Textual research on Wei's departure from meridian valley

Wei Yan's plan to leave Meridian Valley has been controversial for thousands of years. There are many supporters and many opponents, but they are all general and difficult to refute each other. It can be considered that this plan has the possibility of success and failure. So what are the chances of failure and success?

How many/much? Is it worth taking such a big risk for that little chance of success? Should Zhuge Liang have adopted this suggestion at that time? We try to analyze quantitatively by mathematical methods and explain the problem by numbers.

A quantitative index for the success or failure of the Northern Expedition;

First of all, let's analyze several results of the Northern Expedition, which we think can be summarized into the following seven types:

1. victory, that is, panic in the opponent's main force or slay the enemy commander, such as Guan Yu driving the seventh army, such as killing Sima Yi. Get five points.

2. A small victory means defeating or destroying an enemy unit and gaining material benefits, or killing another general and gaining morale benefits. Get 1 minute.

3. Reactive power, that is, the results of both sides are basically the same. Get 0 points.

4. Small defeat, small loss of troops, thousands of casualties. Get-1 minute.

After the defeat, the army lost tens of thousands of people. Get -5 points.

6. Complete victory, that is, capturing Chang 'an and gaining a firm foothold, greatly improved the strategic situation of Shu and Han. Get 20 points.

7. Great defeat, that is, the main force was wiped out, and even important strongholds such as Hanzhong were lost, which greatly hurt the vitality of Shu Han and scored -20 points.

2. The results of Zhuge Liang's six northern expeditions:

First time: win first, then lose, lose Masu, lose Mengda, but accept Jiang Wei, both sides draw, 0 point.

The second time was because of Wei's attack, and the Shu army withdrew. Wei Yan, however, beheaded the enemy general Xinmeile Joint-stock Company. Still 0 points.

Third time: capture Wudu and Yin Ping, and defeat Guo Huai. Small win,+1 point.

Fourth time: defeating Sima Yi and Cao Zhen should be a small victory,+1 point.

Fifth time: shooting Zhang He, Xiao Sheng,+1 min.

Sixth time: I won several games, but I died of overwork in Wuzhangyuan. 1-5 =-4 points.

In this way, the total score of Zhuge Liang's six northern expeditions was-1 point, with an average of -0. 16 points each time, which was a failure on the whole.

In the previous four northern expeditions, Zhuge Liang adopted the tactics of going out of Yangpingguan in the west, taking a smooth road, taking a step-by-step approach and slowly encroaching on Wei. In this way, although it is easy to use troops and Zhuge Liang is superior to the other side in tactical level, he can win small victories in local battles every time. However, it is undeniable that the comprehensive national strength of Wei and Shu is far from each other, the front is too long and protracted, and the supply of grain and grass is unsustainable.

As a result, the troops retreated every time because of poor food and grass, and the victory was handed over. Zhuge Liang finally figured it out in the fifth Northern Expedition and went out directly.

Gu Jie entered Longdong, and the effect was greatly improved. However, due to Zhuge Liang's previous northern expeditions, Wei was on high alert, and Zhuge Liang's life would be exhausted, leaving only regrets. Therefore, Zhuge Liang wanted to destroy Wei and realize the wish of reviving the Han dynasty, and Wei Yanbing went out.

The plan of Meridian Valley is the only one that is likely to succeed, and it can only be used once.

3. Wei Yan's plan:

"Fake soldiers five thousand, negative grain five thousand, straight out of the door, along the qinling mountains and east, when the meridian and north, but ten days to changan. When Mao Wen arrives, he will escape by boat. In Chang 'an, only Shi Yu, Jingzhao Taishouer, Hengmen Dige and Sanren Valley feed. Compared with the east, there are still 20 days, and people will come from Xiegu. In this way, the west of Xianyang can be decided in one fell swoop. "

4. Many conditions for the meridian valley plan to be feasible:

1. Conditions for a surprise victory: After Liu Bei's death, the people of Shu and Han were always on the defensive, and Cao Wei did not enter the army for several years. Cao Wei thinks that Shu Han people have no strength, so if he sends troops suddenly, he can surprise them.

2. The condition of bullying the small by the big: at that time, Cao Pi had just died, and Cao Rui succeeded to the throne soon, and the national government was unstable; Sima Yi lives in Wancheng; senior general

Cao Zhen overseers the right army, stationed in the north of Gu Jie County; General Anxi Xiahou Mao guarded Chang 'an; Xiahou Mao is a high-eyed dude.

Low hands, no actual combat, is by no means Wei Yan's opponent.

3. Internal cooperation conditions: Xincheng Mengda can resist Wei at any time and interfere with Chang 'an reinforcements (Zhang), but

Help Wei Yan.

4. Conditions for knowing yourself and yourself: When Liu Bei was in office, Wei Yan was the satrap of Hanzhong and knew the geographical situation of Hanzhong like the back of his hand.

