In game theory, there is a logical reasoning problem of "three musketeers".
There were 3 musketeers A, B, and C, who hated each other very much and were ready for a duel.
The armor gun method is the best, with a hit probability of 80%.
B shooting method is second, with a 60% chance of hitting.
The C shot method is the worst, with a 40% chance of hitting.
Obviously, A is the strongest, B is second, and C is the weakest.
If it is a one-on-one duel, C is undoubtedly the most miserable, although he also has a certain probability of winning.
But if three people start together, will the results change?
01
If three people shoot at the same time, and each shoots only one shot, who has a better chance of surviving after the first round of gun battles?
The prevailing view is:
A's marksmanship is good, and it is most likely to survive.
But the truly logical conclusion is:
C, who has the worst marksmanship, has the greatest chance of surviving.
When the three musketeers fired, they were all faced with the judgment that it was in their best interest to shoot the other two.
That is, everyone must have a shooting strategy, not a temporary random shooting.
What is the optimal strategy for three people?
Gunner A: The best strategy is to hit B first.
Because B's threat to A is greater than C's threat to A.
Gunner B: The best strategy is to fight first.
Once B kills A, B and C will have a final duel, at which point B's odds of winning are maximized.
Gunner C: The best strategy is to shoot at A first.
Because B's marksmanship is, after all, worse than A's.
If A is killed and C and B are again dueled, C's probability of survival also reaches the maximum.
Mathematically calculate the odds of survival for the three musketeers:
A: 24% (40% X 60% = 24% by B and C)
B: 20% (100% - 80% = 20% shot by a nail)
C: 100% (no one shoots C)
Isn't the conclusion fantastic?
C is not in any danger, and B is the most likely to be out first.
A is also quite dangerous.
Example:
During the Southern Song Dynasty, Mongolia had the strongest military strength, the Jin Dynasty was the strongest, the Southern Song Dynasty was the weakest, and the three kingdoms were all feuds.
According to the best strategy, the Southern Song Dynasty and the Jin Dynasty should abandon their previous suspicions and form an alliance to jointly resist the Mongols.
The Southern Song Dynasty chose to ally itself with the Mongols.
The result was that Mongolia destroyed the Jin Dynasty in only 2 years, and 46 years later, the Mongols destroyed the Southern Song Dynasty, unified China, and established the Yuan Dynasty.
If the Southern Song Dynasty followed the optimal strategy and first allied with Jin, although Jin still had the greatest probability of being the first to perish, mongolia would also be seriously injured.
During this time, the Southern Song Dynasty recuperated and practiced internal skills, and it was likely that its strength would surpass that of Mongolia, which was seriously damaged in strength, and become the final victor.
The rulers of the Southern Song Dynasty were still short-sighted.
Another example:
In the Russian-Ukrainian conflict, the strength of the three parties is as follows:
A: Europe and the United States, the strongest.
B: Russian army, second strongest.
C: The Ukrainian army, the weakest.
There is also an additional condition:
A and B cannot be used directly because they both have nuclear weapons.
A Best Choice:
According to the above principles of game theory, if you directly participate in the conflict, it belongs to the second tragedy.
Therefore, A does not directly conflict with B, let alone with C.
Instead, it is to assist C and bring its strength closer to B.
B and C consume, both lose, and A gets the most benefit.
B Best Choice:
According to the principles of game theory, conflicts belong to the most miserable side.
Therefore, B cannot choose to clash with A or C unless there is absolute strength to crush C.
If the first shot fails to bring down C, C will choose to hug A tightly and enter a war of attrition.
A long war of attrition is most beneficial to A, B is exhausted first, and C is followed.
At this time, B should choose to find allies and greatly improve his strength, and be equal to A, far exceeding C.
At this time, B and C fought and collapsed, and finally formed a balance with A.
C Best Choice:
Do not fight A or B, choose to coexist peacefully with B, secretly ally with A, and constantly improve their strength.
