In another famous illustration, "The Army of the Potomac - A Sharp-Shooter on Picket Duty."

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So this is the guy who is shooting, he's called the shooter and this is the goalie.

这边代表罚球队员,称他为射手吧,这边代表门将

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At the end of the day, the goalie doesn't know the decision of the shooter and the shooter doesn't know the decision of the goalie.

直到比赛结束之前,门将都不会知道你会从哪路罚点球,罚球队员也不知道门将会扑向哪路

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So it's as if that decision is made instantaneously as the shooter is running up.

这就好像所有决定都在,罚球球员起跑的一瞬间完成的

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So the number for the... The payoff for the shooter is his probability of scoring and the payoff for the goal keeper is just the negative of that.

对罚球者来说,他的收益是进球的概率,而门将的收益是其相反数

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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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Let's just look at the shooter, for example.

我们先来看看罚球球员

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