In another famous illustration, "The Army of the Potomac - A Sharp-Shooter on Picket Duty."
VOA: special.2010.07.25
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
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
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
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
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
Let's just look at the shooter, for example.
我们先来看看罚球球员
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