In the gambling industry, much, if not all, depends on the accuracy of the mathematical approach. Gambling house operators and professional gamblers know about this, but those who make plans to get rich quickly in the casino, hoping only for luck, do not want to think about it.
In order to understand the game, you need to know several defining factors, the main ONE being the EXPECTED VALUE . This is the sum of the products of all possible values of a random variable and the probabilities of these values (this is quite simple, if you think about it). Often referred to as mathematical expectation is just the average value. In relation to gambling, mathematical expectation means the PREPONDERANCE of a GAMBLING HOUSE (Casino), which is expressed as the ratio of the average win/loss to the value of the initial bet. The mathematical expectation of each individual hand is the average win/loss on these cards of the player. Actually, the sum of the mathematical expectations of all possible layouts is the total mathematical expectation of the game.
At the same time, the expected value is not the ratio of the average loss to the total amount of money put on the table by the player, since in some games, for example, blackjack or poker, the player can raise the bet after the cards are dealt to him. An additional bet increase does not participate in the calculation of the mathematical expectation of the game/layout when determining the actual value of the BET MADE ( INITIAL BET), but it increases the risk. To compare different games using this parameter, a different value is used – the element OF RISK . The risk element is the ratio of the average win/loss to the total amount of money placed on the table as a bet. This value also allows you to evaluate and compare different games for their profitability and riskiness.
The reason why the casino’s advantage is calculated relative to the initial bet, rather than the average bet, is that if, for example, a player knows that in a given game his advantage is 0.1%, then he can determine that the average win for each$ 100 bet will be 0.10 cents.
There is also such a thing as STANDARD DEVIATION (STANDARD DEVIATION) – a value that characterizes the fluctuations of the Bank when playing this game. As a rule, it is used to determine the probability that the result of a given game session will be within certain limits. The standard deviation of the final result after N bets is the product of the standard deviation for one bet and the square root of the number of initial bets made in a given game session. This is done under the assumption that the bid value is always constant. The probability that the outcome of the session will be within the 1st standard deviation from the mathematical expectation is 68.26%. The probability that the outcome of the session will be within 2 standard deviations is 95.46%. The probability that the outcome of the session will be within 3 standard deviations is 99.74%.
These concepts are used by everyone who treats gambling as a business. They also affect those who ignore math. And the less a person associated with the gambling business pays attention to the mathematics of games, the less likely they are to win.