This surprise attack plan is the most suitable candidate.

5. Conditions for attacking the enemy in vain: At the beginning of the Northern Expedition, Sima Yi and Zhang He, famous Cao Wei generals, were not near Guanzhong, and Wei Jun was a dragon.

No head. After the success of Chang 'an, Ye Zhen's army was isolated and unstable, and it was no match for Zhuge. Zhuge Jun went out of Xiegu and defeated Ye Zhen's army.

Difficult, even if Yeh Jun retreats from Chang 'an, Zhuge Jun will pursue from behind, and Wei and Chang 'an will join hands to adowa Yeh Jun; If Cao Zhenjun retreats,

In Longxi, Zhuge Liang sent people to defend according to the risk, and joined forces with Wei Yan in Chang 'an, and Guanzhong and Longyou settled down.

5. Key steps affecting the final result:

1. Can Wei leave Meridian Valley smoothly in 10 days?

(1) The roads in Woods Valley are steep and difficult to travel, and the marching speed is greatly affected by climate and other factors. So Wei Yan's troops may not be able to.

Enough for 10 days. So it is difficult to get food, so we have to retreat, which is a small defeat. This situation is about 1, and the score is: (-

1) ×10% = (-0.1) points.

(2) The Meridian Valley is not very hidden. Marching in the valley is likely to be noticed by Wei Jun, which is 20%. Wei Jun

After the discovery of the Shu army, two measures can be taken. First, defending taniguchi and other dangerous places made Wei Yan retreat, which was a small defeat. Second, in

If Wei sets an ambush in a dangerous place, Wei will basically be completely annihilated, which can be regarded as a great defeat. The two schemes are calculated at 50% each. Zeviyan

If troops are detected, the score is:10 %× (-1)+10 %× (-5) = (-0.6).

2. After leaving Meridian Valley, can Wei quickly defeat Wei Jun and occupy Chang 'an?

Wei has a 70% chance to leave Meridian Valley smoothly. When the defenders of Chang 'an found Wei Yan's troops, they might take three measures.

：

(1) According to the city's defense: Although Xiahou Mao is a pustule, there are still Shi Yu, Jingzhao Taishou and other officials and their strategies in Chang 'an.

To be reckoned with, he will stick to his advice. Considering Xiahou Mao's impatience and belligerence, the possibility of this situation accounts for about 40%.

This is very unfavorable to Wei Yan's troops. Wei Yanxi will fight a tough battle, and Chang 'an is very risky. Wei Yan's troops successfully besieged the city.

The probability will not exceed 30%.

(2) Going out of the city for decisive battle: The probability of this happening is about 30%. Although Wei Yan's military quality is far superior to Xiahou Mao's,

But the soldiers from afar are exhausted, and the number and arms are even less dominant. If Xiahou Mao's troops fail, they may return to Chang 'an defense smoothly. In fact,

Wei Yan successfully defeated Xiahou Mao's troops, and the chance of capturing Chang 'an could only reach 60%.

(3) Abandoning the city: the possibility of this situation accounts for 30%.

Based on the above three situations, the probability that Wei Yan can capture Chang 'an is 70%×(40%×30%+30%×60%+30%).

=42%。

If Chang 'an cannot be captured, the possibility of getting into trouble is 28%.

3. Whether Zhuge Liang can reach Chang 'an before Wei Jun's main force destroys Wei Yan's troops.

If Zhuge Liang's troops want to get to Chang 'an in time, they must either completely defeat the main force of Wei Jun's frontal defense or use a branch.

Team such as suspected soldiers, contain Wei Jun, to enter. Considering the ability of Wei and Shu commanders and the terrain near Yangpingguan, Zhuge Liang

Defeat Wei Jun's main force and successfully rescue Wei Yan's troops should be at least 50%, so Wei Yan's troops are isolated in Chang 'an.

The possibility of land is also 50-50. If Zhuge Liang cannot arrive in time, according to Wei's situation, there are the following possibilities:

(1) At this time, Wei Yan has captured Chang 'an. Wei Yan had to retreat, but if the enemy pursued him, his troops would certainly be damaged.

Lost, and the morale of the troops is easily frustrated, and there is a great possibility of desertion. We think Wei Yan can withdraw most of his troops.

Sex 60%, small defeat. The score of this situation is: 42% × 50 %× 60 %× (-1) =-0.126, and Wei Yan's troops are mainly in Wei Jun.

The possibility of adowa is 40%, and the score is: 42 %× 50 %× 40 %× (-5) = 0.42.

(2) Wei Yan did not occupy Chang 'an at this time: the situation depends on the time that Wei Yan's troops learned that the main force had lost and the situation of Wei's reinforcements.

