Order?"

Zhang Yue whispered a few words to Shi Deyi.

Shi Deyi was slightly surprised and then said: "We will go down and prepare now."

After a while, the servant Shi De came to the palace carrying a sealed wooden barrel and handed it to Zhang Yue.

Everyone saw that there was only a hole as big as a bowl in the barrel, but they could not see what was in the barrel.

Zhang Yue immediately raised the barrel and said, "Your Majesty, I asked Shi Deyi to take twenty stones, and an unknown number of them were painted with colored stones. Only Shi Deyi in this palace knows how many colored stones there are."

"I, Your Majesty and Feng Jing will make a bet today. Let's each guess how many colored stones there are in this bucket. Whoever gets closer wins!"

The official smiled when he heard this and said: "Interesting, let me guess first, there are 75%, which is fifteen colored stones."

Zhang Yue smiled and asked Feng Jing, "Where is Mr. Feng?"

Feng Jingdao: "Five colored stones."

Everyone heard that Guan Jia and Feng Jing were blindly guessing the colored stones in the bucket based on the winning rate they just discussed against Xixia.

Although there is no connection between the two, the meaning of anger is obvious.

Zhang Yue said: "Then let me give you a guess. I will guess the number of ten."

After finishing speaking, Zhang Yue said to another chamberlain: "Take four pills first."

After hearing this, the waiter reached out and took out four stones from the bucket, but found that three were colored stones and one was an ordinary stone.

Seeing this, the official smiled and said, "It seems that I have won."

Zhang Yue said with a smile: "Then your Majesty still insists on fifteen, so let me change it. I will change it to twelve colored stones. Mr. Feng, do you need to change it?"

Feng Jing hesitated and said, "I'll change it to seven."

Immediately Zhang Yue said to the chamberlain: "Take four more."

But the waiter took out four more stones, two of which were colored stones and two of which were ordinary stones.

Zhang Yue smiled and said: "Your Majesty, I changed it to eleven. Your Majesty, will you change it?"

When the official heard this, he thought for a moment and said, "If you don't make fun of me, I won't change it."

Zhang Yue looked at Feng Jing and said, "Do you want Mr. Feng to change it?"

Feng Jing pondered slightly and said, "I'll change it to eight."

The waiter took out four more stones from the bucket, but found one colored stone and three ordinary stones.

This time the emperor Feng Jing, Zhang Yue and the others did not change.

Finally, Zhang Yue ordered his chamberlain to pour out all the stones in the bucket. Everyone counted clearly that there were ten colored stones and ten ordinary stones.

Shi Deyi trembled all over, knelt down and said: "Your Majesty, I am indeed so lethargic. I am guilty of death!"

At this moment, no one was smiling, but the official himself looked a little unhappy.

There were no words from the ministers in the palace, especially Feng Jing, whose expression was extremely solemn. Everyone was thinking carefully about the meaning of the story about Zhang Yue just getting the colored stones in the barrel.

The example Zhang Yue gave is Bayes' theorem.

Bayes' formula is a probability theorem in the 18th century. Nowadays, it has been widely used in various aspects such as artificial intelligence.

Everything in the world is a matter of probability. Theoretically speaking, the national football team can also beat the Argentine national team. It is just a matter of probability.

Bayes' theorem is mainly used to find inverse probability, and its specific application is similar to the colored stones in the bucket above.

First take a prior probability and multiply it by a likelihood function.

For example, the emperor said that the winning rate of attacking Xia was 70%, Zhang Yue was 50%, and Feng Jing was 30%. This is the prior probability. Without experiments, no one knows.

Unless you pour out all the stones in the bucket, no one knows how many colored stones are in the bucket.

The same is true for the attack on Xia. If the Song army did not send troops, no one could tell what the chances of victory would be.

Except for the emperor, Zhang Yue, and Feng Jing, as well as Lu Huiqing's 90% and Sima Guang's 00%, everyone actually made a probabilistic judgment based on their own experience.

This is called the prior probability.

Everyone is guessing the blind box.

So first take out four stones from the twenty stones and see how many there are. If you don’t try anything, you will never know what the result will be.

After there are three colored stones among the four stones, a probability of 75% is obtained. This is the possibility function.

You multiply this possibility function by the prior probability to correct your previous guess to get a closer result.

Of course, once is not enough, you have to try it again. The more you try, the closer you get to the real probability.

So there are BO5 and BO7.

A priori means to act before you act, and a posteriori means to act before you know, and it is true knowledge that comes from practice. There has been debate in philosophy for countless years about the issue of a priori and a posteriori.

At this moment, everyone in the palace was silent. Zhang Yue's realization was epoch-making. When most people were still struggling with whether to change the law or not, whether to attack Xia or not, Zhang Yue stood up and said that you are all too low.

What's the difference between you guys making so much noise and guessing the blind box over there?

The prior probability is important, but what we want to improve is the probability issue, rather than standing still and guessing right or wrong.

How to be the only one? How to be the only one?

Those officials say all day long that I do great things without sacrificing my own life, and that I have both sides.

As everyone knows, showhand is a kind of wisdom. You must not blindly bet all your money on the gambling table without looking at the hole cards.

Seeing that none of the ministers could take what Zhang Yue said, the official finally said: "Qing Zhang, it's up to you to explain the meaning in detail!"

Zhang Yue looked around, and all the ministers were speechless at this moment.

Zhang Yue said: "Your Majesty, what I want to say is that the more you practice, the more you know, and the more you know, the more you can practice!"
Chapter completed!