### Education, The science

# Dependent and independent events. About Casino

Here is a player in the casino feverishly looking at the tape measure, the ball measures the way, or the slot machine decides the fate of your money. The player lost, but in fact very, very soon he will recoup. After all, so many times no luck, it was not necessary. So, now he will definitely win, well, according to the theory of probability, bad probabilities end with each time. No, they do not end. Every time roulette starts its journey, it is always the way from scratch. Because multiple fallouts of the same color are independent events. And it is not worth much hope, it is better to read a textbook or at least this article.

**Without extremes**

Of course, as in a casino, life is rare. In life, everything is permeated with threads of interdependence, God does not play with accidents. But we are not considering life processes, but the theory of probability. Dependent and independent events are simply terms. When a person does not see the connections in the world - this is a sign of low intelligence, when he sees too many connections - it looks like paranoia, especially if there is an inability to take a critical approach to arguments. So it's better without extremes.

**Subtle difference**

What are dependent events? For example, you have a bag with black and white chips, there are a certain number of them and the number of two types is equal. If the first time you accidentally pulled out a black chip, the probability of pulling the next time white - more. That is, two events - pulling chips of different colors - turn out to be dependent. But if you add the same black chip after drawing black and try to pull the chip again, then it will be independent events.

**On practice**

Players at roulette often think that if the previous time they were not lucky, now they will definitely be in the ladies, sort of like the total "amount of luck" is a constant value. However, the independence of events during roulette rotation is obvious even to people who are not specialists in probabilities. With slot machines is even easier - they are designed for a certain number of winnings. Independent events? No, the dependent. The only caveat - the calculation when programming the machine is that the total amount paid by the player is partially returned to him in the form of winnings, but several times the player gradually gets rid of his money. So if you want to play with luck - more than two or three times do not play. The more you play the machine, the more you lose. A roulette in comparison with the machine - it's generally quite difficult.

**Probability Mathematics**

Let's say red and black drop out randomly. And the probability of falling out of one color will be 0.5. Do you want to estimate the probability that one color will drop out two times in a row? This is not difficult, although it is not obvious. To find the desired one, the value of one probability must be multiplied by the value of the second, that is, it turns out that the probability of dropping, say, red two times in a row is 0.25. And even then you will see it only on a large number of roulette spins. Errors will be, but they are immaterial. But three times in a row red will fall in the probability of 0,125. Not so much.

So all the games "for doubling" - a trap for not very smart people, and it seems, invented by the creators of casinos and bookmakers. And in general, all casino strategy games with probability - this is a version of magic, not a reasonable calculation. The only way to win is to deceive the "human factor". But this sometimes affects criminal law.

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