Probability theory wisdom-gambler fallacy

If a person gambles in a casino, such as playing slot machines, and you are unlucky at first and lose a lot at first, then you will have a strong feeling that you will win soon, but this is an illusion. Gambling is a completely independent random event, which means that the result of the next hand has nothing to do with the previous result, and what has happened will not affect the future. We can consider a simple example. Suppose there are six balls in the bottle, and 1~6 is written as the winning number each time. In the lottery, you should randomly choose one of the six balls, and the chances of getting these six balls are equal, all of which are 1/6. Now suppose that the previous Mark Six Lottery did appear more than twice, then when you draw this lottery ticket, will you, these balls won't remember you at all, and the probability that anyone who won the second ball won't come and let you draw is still 1/6. The law of large numbers does exist in probability theory. For example, if you draw a lottery enough times, the probability of different results is equal to their probability. For this example, if you draw enough, you will get the result of two and the result of six. However, people often misunderstand the theorem of random large numbers and think that randomness is uniform. If what happened in the past period of time is not so unified, people will mistakenly think that they will try their best to smooth it out when returning, and the extra 2 will balance the extra 6, but the working mechanism of the law of large numbers is not balance. What he really means is that if you draw more sweepstakes in the future, you will get so many twos and so many sixes, and your previous mistakes will become insignificant. We often, uh, some people think they understand this probability. They will write, for example, the number two has been out for three consecutive periods, then the number six has been out for five consecutive periods, then there are two winning numbers in the next period, and the probability of occurrence is obviously greater than six. This is completely wrong. The probability of two and six appearing next time is equal. This is a famous mistake, known as the gambler fallacy. Everyone in casinos all over the world is making this mistake. Looking back now, this is actually a very simple truth. But this kind of mistake is staged in different ways in life. For example, there is a joke that a person always carries a bomb when flying. He thinks that no terrorists will blow up a plane, because it is very unlikely that there are two bombs on a plane at the same time. For example, a soldier said on the battlefield that if a bomb explodes next to you in a battle, you should jump into the crater quickly, because it is unlikely that two bombs will hit the same place, which is caused by ignorance of independent random events.