So I shoot to the left and the goalie dives to the left, my payoff is what? It's 4.

我从左路射门而门将也扑向左路时,我的收益是4

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So on the horizontal axis is my belief, and my belief is essentially the probability that the goalie dives to the right.

横轴表示的是我的信念,我的信念表示,我认为门将扑向右路的概率

耶鲁公开课 - 博弈论课程节选

If I shoot to the left and the goalie dived to the right, then I score 90% of the time, so my payoff is .9.

如果我从左路射门而门将扑向右路,那我有90%的概率进球,即我的收益就是9

耶鲁公开课 - 博弈论课程节选

So if I shoot to the right and the goalie dives to the left, then I score with probability point 9 or my payoff is 9.

如果我从右路射门而门将扑向左路,我进球的概率是90%,即收益是9

耶鲁公开课 - 博弈论课程节选

Conversely, if I shoot to the right and he or she dives to the right, then I score 40% of the time, so here's my payoff 4.

相反如果我从右路射门而门将扑向右路,我进球的概率是40%,收益是4

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And here's my green line representing my expected payoff as the shooter, from shooting to the right, as a function of the probability that the goalie dives to the right.

这条绿线表示作为一个罚球球员,我从右路射门的收益,是门将扑向右路概率的一个函数

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Notice here, just to underline something which came up at the end last time, that doesn't just mean beliefs of the form, the goalie's going to dive left or the goalie's going to dive right.

我再提一下,上一讲最后的结论,大家需要引起重视,我并不是说信念是这种形式的,即门将会扑向左路或者门将会扑向右路

耶鲁公开课 - 博弈论课程节选

If I shoot to the left and there's no probability of the goalie diving to the right, which means that they dive to the left, then my payoff is 4, meaning I score 40% of the time.

如果我从左路射门,而门将不会去扑向右路,也就是说他会扑向左路,此时我的收益是4,也就是说我进球的概率是40%

耶鲁公开课 - 博弈论课程节选