The mathematical theory of casino games.

It is generally accepted that the main product in the casino is adrenaline. Often we hear that the casino offers to extend the “happy ticket”, they say much less often that the casino sells the service. In fact, the main casino product is the excitement of winning. In this article we will consider the basic principles on which the work of gambling houses is organized, the justification of the institution’s profits, and what role https://www.suissecasinoenligne.com/roulette/ plays in its activities.

Let's start the review by examining the basic mathematical laws on which gambling is built. How are math and casino related? After all, all the games in the casino were invented and developed precisely by mathematicians. Is it possible to use their own weapons to gain an advantage in a gambling house?

Math casino games

Consider the processes that occur in gambling, from the point of view of probability theory, and try to determine whether casino games obey mathematics.

Throwing a coin, it can be argued that any of its sides can fall out with the same probability. There are only two possibilities - either an eagle or a tails will fall out. Is the likelihood that a coin will be tails when tossing a coin is equal to? (50%), that is, we have the right to expect that in half the cases there will be a tails. Often speaking of probability, they use the word chance. The chance that when tossing a coin it will fall tails up is 50%

The probability shows how often the expected result can be achieved, and can be represented as the ratio of the expected outcomes to the total number of all possible outcomes over a sufficiently long period of time with a large number of repetitions.

Mathematical expectation when playing roulette

We calculate the mathematical expectation when playing roulette (the American version with two zero-zero and double zero sectors) at a bet of $ 5 per color (black): 18 \ 38 x (+ 5 $) + 20 \ 38 x (-5 $) = -0.263

As you probably already noticed, in both examples, the value of mathematical expectation has a “-” sign, which is typical for most casino bets. Negative expectation in practice means that the longer the game lasts, the more likely it is for a player to lose.

Casino Edge (House Edge) - the value opposite to the player’s mathematical expectation and showing what percentage of the bets made during the game for a certain period of time is held in favor of the casino. Now we will consider the most popular type of game in the casino, Do you know which one? The most popular casino game in the world is the game of roulette. The casino advantage in European roulette is 1 - 36/37 = 2.7%, in American roulette it is already 1 - 36/38 = 5.26% (due to two zeros) . This means that if you play roulette and bet a total of $ 1,000 for a certain time, then it is likely that in the end, about $ 27 (European roulette) and $ 54 (American roulette) will go to the gambling establishment. There are fewer casino preponderance in board games (Baccarat, Blackjack or Craps), so the chances of winning are higher.

As an example, let's calculate what are our chances in a casino when playing the American version of roulette, the gaming wheel of which, I recall, has 38 sectors (1-36 digits + 2 sectors of zero). Suppose we bet on a number. Payment of the prize, in this case, is made in the ratio of 1 to 36

The probability of winning in this case is 1 \ 38 or 2.63%

Possible player winnings (as a percentage of the bet): 1/38 x 36x100 = 94.74%

Casino percentage: 100 - 94.7 = 5.26%

Mathematical expectation: [(1 \ 38) x 36 (+1)] + [(37 \ 38) x (-1)] = -0.0263

That is, with every dollar you put, the gambling house hopes to earn 2.63 cents. In other words, the mathematical expectation of winning a player when playing American roulette in a casino is -2.6% of each of your bets.