Which is correct, gambler fallacy or probability?

Probability, of course. The gambler's fallacy is one-sided. Probability is to look at the problem systematically;

Example:

What is the probability that a coin will face up for the sixth time after you face up for five times in a row? Or 50%?

The gambler fallacy holds that the probability of an event in a random sequence is related to the previous events, that is, the probability of its occurrence will increase with the number of times that the event has not happened before.

If a fair coin is tossed repeatedly, and the tails are thrown several times in a row, gamblers may mistakenly think that there is a better chance of throwing heads next time. This is an informal fallacy.

The gambler's fallacy can be proved by tossing a coin repeatedly. When you toss a fair coin, the probability of heads up is 0.5 (half), and the probability of heads up twice in a row is 0.5×0.5=0.25 (one quarter). The probability of throwing the head three times in a row is equal to 0.5×0.5×0.5= 0. 125 (one eighth), and so on. Now suppose we have tossed our heads four times in a row. The gambler fallaciously said, "The next time you throw your head, it will be five times in a row. The probability of five consecutive head throws is (1/2)5 = 1/32. Therefore, the chance of the next correct vote is only 1/32. "

First of all, one thing is certain: no matter how many heads are hit in front, the chance of hitting the tail next time is always 50%. There is no doubt that this is also the case.

Secondly, this fallacy is actually untenable. The probability of five consecutive positive events is one in 32, which is true. However, this 32 1 is for five consecutive coin-operated events, not 1 coin-operated events! That is to say, if 5 coins in a row are taken as 1 overall events, 32 such events will produce 1 five consecutive positive events. Anyway, it's easy to understand that you regard the coin toss five times in a row as a 1 overall event.