"If you don't take this basic, but some unnatural, basic mathematical probability method as a part of your life, then in the long life, you will be like a person who kicks one leg in an ass game. This is equivalent to giving others a huge advantage. " Charles Munger.

First, the nature of the world.

Probabilistic thinking is to look at the world from the perspective of probability, think about problems and make decisions. The idea is actually very simple. The higher the probability, the greater the chance of winning and the better the result. Failure to pursue absolute security and stability will lead to missed opportunities. Nor will we take risks by "courage", but we will make more rational choices by probability.

Probability originated from the story of mathematicians Fermat and Pascal, who solved the classical problem of points with letters and laid the foundation of conceptualism. Since then, "unknowable" has become "uncertain", "unknowable" means that there is no way to the future, and "uncertain" means that we can know the probability and make predictions.

The probability of feeling is about 50%, and the probability of knowing is 50. 1%, which is very different. According to the law of large numbers, if the probability of finding it is 50. 1%, as long as you insist on betting, you will definitely make money and earn a lot of money. The probability of feeling is about 50%, and you don't know whether it is greater than 50% or less than 50%.

There was once a gambler who also studied probability. He once thought, what is the probability that there is at least1"6" when you roll the dice four times? He thought it was 1/6 every time and 4/6(2/3) every four times, much more than 50%. Sure enough, he won a lot of money in this way. Later, he studied the probability that two "6" appeared 24 times in a row on two dice. He thought that the probability of two sixes appearing every time was 1/36, and 24 times was 24/36 or 2/3, so he bought it again, and this time he lost miserably.

What's the problem? The probability is wrong. Later he found Pascal and knew how to lose.

When the dice are thrown four times in a row, there is at least a probability of 1 "6 ":

P = 1 -(5/6)^4 ≈ 5 1.8%

The probability that "12" appears at least 1 time when the dice are rolled 24 times in a row:

p = 1 -(35/36)^24≈49. 1%

Charles Munger said: For us, investing is equal to going out to bet on horses. We are looking for a horse with a half chance of winning and odds of three to one. What you are looking for is a bet with wrong odds. This is the essence of investment. You must have enough knowledge to know whether the odds of gambling are wrong. This is value investment.

The most basic thing of probabilistic thinking is to calculate expectations. Knowing the probability of success can make a better choice.

Second, expectation and variance.

Mathematical meaning: it is the average value.

Calculation formula: e (x) = p1x1+p2x2+pnxn.

Example: What is the expected number of dice points?

1*( 1/6)+2*( 1/6)+3*( 1/6)+4*( 1/6)+5*( 1/6)+6*( 1/6)=3.5

A gambling game, the winning profit 100 yuan, the probability is 50%, and the losing loss 80 yuan, the probability is 50%. Should we participate?

Simply calculate the expectation: e =100 * 50%-80 * 50% =10 yuan. Can participate.

Buffett said: "The probability of loss is multiplied by the amount of possible loss, then the probability of profit is multiplied by the amount of possible profit, and finally the former is subtracted from the latter." This is what we have been trying to do. This algorithm is not perfect, but it is as simple as that. "

In order to make the expectation become positive or larger, it is necessary to improve the income and success probability, and reduce the loss and failure probability.

An obvious way to make money through the probability system is the casino. In ancient times, the probability of buying a size in a casino was the same, but the probability of buying a size for another size was even greater, and the expectation became positive, which was sure to make money in the long run.

Modern casinos, although it seems that the probability is equal, will draw, for example, 2% of the money won as a casino draw. For gamblers, you don't have to smoke if you lose, but only 2% if you win, which seems to be a good deal. But it is this 2%, the casino's expectations will become positive, and in the long run, it will definitely make money, and gamblers will definitely count money. Gamblers want to win the banker's money by luck, and the banker depends on probability. From the moment the gambler enters the arena, winning or losing is already doomed.

Similarly, the exchange of stocks and coins. In fact, in the short term, trading the nature of all casinos, because the exchange charges transaction fees, is a bit similar to the casino's draw, or there is no possibility of losing regardless of winning or losing, which is even more ruthless.

The most commonly used tool for calculating expected value is "decision tree". You can read another article, Decision Tree-How to Make Decisions in the Face of Uncertainty.

2. Variance: Sometimes, it is not enough just to know the expectations.

Mathematical meaning: dispersion, fluctuation and risk.

Calculation formula: d (x) = [(x1-x) 2] * p1+[(x2-x) 2] * p2+ ...

Example: What is the variance of the number of dice?

( 1-3.5)^2+(2-3.5)^2+ (6-3.5)^2=8.75*( 1/3)

Sometimes, expectations are not enough.

For example, in the above example, in a gambling game, the winning profit is 100 yuan, with a probability of 50%, and the losing loss is 80 yuan, with a probability of 50%. Did you take part in the gambling? We have come to the conclusion that according to our expectation, we will participate, and I think you are willing to participate.

However, if we add a word to the original question, the gain won is 6.5438+0 million yuan, and the loss lost is 800,000 yuan. Are you still willing to participate? You may want to think about it at this time. Why? Because the risks are different.

Different people have different risk tolerance. For some people,1100,000 yuan and 100 yuan are tolerable losses, so it is more likely to make decisions as expected. But if a person saves 400,000 yuan to buy a house, then the risk is unbearable and the possibility of buying is not great.

Variance describes the magnitude of fluctuation or risk. It is expected to be 6,543,800 yuan, which does not mean that it will definitely earn 6,543,800 yuan. You also need to consider the size of the risk.

Third, it is always difficult to apply "probabilistic thinking".

Probability is something closer to the essence of the world, but it is actually more difficult to use probabilistic thinking in daily life.

The first step of probabilistic thinking is to "probability" some things in daily life, but the probability of many things in daily life can't be quantified, and neither can the probability. For example, if I buy a class and join a community, what is the probability that I will gain something? What are the chances (how many things can be harvested)? These are difficult to quantify.

In addition, the human brain is not good at probabilistic thinking, so it will avoid thinking like this, because it takes too much brain power. For example, if you take a course, you don't think: What are the chances that I will benefit from taking this course? What can you get? Can it exceed the course fee I paid?

Although both internal and external causes make "probabilistic thinking" difficult, we still need to force ourselves to skillfully use this way of thinking. If the probability and odds can't be quantified, assume one first, and then verify it, so that you can have reference when you make a decision next time. The human brain is not used to "probabilistic thinking" by nature, so it forces itself to think like this with some tools.

There must be a huge difference in thinking quality between people who are used to probabilistic thinking and those who never use probabilistic thinking. Munger said: "I have worked with Buffett for many years. He has many advantages, one of which is that he can think automatically according to the decision tree theory and the basic principles of arranging team members. "