Traders will all talk about "probability" and know that they need to buy and sell with the trend on the chart. Baccarat players also know "probability", and there will be various numbers on the road sheet to assist decision-making. But many of these "probabilities" are not "high probabilities", and there are many cognitive biases in them...
? ? First, ask a question about a game: tossing a coin, if it is thrown for the first time The result is positive, the second time is positive, the third and fourth time are also positive. What is the probability of heads coming up on the fifth toss? My friends and I have discussed this issue before. Some think the probability of the fifth throw being heads should be 1/32 (1/2 to the fifth power), while others think the probability of the fifth throw being heads is still 1/32. 1/2. So which one is correct? The actual probability of the fifth throw being heads is 1/2. At this time, those friends who think it is 1/32 fall into the gambler's fallacy.
Let’s first look at what is the gambler’s fallacy? The gambler's fallacy is also called the Monte Carlo fallacy. Monte Carlo is the name of a large casino in Monaco. Monaco is a small country located in southeastern France. Because its gambling industry is particularly developed, it is also known as the gambling city. Gambler's fallacy, which is a fallacy of probability, believes that the probability of an event occurring in a random sequence is related to previous events. That is, the probability of an event occurring increases with the number of times the event does not occur.
? Returning to the coin-tossing game, first of all, we must make it clear that each coin toss is a random event, and the probability of heads is 1/2. The result of the first coin toss does not affect the second toss. In the same way, the second, third, and fourth times will not affect the result of the fifth coin toss. Some people may be curious. The probability of heads after tossing a coin five times should indeed be 1/32. So why is the probability of heads after the fifth toss in the game 1/2? So we need to clarify another point - when to calculate the probability of a positive result. If before tossing a coin for the first time, we calculate the probability that all five tosses will be heads, then it is indeed 1/32, because we need to calculate all the possible situations of tossing five times in advance, which is five times 1/2. power. After tossing the coin four times, since the results of the four heads are known, the probabilities of the first four times are not included in the calculation. If the game calculates the probability of heads appearing for the fifth time, it is still just a random event. Naturally, there are only two possibilities, positive and negative. The probability of it throwing heads is 1/2!
Regarding this coin tossing game, some people use the law of large numbers to explain it. The law of large numbers means that if the experiment is repeated many times under the same experimental conditions, the frequency of random events will be closer to its probability. That is to say, as long as you toss enough times, the number of heads and tails that appear in the end must be half and half. This also shows that chance contains some kind of inevitability.
? As for the probability cognitive bias, it will be believed that if there have been four consecutive heads, then the probability of tails appearing for the fifth time must be higher than that of heads. Because according to the law of large numbers, the number of heads and tails should be equal. But if there are four consecutive heads, it is far from reaching the number of samples that meets the standard of large numbers. Even if it is ten, twenty, or even fifty times in a row, it cannot be compared with the "number" in the law of large numbers. We can regard the number of times in this law of large numbers as close to positive infinity, so using the law of large numbers to analyze the probability of the fifth coin toss is wrong!
In addition, there is also a fatalistic mentality that believes that randomness is just a pseudo-random table. The more positive results are removed from the table, the more negative results are left. According to fatalism, in the coin tossing game, there have been four heads, so the fifth time tails must be more likely than heads. In fact, the fatalism here is similar to the law of large numbers above. It also makes the mistake of too few samples. Since the number of coin flips is not enough, it cannot be used for reference.
There are many things in our lives that are related to the gambler’s fallacy and probability cognitive bias. It is very necessary to clarify the correct calculation of probability.
If next time my friend tells me how fun the casino is and how much money I win, I will first recommend him to read this article, and then recommend him to do futures! ^_^