This is also the process of constantly consuming A and B.
After waiting for your strength to be almost equal to A or B, your own safety is guaranteed, and there is no need to duel.
If you choose to ally with A, it is equivalent to pinning your hopes for survival on A completely, which is very dangerous.
02
In the foregoing, there is an assumption that all three people clearly understand the hit rate of the opponent's gun.
But in reality, each side will hide its true strength, and even deliberately appear weak.
In this way, information asymmetry is formed, so that other parties cannot see the truth clearly, and wrong judgments are produced, and it is possible to eventually change the results.
If A disguises himself, let gunners B and C think that A's marksmanship is the worst.
In this case, the ultimate survivor must be A.
Therefore, the opponent who hides the strength is the most terrible.
Assuming that the three people do not know each other's opponents, now use mathematics to reveal the truth.
A faces 4 situations:
1. Shot by B;
2. Shot by C;
3. Shot by B.P.C.;
4. A is not shot by B-C.
The above probability is 25%.
Calculate the survival rate of 3 people:
A survival rate: 31%.
Shot by B: 25% X 40% = 10%:
Shot by C: 25% X 60% = 15%;
Shot by B:25% X 40% X 60% = 6%.
B survival rate: 23%.
Shot by A: 25% X 20% = 5%;
Shot by A: 25% X20% X60% = 3%.
C survival rate: 17%.
Shot by B: 25% X 40% = 10%;
Shot by A and B: 25% X 20% X 40% = 2%.
It can be seen that in the case that gunners do not know each other's hit rate information, the gunner with the highest hit rate has the greatest chance of survival, and C, who has the worst marksmanship, has the lowest probability of survival.
Therefore, in the duel, it is very important to know oneself and know the other, if you blindly attack, the worse the strength, the faster you will die.
At the same time, it can also be seen that even the strongest A has a much lower probability of winning the final victory than the probability of defeat.
The conclusion is that even if the world's martial arts are the first, they cannot easily choose to fight with other groups.
In the Russian-Ukrainian conflict, under the condition that the strength of the three parties remains unchanged and the will to fight remains unchanged, no matter how flexible the tactics are, no matter how powerful the weapons, C is the most miserable, B is not much better, and A will also be seriously injured.
03
Well, after the first round of fighting, whether or not they knew the combat power of others before, they now know each other and enter the Mingpai.
Enter the second round of duels.
After the first round of gunfire, C may face A, may face B, and even face both A and B, unless in the first round A and B are both dead.
In the Russian-Ukrainian conflict, the death of both A and B cannot happen.
So from the second round, C must be at a disadvantage, because whether it is A or B, their shooting rate is higher than C's shooting rate.
This is C's sorrow.
C, who has the worst hit rate, plays some tricks and is likely to win temporarily in the first round of gunplay.
However, if A and B do not die twice in the first round of gun battle, after the end of the second round of gun battle, C's chances of survival must be lower than that of A or B.
In the second round of gun battles, the odds of survival are roughly calculated as follows:
1. Suppose A vs. C: A has a 60% survival rate and C has a 20% survival rate.
2. Suppose B vs. C: B has a survival rate of 60% and C has a survival rate of 40%.
Conclusion: The worst in the competition can win a while, but in the end it often does not work.
To summarize the rigorous mathematical calculations that show the probability of survival after two rounds of gunfire, the three parties will survive:
First Round:
A shoots B, B shoots A, C shoots A.
The survival rate of A is 24% (40% X 60%), the survival rate of B is 20% (100% - 80%), and the survival rate of C is 100% (no one shoots C).
Second Round:
Scenario 1:
A live B death (24% X 80% = 19.2%) (actually impossible)
A shoots C, C shoots A, A has a survival rate of 60%, and C has a survival rate of 20%.
Scenario 2:
B live A death (20% X 76% = 15.2%) (actually unlikely)
B shoots C, C shoots B, B has a survival rate of 60%, and C has a survival rate of 40%.
