Why are some people always reluctant to leave the gambling table?

Author: Wu Quan

A coin has only two sides, heads and tails. So, each time you toss it, the probability of getting heads is one in two. Toss it twice, and the probability of getting heads twice in a row is one in four. Toss it three times, and the probability of getting heads three times in a row is one in eight. And so on, the probability of getting the same result consecutively is getting smaller and smaller.

Now, suppose I am a gambler, gambling in a casino, betting on guessing the size. Guessing the size is essentially similar to flipping a coin, the probability is 50-50. I guessed small for 3 consecutive times, but all the numbers came up big for 3 consecutive times. At this time, I thought to myself, since the probability of getting all the numbers big for 4 consecutive times is only 1 in 16, then the probability of getting small in the next round must be even higher, so I will continue to guess small in the next round!

Do you think I'm right? It sounds reasonable, but if you think so, you're falling into the classic gambler's fallacy.

In fact, although the probability of getting a big number in four consecutive bets is only one in sixteen, the probability of getting a big number or a small number is always 50-50 for each bet. Not to mention that the previous bets got a big number three times in a row, even if the bet got a big number 300 times in a row, when the results of these 300 bets are settled and the 301st bet is started, the probability of getting a big number or a small number is still 50-50 - in other words, each bet is an independent event, and no matter what the previous results are, they will not affect the probability of a single bet.

In fact, if we replace "big and small" with "win and lose", it is the same. When guessing big and small, my probability of winning and losing is also 50-50 in each round. No matter whether I lose more or win more in the previous round, every time a new round starts, my probability of winning is always 1/2.

Unfortunately, many gamblers cannot see this point. They always think that since they have lost many bets in a row tonight, the next bet must have a higher chance of winning. It is with this mentality that they gamble one bet after another and cannot stop, and even borrow usury to try to win back the "next bet".

This fallacy is not only committed by gamblers. The reason why the gambler's fallacy is so deceptive is that it has its root in the "law of small numbers".

Theoretically, if I bet on the size for 100 million times in a row, the distribution of the number of times the number is big or small is indeed very close to 1:1. However, if it is only a few times, dozens of times, or even hundreds of times, these times are too few - in such a small sample size, any kind of distribution is possible, and it is very likely that the number will be big or small for a certain number of consecutive times. No wonder it can confuse people.

In fact, the gambler's fallacy can be seen everywhere in our daily life.

Take applying for a loan from a bank for example. An Indian study found that whether your loan is approved depends in part on the time and order in which your documents are viewed by the examiner. For example, if the examiner approves three loan applications in a row within one day, he or she will be more likely to reject the fourth application. The same is true in reverse: after rejecting several loan applications in a row, it will be more likely to approve the next one. This is obviously unfair to loan applicants.

Similarly, if you participate in the preliminary round of a singing show and the previous contestants have all passed, your chances of passing will be lower. If you participate in a round of interviews at a large Internet company and the previous candidates have all entered the second round of interviews, your chances of being eliminated will be higher.

I wonder if you have similar judgmental tendencies yourself? Be careful next time.