雙語暢銷書《艾倫圖靈傳》第5章:解謎接力賽(118)

Much of the mathematical work had been done by von Neumann, taking up ideas first published by the French mathematician E. Borel in 1921.

這裏面很多的數學工作都是由馮·諾伊曼做出的，他推進了法國數學家E.博雷爾1921年的論文中的想法。

Borel had defined 'pure' and 'mixed' strategies in game-playing.

博雷爾定義了遊戲中的純策略和混合策略。

Pure strategies were definite rules, setting out the proper action in any contingency;

純策略是確定的規則，任何情況下的動作都是設定好的，

a mixed strategy would consist of two or more different pure strategies, to be chosen at random, but with specified probabilities for each strategy according to the contingency.

而混合策略則包括多個純策略，可以由人們從中選擇，而根據情況，每種選擇都帶有特定的概率。

Von Neumann had been able to show that for any game with two players, with fixed rules, there would exist optimal strategies, usually mixed, for each player.

馮·諾伊曼證明，對於任何只有兩個玩家的特定規則的遊戲，對每位玩家來說，都分別存在着最優策略。

Alan would very likely have attended his talk on the game of Poker, given at Princeton in 1937, which illustrated the result

1937年在普林斯頓，艾倫很可能跟他討論過撲克遊戲，而且他給艾倫講了這個結論。

It was von Neumann's beautiful, if depressing theorem, that in any two-person game both players would be locked into their 'minimax' strategies,

馮·諾伊曼的這個漂亮理論，使對於任何兩人遊戲注，雙方玩家都被限制在最大值最小化的策略中，

both finding that all they could do was to make the best of a bad job, and to give the opponent the worst of a good job, and that these two objectives would always coincide.

雙會都會看到，他們能做的就是把自己的最壞的局面搞好，同時把對手的最好的局面搞糟，這兩個目標要同時達成。