Scenario 3:
A and B live (24% X 20% = 4.8%)
Repeat the first round.
Scenario 4:
A and B are dead (76% X 80% = 60.8%) (actually unlikely)
The gun battle is over.
It can be seen from this that if the strength of the tripartite conflict does not change, the conflict is meaningless except to weaken each other.
The final calculation of the mathematics is as follows:
The viability of A is 12.672%.
(19.2％ X 60％) + (4.8％ X 24％) = 12.672％
The survival rate of B is 10.08%.
(15.2％ X 60％) + (4.8％ X 20％) = 10.08％
The survival rate of C is 75.52%
(19.2％ X 20％) + (15.2％ X 40％) + (4.8％ X 100％) + (60.8％ X 100％) = 75.52％
C, who has the worst marksmanship, still has the greatest chance of survival, and A and B, who have better marksmanship, still have a much lower chance of survival than C.
But this is only ideal.
In reality, if either A or B is gone, C will not exist alone.
04
Suppose that instead of firing at the same time, they take turns firing one shot.
C's chances are better than his strength.
C will not be killed by the first shot, and he may have a good chance of shooting first in the next round.
It is assumed that the order of firing is A, B, and C.
After A shoots B (80% chance), it is C's turn to shoot, and C has a 40% chance of killing A with one shot.
Even if B dodges A's first shot and it is B's turn to shoot, B will still aim at A, who has the best marksmanship, and shoot.
Even if B shoots A, the next round is still C's turn to shoot.
If the firing order is B A C, the result is the same, and the next round is still C shooting.
If C shoots first, C can shoot at A first, and even if C doesn't hit A, A's best strategy is still to shoot B.
However, if C hits A, the next round is B shooting C.
So the best strategy for C is to shoot randomly, as long as C does not hit A or B, he is in a favorable situation in the next round of shooting.
Whether they can win in the game depends not only on their strength, but also on the relationship between them.
B and C are actually an alliance relationship, first kill A, at least the balance of strength, their chances of survival have increased.
Who is more likely to betray and who is more likely to be loyal?
Members of any alliance will always weigh the pros and cons, and once the benefits of betrayal outweigh the benefits of loyalty, the alliance will break down.
In the alliance of B and C, B is the most loyal.
This is not because B itself has a more loyal quality, but because of the relationship of interests.
As long as A does not die, B's muzzle will definitely aim at A.
But this is not the case with C, C does not aim at A and shoots indiscriminately is obviously against the alliance relationship, and the result of C doing so will put B in a more dangerous situation.
Only by cooperating can we fight against strong enemies.
Only if B and C cooperate can we kill A first, or at least balance.
If B and C are not in harmony, B or C alone are not superior to A, and must be solved by A successively.
In reality, B tries to woo C and isolate A.
But C chose to ally with A and fiercely confronted B.
In this way, C is the most dangerous.
Even if B loses, the next step, A will enslave C.
Not convinced?
Look at the Three Kingdoms.
Initially, Cao Cao was the strongest, Followed by Sun Quan and Liu Bei.
In order to resist the powerful Cao Cao, Sun Liu's two families had to unite and prepare for the Battle of Chibi.
In the Battle of Chibi, Sun Quan contributed the most, and Liu Bei actually did not contribute much, but Liu Bei developed through this victory.
The strength of the three sides was gradually balanced, and Cao Cao trunceed for 10 years.
After that, Liu Bei and Sun Quan were not united with each other, only caring for their own interests, and even fighting.
Not long after, Liu Bei's Shu state was enslaved and annexed by Cao Cao's State of Wei.
Soon after, Sun Quan's State of Wu also ended up with the same fate.
In the Russian-Ukrainian conflict, only the balance of all parties is the best choice.
As for C, who has the worst strength, he does not understand the principle of balance, or is a pawn, or a noisy moment, and everyone is lost.
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