雙語暢銷書《艾倫圖靈傳》第5章:解謎接力賽(119)
Poker, with its bluffing and guessing, was a better illustration of the von Neumann theory than chess.
A game without concealment, such as chess, von Neumann called a game of 'perfect information',
沒有隱藏信息的遊戲，比如國際象棋，被馮·諾伊曼稱爲全信息遊戲。and he proved that any such game would always possess an optimal 'pure strategy'.
而且他證明，任何這類遊戲，總是擁有理性的純粹策略。
In the case of chess, this would be a complete set of rules for what to do in every contingency.
在國際象棋的中，這將是一套完整的指南，記錄了在每種局面下應該怎麼走。There being far more possible chess positions than plugboard positions for the Enigma, however, the general von Neumann theory had nothing of practical value to say about the game.
國際象棋的所有局面，比謎機的配線板設定還要多得多，但馮·諾伊曼理論並沒有考慮到實用價值，It was an example of where a high-powered, abstract approach failed to be of use.
這是一種強大的抽象方法，但不能付諸應用。Alan and Jack Good's approach was quite different in nature, being for one thing concerned not so much with a theory of the game, but with a discussion of human thought processes.
艾倫和傑克·克德的想法與此不同，艾倫不關心博弈論，他關心的是人類思維的原理。In their analysis it first had to be assumed that there was some sensible scoring system,
在他們的分析中，首先設想要有一套合理的評估系統，awarding a numerical value to the various possible future positions on the basis of pieces held, pieces threatened, squares controlled and so forth.
根據當前存活的棋子、危險的棋子、控制的棋格等等，來對每一種着法的價值進行評估。With this agreed, the most crude 'definite method' would be simply to make the move that maximised the score.
在這個基礎上，機械的方法基本上就是執行評估價值最高的着法。The next level of refinement would take the opponent's reply into account, using the 'minimax' idea to choose the 'least bad' move.
進一步的改進，是把對手的反應也考慮進來，根據最大值最小化的原則，來制定下一步的着法。In chess there would normally be about thirty possible moves for each player, so that even this crude system would require about a thousand separate assessments.
在國際象棋中，對每個玩家而言，每步通常有大約30種着法，這樣一來，哪怕是最簡單的系統，每步也要進行將近1000次評估，A further step of looking ahead would require thirty thousand.
如果要再往後看一步，那就要進行30, 000次評估。
