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. "
The above demonstration steps are fallacious. If a coin is fair, the probability of throwing its tail is always equal to 0.5 by definition, and it will not increase or decrease. The probability of throwing tail is always equal to 0.5. The probability of throwing the head five times in a row is equal to 1/32(0.03 125), but this means before the first throwing. After throwing the head four times, because the result is known, it is not included in the calculation. No matter how many times the coin has been thrown, the chances of throwing heads and tails next time are still equal. In fact, the probability of 1/32 is calculated based on the assumption that the first positive and negative opportunities are equal. It is a fallacy to think that it is more likely to throw a negative because it has been thrown many times before. This logic only works before the first coin toss.
The famous Martinagle lose-lose system is an example of gambler's fallacy. The operation method is that the gambler bets 1 yuan for the first time, bets on 2 yuan if he loses, enters 4 yuan if he loses, and so on until he wins. This situation can be explained by the mathematical theorem of random walk. This system or similar systems take great risks to get small returns. Only with unlimited capital can this strategy succeed. So it's best to put a fixed amount at a time, because it's easier to estimate the average hourly winning or losing amount.