If people seeking to beat a casino have studied some sections of probability theory, then they would have managed to save a lot of money

## Roulette

In the roulette, the profit of the institution guarantees the Zero section, and in the American version, also Dabble Zero. The wheel, or “turntable”, is divided into 37 cells, 36 of them put down numbers from 1 to 36, and in the last – zero (in the USA 38, of which two zero). You can put on specific numbers or groups of numbers or on “equal chances”: black-red and even,. Profit when falling out numbers is much higher than when guessing color or parity.

If there were no Zero cells, the probability of winning for a player who put, say, on black, would be 18/36, or 50%. But because of another cell, it is reduced to 18/37. In other words, the institution has an “additional” share of a chance to win – 1/37, that is, 2.7%. In the American version, due to the second zero, the discrepancy is twice as much and is 5.4%.

When a person puts on a specific number, the gambling house also remains in the plus, despite the fact that the winning seems to be generously paid at the rate of 35 to 1. The player’s chances of losing are 36 out of 37, and the chances of winning are only 1 out of 37. That is, from each ruble put on a specific number, the casino will receive

or the same 2.7%. This does not mean that players are always in the red, but they have much less chance of leaving with extra money than to lose their existing.

## Bones, or Craps

The rules of the game are straightforward: the player (shooter) throws two bones, and if the sum of the glasses on them is 7 or 11, he wins if 2, 3 or 12 – loses. When another amount falls on the cubes, the shooter throws them to the winning or losing combinations. The rest of the participants are betting, trying to guess how the bones will fall.

It would seem that everything is honest, because the casino does not directly participate in the game. Nevertheless, the gambling house remains in profits – the size of the bets is determined so that the participants receive the winnings less than the “set”, that is, calculated according to the laws of probability theory. For example, the chances that combinations of 6+6 or 1+1 will fall on the cubes are 1 to 36, but the rate for them is issued at the rate of 30 to 1. If the winnings were proportional to the probability, then the size of the Kush would be calculated at the rate of 35 to 1. In the same way, the casino underestimates the winnings for other combinations, taking away the difference.

## “One -armed bandits”

The casino is primarily associated with roulette and poker, but, according to statistics, 61% of visitors to gambling houses spend time fighting with “one -armed bandits” (data from the American gambling association for 2013). The rules of the game on automatic machines are extremely simple, and the frivolous minimum bet makes them affordable even for the poorest players.

Once upon a time, the “bandits” were mechanical, and, pulling the handle, the player lowered the spring that spun drums with pictures. Today, the wheels and gears replaced the computer chip, and the cherries, lemons or card nominal nominal nominal are displayed on the screen. As before, a combination of three identical pictures is considered winning.

Formally slot machines work honestly and stop the drums, obeying the teams from the random number generator. In fact, each Bandit is programmed to return to the players a certain percentage of invested money-usually from 80 to 90%, although the share of the Las Vegas casino has been set up to 98%.

There are no contradictions here: the moment of stopping of each drum is really determined by a random number. But the computer does not use the issued value directly.

Instead, the machine calculates according to a certain algorithm: multiplies, divides and translates from the language of numbers to the language of pictures according to pre -compiled tables. And it is here that the percentage of winning results is laid: by changing the parameters of the table, you can make a “bandit” more or less “generous”.

## Damn wheel strategies

Attempts to deceive Fortune for more than one hundred years. On the Internet you can get free, and sometimes for a lot of money, get acquainted with dozens of “one hundred percent strategies” of the game of roulette (for some reason it seems to players that it is easiest to “hack” the wheel). It is useless to fight the theory of probabilities, but people are stubbornly trying.

### Martingale does not work

One of the oldest strategies for playing roulette requires the player to put on red or black (or even-notch) and double the bet when losing. Sooner or later, the player guesses and breaks the bank.

The scheme seems logical, but in fact, the total winning will not exceed the size of the initial rate. Let the player put on black and guesses on the sixth turnover (the players say – the back). Then his balance looks like this:

At every step, the chances of guessing are 18 to 37 because of Zero, so with a sufficiently large number of spins, the player is in the minus.

In addition, Martingale lovers often have to make many attempts and each time to double the consumption. If the money ends earlier than the “strategist” guesses, he will lose a huge amount. Finally, casino owners are well aware of Martingaile, and the size of the maximum rate in all gambling houses is limited. Putting almost the maximum and losing, a person loses a chance to return the money.

### The strategy with positive progression does not work

Unlike fans of Martingale and similar schemes, players using the so -called strategies with positive progression increase bets after winning and most often lower after losing.

The schemes with a positive strategy do not allow to quickly lose, but it will not work to enrich with their help either, because the casino always more likely, no matter what bets the player. The balance when using such strategies looks approximately as follows:

### Favorite number does not work

The player all the time puts on the same number, hoping that the winnings of 35 to 1 will cover his consumption. “Strategists” do not consider that the numbers fall evenly only with an infinitely large number of revolutions. And in a real game with a high probability for 36 spins, the selected number will not play once-simply because some other number will fall twice (by the way, the Biarritis system, also very popular among visitors to casino) is based on this fact).

If lovers to put 36 times in a row on the same number conducted a simple calculation, they would become more pressing. We indicate the probability that for 36 spins the numbers will never coincide, like

We will choose any number as a loved one and we will “check” it with falling numbers. The likelihood that any next spin will give a non -pair of 1 – 1/37 (since there is still a zero, in the denominator of the fraction will be not 36, but 37). The probability that any of the subsequent revolutions will not give a pair again is 1 – 2/37, then 1 – 3/37 and so on. To find out with what probability all numbers for 36 backs will be different, you need to change all these probabilities. In general, the formula looks like this:

Where **!** – Factorial (**m!** – This is a change in all numbers from 1 to M), **n** – The number of wheel turns.

Due to the huge denominator, there will be such a small number that there is not enough space on the screen of an ordinary calculator to show it. For example, for 36 spins, the denominator of the fraction is 2852739177237238760561717108340529278232767461712708093041, and the value itself is 0.00000000000000000000000000000000000000003505. That is, the chances that the numbers will never be repeated for 36 spins, there is practically no.

The probability that for any selected number of revolutions we will get at least one pair is equal

If we calculate this parameter for a specific number of spins, then at four rpm of the wheel, the chances of at least one “twins” will amount to 15%, at 7 revolutions – 45%, and at 18 – already 99.3%!

### Strange

**Office coincidences**

Lottery lovers also often underestimate the power of probability theory. In September 2009, the number of Bulgaria National Lottery fell in the number of 4, 15, 23, 24, 35 and 42. Four days later, these six numbers fell out again. The organizers of the lottery were suspected of fraud, an investigation was conducted that found that everything was honest. The calculation shows that the probability of repeating the six numbers in the Bulgarian lottery, which has been held for 52 years twice a week, is very high.

The result of each draw may coincide with the result of any of the previously carried out. The number of pairs of “six”, which can be made from all the draws, is calculated by the formula:

The idea is similar to the idea of the Biarritis strategy: the chance of winning is especially high after a long series of failures. Subconsciously, it seems to a person that it is impossible to lose all the time and after the black strip he will certainly tear the bank.

The creators of automatic machines spur this hope: “bandits” programmed with increased frequency to issue winning combinations to a level above or below the main line. The player sees that the drum “almost swollen”, and again and again throws the tokens into the monetary receiver.