The process of proof that everyone can understand the theory of the schmerle theorem for clear chess games (winning solutions for playing chess, go, and chess)

The Chinese proofs of the theoremble theorem circulated on the Internet are not so easy to understand. So here I will describe my general proof.

Schmerlot's theorem: in a clear-cut chess game (such as Chinese chess and chess) that will surely end in a limited number of steps. In any particular situation, set a first-to-second, after B, either a will win the next method, B will win the next method, or A and B will both follow the next method.

It indicates that induction is used.

Take the next method combination of adjacent A and B as the one-round method in this proof. Prove that for a limited number of rounds of chess games (formal start is also a situation), either a has a winning method (1), or B has a winning method (2 ), either A or B has a method (3 ). We can find the inevitable and definite conclusion on the definite situation.

Step 1:

First prove that only one round of games, a knows that the round of playing chess can win W, lose L, Ping (TIE ). If there are W in the round routing selection, a must be W. If there are no w but T in the round routing selection, a must be T. If you select L for all rounds, A can only fail.

For example, subgame 1

Prove that for two rounds of games, a also knows all the W, L, and t situations, and a will choose a method that is advantageous to him. For example, in the case of sub-Game 3.

By extension, for games that end in n-1 rounds, A can make a wise choice. N is also true. Pass.

Note 1: This principle is not applicable to games that can be played infinitely. However, in fact, Chinese chess and international chess games in a limited step do not play a game (or play a similar role) so every opponent of Chinese chess and chess is a game that will surely end in a limited step)

NOTE 2: This proof is different from what has been circulated on the Internet. It seems that the fools do not play chess. They did not merge the adjacent steps A and B into a round, but only merged them into a round, it becomes that every time a is a first, every time a is a first choice, so that every normal person can easily read this proof.

NOTE 3: This proof is also effective for B's competitive situation, that is, B's chess skills are too superb. Every time B falls into the game, a's choice is only defeated. Remember, there is a possibility that the next move of A and B is also the next move in a round.

Note 4: There are some special rounds. Maybe a's next move, B has been awarded, and B will not be used. For example, if a in Chinese chess eats B's veteran, B does not need to take action. This is a winning round. This is also a round. Avoid some people say that the definition of the round is vague.

Note 5: It is easy to use a computer to find the best way to play a simple game, such as a woman, a three-game, a Chinese chess mess, or a five-game on a small Board (such as 7x7, however, for games such as chess and games that have been fully started, computers cannot find the optimal solution because of their limited computing power and storage space, those typical chess games are more likely than the total number of atoms in the universe.

Note 6: The theoremble theorem only proves that there must be an optimal method, but it does not help to find a specific optimal method.

The process of proof that everyone can understand the theory of the schmerle theorem for clear chess games (winning solutions for playing chess, go, and chess)