Here is a player in a casino feverishly looking at roulette, a ball measures the way, or a slot machine decides the fate of your money. The player lost, but very, very soon he will recoup. After all, so many times unlucky, the unnecessary fell out. So, now it will definitely win, well, according to probability theory, bad probabilities end each time. No, they do not end there. Every time roulette begins its journey, it is always a journey from scratch. Because repeated drops of the same color are independent events. And you shouldn’t hope much, it’s better to read the textbook or at least this article.
Without extremes
Of course, as in a casino, it rarely happens in life. In life, everything is riddled with threads of interdependence; God does not play with chance. But we are not considering life processes, but probability theory. 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 be critical of the 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 you randomly pulled out a black chip for the first time, the probability of drawing the next time white is greater. That is, two events - drawing chips of different colors - turn out to be dependent. But if you add the same black chip after stretching black and try to pull the chip again, then these will be independent events.
On practice
Roulette players often think that if they weren’t lucky the previous time, then now they will certainly be in the queens, it seems like the total “amount of luck” is a constant. However, the independence of events during roulette rotation is obvious even to people who are not experts in probability. With slot machines it is even easier - they are designed for a certain number of wins. Independent events? No, addicted. The only caveat is that the calculation when programming the machine is that the total amount contributed by the player is partially returned to him in the form of winnings, but the player gradually gets rid of his money a few times. So if you want to play with luck, do not play more than two or three times. The more you play the machine, the more you lose. And roulette in comparison with a slot machine is generally quite difficult.
Probability math
Let's say red and black fall out by chance. And the probability of falling out of one color will be 0.5. Do you want to assess the likelihood that one color will fall out twice in a row? This is not difficult, although not obvious. To find the desired one, you need to multiply the value of one probability by the value of the second, that is, it turns out that the probability of falling, 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 insignificant. But three times in a row red will fall in probability 0.125. Not so much.
So all double games are a trap for not-so-smart people, and it seems that it was invented by the creators of casinos and bookmakers. And in general, all casino game strategies with probability are a variant of magic, and not a reasonable calculation. The only way to win is to deceive the “human factor”. But this sometimes affects criminal law.