after two hours thorp won 17 thousand dollars. needless to say, the owner of a gambling house didn’t share thorp and his companion’s delight with regard to a successful comeout of the trial and the next day did his best to prevent thorp from joining in the game. later on thorp tried to penetrate into other gambling houses, but the news of him had already spread far and wide, so that the doors of all the gambling houses appeared to be closed for him. several times having adjusted a fake beard or having got a make up of a chinese, thorp managed to get to the gaming-table, but in any disguise his constant gain invariably gave him away. thorp had to refuse from further checking of the strategy developed by him”. though “additional checks” were necessary” only to enrich the pockets of the talented mathematician. one could hardly doubt that e.thorp managed to create a real winning strategy! however, since he could no longer benefit from his discovery himself, he decided to render welfare assistance” to his colleagues having published in 1961 a small article in an american academic journal (thorp e.o. “a favourable strategy for twenty-one”, proc.nat.acad.sci., 47, 110-112, (1961)). and despite the small size of the article and, consequently, an extremely condensed form of persentment, made it comprehensible for rather a narrow group of professionals, one can be sure that a number of american scientists and their friends certainly “improved” their material situation (owners of gambling houses were unlikely to read scientific magazines at that time). best casino gambling pay-outs nobody comes to a casino simply because they want to have fun. underneath this vague reason is the desire to bring home cash, and lots of it. indeed, casino gambling is a way to get your hands on lots of cash in a short time. however, it can also be the way to lose cash in an even shorter time. the thing with casino gambling is that the games have different pay-out rates. for example, spending half an hour in the slots will not help you reach the hundred dollar mark unless you win the jackpot. but if you go and spend time at the roulette table, you can reach the 200-dollar mark without waiting for 30 minutes. likewise, you could lose all your casino gambling money at the roulette table in a shorter time than it will take you to lose $10 at the slots. the trick to maximize casino gambling profits is to choose the right games to play. high pay-out games usually give you more money for limited funds. however, skill is highly needed in playing these games. being a novice and attempting this game with the more experienced players only make you lose your funds. the rules may vary in different casinos, but still the most favored high-paying games are blackjack and video poker. depending on your casino’s blackjack rules, blackjack is a game wherein a player can expect high returns providing he plays wisely. there are many variations in blackjack rules like the number of card decks, splitting and doubling bets, and other rule variations. years back, most casino gambling websites offer great odds. if played strategically, the player even gets valuable advantage. however, rules change and now, the odds are in the casino’s side regardless of the player’s strategy. so to ensure good pay-outs in playing blackjacks, it is to your favor to seriously consider being an advance blackjack player. of course, not everyone is born with jacks and aces in their hands. but learning good blackjack strategy is easy. there are many free and downloadable blackjack software tools that you can download and practice on. also, blackjack books are available at most bookstores. these books are usually authored by top blackjack players who have gained fame and fortune in playing the game. don’t frown because nothing is easy these days. being a winner requires effort, so that at least you can enjoy yourself doing it. with regul
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