The probability of a favorable result out of all chances can be expressed in the following way: the probability (р) equals to the total number of favorable results (f), divided on the total number of such chances (t), or pf/t. However, this is true only for cases, when the situation is based on net randomness and all results are equiprobable. For example, the total number of possible results in dice is 36 (each of six sides of one dice with each of six sides of the second one), and number of ways to turn out is seven, and total one is 6 (1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1). Thus, the probability of obtaining the number 7 is 6/36 or 1/6 (or about 0,167).  Usually the idea of probability in the majority of gambling games is expressed as "the correlation against a win". It is simply the attitude of adverse opportunities to favorable ones. If the probability to turn out seven equals to 1/6, then from each six throws "on the average" one will be favorable, and five will not. Thus, the correlation against obtaining seven will be five to one. The probability of obtaining "heads" after throwing the coin is one half, the correlation will be 1 to 1.  Such correlation is called "equal". It is necessary to approach cautiously the expression "on the average". It relates with great accuracy only to the great number of cases, but is not suitable in individual cases.

The general fallacy of all hazardous players, called "the doctrine of increasing of chances" (or "the fallacy of Monte Carlo"), proceeds from the assumption that each party in gambling game is not independent of others and that a series of results of one sort should be balanced shortly by other opportunities. Players invented many "systems" mainly based on this erroneous premise. Workers of a casino promote the application of such systems in all possible ways to use in their own purposes the players' neglect of strict laws of probability and of some games.  The advantage in some casino games can belong to the casino croupier or a banker (the person who collects and redistributes rates), or any other participant. Therefore, not all casino players have equal chances for winning or equal payments. This inequality can be corrected by alternate replacement of positions of players in the game. However, workers of the commercial gambling enterprises, as a rule, receive profit by regularly taking profitable stands in the game. They can also collect a payment for the right for the game or withdraw a certain share of bank in each game. Finally, the establishment always should remain the winner. Some casinos also introduce rules increasing their incomes, in particular, the rules limiting size of rates under special circumstances.  Many gambling games include elements of physical training or strategy with an element of chance. The game called Poker, as well as many other gambling games, is a combination of case and strategy. Bets for races and athletic competitions include consideration of physical abilities and other elements of mastery of competitors. Such corrections as weight, obstacle etc. can be introduced to convince participants that chance is allowed to play an important role in determination of results of such games, in order to give competitors approximately equal odds to win. Such corrections at payments can also be entered that the probability of success and the size of payment become inversely proportional to one another.   For example, the sweepstakes reflects the estimation by participants of different horses chances. Individual payments are great for those who stake on a win on horses on which few people staked, and are modest when a horse wins on which many bets were made. The more popular is the choice, the smaller is the individual win. The same rule is also valid for rates of handbook men at athletic competitions (which are forbidden in the majority states of the USA, but are legalized in England). Handbook men usually accept rates on result of the match which is considered to be a competition of unequal opponents. They demand the party, whose victory is more probable, not simply to win, but to get odds in the certain number of points. For example, in the American or Canadian football the team, which is more highly rated, should get more than ten points to bring equal payments to persons who staked on it.  Unfortunately, it is possible to intervene in all these procedures that support the influence of the case. Cheating is possible and quite probable in all kinds of gambling games. The shameful brand stamped on gambling games was mainly the result of the dishonesty of their organizers, and the majority of legislative interdictions are aimed at prevention of cheating. However, the efforts of many governments were directed, primarily, at not prevention of cheating but at collection of taxes (the more, the better) from the gambling establishments. Taxes can be raised depending on the profit of owners of an establishment or from players, as well as directly from turnover of a gambling bank or a TOTALIZATOR.

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