Much of the mathematical work had been done by von Neumann, taking up ideas first published by the French mathematician E. Borel in 1921.
这里面很多的数学工作都是由冯·诺伊曼做出的，他推进了法国数学家E.博雷尔1921年的论文中的想法。
Borel had defined 'pure' and 'mixed' strategies in game-playing.
博雷尔定义了游戏中的纯策略和混合策略。
Pure strategies were definite rules, setting out the proper action in any contingency;
纯策略是确定的规则，任何情况下的动作都是设定好的，
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.
而混合策略则包括多个纯策略，可以由人们从中选择，而根据情况，每种选择都带有特定的概率。
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.
冯·诺伊曼证明，对于任何只有两个玩家的特定规则的游戏，对每位玩家来说，都分别存在着最优策略。
Alan would very likely have attended his talk on the game of Poker, given at Princeton in 1937, which illustrated the result
1937年在普林斯顿，艾伦很可能跟他讨论过扑克游戏，而且他给艾伦讲了这个结论。
It was von Neumann's beautiful, if depressing theorem, that in any two-person game both players would be locked into their 'minimax' strategies,
冯·诺伊曼的这个漂亮理论，使对于任何两人游戏注，双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.
双会都会看到，他们能做的就是把自己的最坏的局面搞好，同时把对手的最好的局面搞糟，这两个目标要同时达成。