Is the casino always winning the customer? Whose side is mathematics on?

Scientists have not concluded when the games began. But certainly a long time ago, in the time of the Greeks and Romans. Gambling gradually became an indispensable component of the social life of famous people. The first legally permissible gambling house, appeared in Italy in Venice in the first half of the 17th century. Casino has become a place not only for games, but also for talking about business.

It is known that Louis Bonaparte was the first visitor to the Parisian entertainment hall and approved of it. In the 19th century the casino was a protected and special place where the guards allowed guests to enter only well dressed.

Anyone who has tried to play at the casino, wondered: “Why does the casino always win? Is there a valid winning scheme?”. Players choose a suitable scheme for victory. Maybe it’s a matter of luck and not math and formulas? Let’s be realistic. Not all casino visitors are very aware of mathematics, and in particular the law of large numbers and Markov chain theory. Perhaps if they were familiar with those theorems, their wallets would not be empty and the casino would not have received such a huge profit.

The games are based on chance. It is and favorite roulette, cards, dice and even slots. For example, in poker the professionalism of the participant will in any case affect the outcome of the game. The same applies to blackjack.

Let’s see point by point. What is the game of roulette?


The word is translated from French as the wheel. There is a version that Pascal invented the roulette table who tried for a long time to create a perpetual motion machine. But in no way could he assume that roulette will be one of the most popular games of chance in the world and will have a purely commercial function, aimed at the enrichment of either party.

In this game the institution win is based on the section called “zero”. In the American version it is known as “double zero”. The wheel popularly called the “Spinner” has thirty-seven numbers. In 36 there is a number from one to 26, in the last (37) it is zero. In the American variation there are 38 cells and two of them are labeled “0”. Although they originally invented it in France. But the Americans fell in love with her. This type of roulette quickly became popular in the United States and was called “American”. Roulette with a single branch of “zero” was called “European”. There were many variations of roulette. They even invented the third cell with “0” or reduced the number of numbers.

The player can put either the available figures or their groups. You can also bet on black or red, as well as odd or even numbers. But the amount of profit in this case will be much less than in case, if you hit the specific number or group of figures.

If it were not zero, it would be much easier to win and the player’s chances could be greater. But it turns out that there is still an advantage in the participation of the casino against the player that is 2.7%. In the American variant – 5.4%.

We imagine that the player chooses a certain number and places his bet. Therefore, the chances of winning are 1 out of 37 and the loss is 26 out of 37. Casino receives a good profit according to the formula: (36/37 X 1 peso) – (1/37 X 35 pesos) = 1/37 pesos (more than 2.5 cents).

Of course, the player has a chance of winning, but it is very small and the club has more possibilities to enrich and add the participant’s money to the treasury.

Dice or craps

According to the research of historians, dice were invented in ancient Greece. When archaeologists intervened in the case, they proved that they appeared much earlier. But the game closest to modern dice appeared in England on the threshold of the 11-12 centuries. During the Crusades the soldiers had fun with Hazard. The game quickly became popular. He had a lot of sympathy in the upper strata of society. The dice were then taken to France, where they were named craps.

The rules of the game are very simple. The participant rolls a pair of dice. The benefit depends on the number of points. The player has won, if the amount was seven or eleven, lost, if two, three or twelve came out. There are other amounts that promise neither profit nor loss. The person throws them until they win or lose.

In the game there are other members who make their predictions, trying to guess which result will fall. Casino in this case has nothing to do with the game, as the player rolls the dice and is responsible for the result of the roll.

But again, the casino wins. Why? The size of the bets is such that players will benefit much less than they could, if it were calculated on the basis of probability theory.


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