The marching speed will be different, but the possibility of being wiped out by the Wei army is at least 70%, which is a big defeat. There may be three losses.

Success is a small failure. In this way, the score of this case is: 28% × 50% × 70 %× (-5)+30 %× (-1) =-0.53.

4. If Zhuge Liang's troops arrive in Chang 'an smoothly, can they hold Chang 'an?

If Zhuge Liang's troops arrive at the gates of Chang 'an smoothly, the situation will be different according to whether the combat situation of Wei Yan's troops is smooth or not.

(1) If Chang 'an has not been captured by this time, the situation will be very bad. If Zhuge Liang's main force fights Wei Jun, it will be fought by.

Yu Shu's army is mainly infantry, while Wei has more cavalry. In addition, the flat terrain near Chang 'an is conducive to cavalry fighting and confronting Zhuge Liang's department.

The team will be at a clear disadvantage. Zhuge Liang's best choice at this time was to rescue Wei Yan's troops and retreat in time. But the difficulty of safe evacuation is not small.

Chanda At this time, there may be five results:

1) successfully defeated Wei Jun's first unit, with a small victory probability of 10% and a score of 28%×50%×20%×(+ 1).

=0.028

2) Defeat Wei Jun reinforcements, retreat, and win a total victory. The probability is only half, and the score is 28%×50%× 10%×5=0.07.

3) Defeat Wei Jun's main force and occupy Chang 'an. In order to win completely, the possibility is only half. Score: 28%×50%×5%×

20=0. 14

4) basically retreat safely, but the troops suffered small losses, which was a small defeat. The probability is about 30%, and the score is 28% × 50 %× 30 %× (-

1)=-0.042

5) Being defeated by Wei Jun's main force, with heavy losses, is a big defeat, with a probability of about 30% and a score of 28% × 50% × 30% × (-

5)=-0.2 1

6) The whole army was annihilated or pursued, endangering the safety of Hanzhong. 20% probability, complete failure. The score is 28%×50%×20%.

×(-20)=-0.56

In this way, the comprehensive score of this situation is: 0.07+0.14+(-0.21)+(-0.042)+0.028+(-0.56).

= (-0.57) point

(2) If Wei Yan's troops had captured Chang 'an by this time, the situation would be greatly improved: Zhuge Liang could hold on to Chang 'an or cooperate with Wei Jun.

Field battle. The commanders of the counties near Chang 'an are mostly incompetent, and it is impossible to pose too much threat to the Shu army without surrendering. At this time, Wei has 3

Those who succeed may give up Chang 'an, and 70% may send troops to attack. Cao Zhen is no match for Kongming, even Sima Yi is not too big.

A chance to win. The Shu army can eat in the enemy country, solve part of the problem of rations, and immediately let Jiang Wan and others transport the food here, so that Chang 'an can be basically gone.

Worried. At this time, there are the following possibilities:

1) Wei gave up Chang' an: To achieve complete victory, there is a 30% chance: the score is 42% × 50% 30% × 20 = 1.26.

2) Wei will not give up Chang 'an: At this time, the situation is very complicated, which can be roughly summarized into two possibilities:

& lt 1 & gt； Mengda responded at an appropriate time and went to Shang Yong, Xincheng and other places. He said that they were riding on the city and wanted to go to Shu, but they were heard.

The news will be chaotic. Sima Yi has nothing to do, and Cao Xiuzhi's generation is too late to move when they hear the news. If Mengda succeeds, Soochow will definitely send troops to meet him.

Cheap, Chang 'an worry-free, it is even possible to capture Luoyang and defeat Wei in one fell swoop. The probability is 80%.

Score: 42% × 50% × 70% × 80 %× 20 = 2.35.

& lt2> Wei's attack on Chang 'an is unlikely to exceed 20%.

Score: 42 %× 50 %× 70 %× 20 %× (-20) =-0.59.

In this case, the comprehensive score of this situation is 1.26+2.35-0.59=3.02.

The final score of Wei plan:

Based on the above four categories, Wei Yan's final score is:-0.1-0.6+0.42-0.53-0.57+3.02 =

1.64

Far higher than Zhuge Liang's score of -0. 1.

Conclusion:

Wei Yan's plan, although the possibility of realization is not very high (about 35%), once it is realized, it will gain huge benefits, even losses.

Defeat, the loss to the Shu army is not great (the possibility of complete defeat is less than 10%), which can be said to be an investment with medium risk and high return.

, is feasible. However, due to the disparity of Wei Shu's national strength and strength (the land area is 4: 1 and the military strength is 7: 1), in order to realize Liu

The long-cherished wish of the compilation is that only by surprise attack, using strange tricks and taking strange risks can we get ahead. So, there was the meridian valley plan put forward by the strange man Wei Yan.

This is necessary.

So leaving the meridian valley was the only choice at that time.