So we're going to show how this technique is going to help us shoot penalty shots in soccer.

我们讲学到博弈理论讲如何,帮助我们在足球比赛罚球

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

We can think of this as the decision happening at the instant at which you kicked.

我们可以认为罚球队员,在球被踢出的瞬间才做出决定

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

Okay, you can kick up and down, that's true. Okay, that's true actually, that's true.

你可以选择罚球的高度,这一点很对,很有道路

耶鲁公开课 - 博弈论课程节选

So this line represents the expected payoff of shooting to the middle as a function of the probability that the goal keeper dives to the right.

这条线表示从中路射门时罚球者的收益,是门将扑向右路概率的一个函数

耶鲁公开课 - 博弈论课程节选

So this weekend a penalty was missed exactly by somebody ignoring this rule.

这周末的点球未射进,绝对是因为罚球球员不懂这个规律

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

Players don't make their decision before, and then stick with it necessarily.

罚球球员事先没有做好决定,而是见机行事

耶鲁公开课 - 博弈论课程节选

There are three ways, the goal--the attacker could kick the ball.

罚球队员可以选择三种不同射门路径

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

And their aim is to kick it into the goal.

罚球者的目标是射进这个球

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Good, so one thing that's clearly missing here is I'm ignoring that in fact right footed players find it easier to shoot to their left, which is actually the goalie's right.

很好,我们忽略了这一点,我们忽视了实际上惯用右脚的球员,从左路射门会更容易些,罚球球员的左路就是门将的右路

耶鲁公开课 - 博弈论课程节选

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

我们先来看看罚球球员

耶鲁公开课 - 博弈论课程节选

So in reality, we need to take into account a little bit more, and in particular, we need to take into account the abilities of players to hit the ball accurately and/or hard.

所以分析实际情况时要深思熟虑,比如说,我们需要把罚球队员的,射门力度跟精准度考虑在内

耶鲁公开课 - 博弈论课程节选

So the payoff here is something like u1 if the goal keeper dives to the left is equal to 4, by which I mean there's a 40% chance of scoring.

收益u1表示门将扑向左路时,罚球者从左路进攻的收益是4,也就是说球被射入球门的概率是40%

耶鲁公开课 - 博弈论课程节选