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You might be better kicking to the left or to the right depending on whether you're right handed or left handed.
你最好从左路还是右路射门,和你是左撇子还是右撇子有关
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Finally, let's do it in green, let's look at the payoffs, the expected payoffs if I shoot to the right.
最后,用绿线来表示吧,我们来看看我从右路射门的预期收益
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However, there's one other variable that you want to be aware of and that is, he knows he ought to be going straight ahead like that, but he also knows that his right flank is open.
然而,还有其他变数是必须考虑到的,那就是,士兵知道他是向前直行的,但是,他同样知道他的右路是洞开的
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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
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One more issue is, you have another decision when you run up to hit this, hit the penalty other than just left and right.
另一个问题是,在你主罚点球的时候,除了左路右路外还有别的需要考虑吗
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And there is no belief you could possibly hold given these numbers in this game that could ever rationalize shooting the ball to the middle.
在给出的这些数据下,无论你认为门将有多大概率会扑向右路,从中路射门绝对不是一个合理的选择
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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
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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
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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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If you can kick the ball very hard, but not very accurately, then if you try and shoot to the left or right, you're slightly more likely to miss.
如果你只会大力抽射但是缺乏精准,当你射向左路或者右路时,你有可能会射偏
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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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How many of you would shoot to the right?
又有多少人选择右路
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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
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It's the expected payoff to Player 1 if shooting to the left as it depends on the probability that the goal keeper dives to the right.
它表示参与人1,从左路射门的预期收益,与门将扑向右路的概率有关
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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
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He could kick the ball to the left, the middle, or the right.
他可以选择左路,中路,右路
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The goalie can dive to the left or the right.
门将可以选择扑向左路或者右路
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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
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And if the goalie dives to the right, you're best off shooting to the left, second best off shooting to the middle, and worst off by shooting to the right; and that's kind of common sense.
如果门将扑向右边,你最好从左路射门,其次从中路射门,从右路射门是最差的选择,这些都是常识了吧
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So, not surprisingly in this game, it turns out that if the goalie dived to the left you're best off shooting to the right, second best off shooting to the middle, and worst off shooting to the left.
因此毫无争议地说,如果门将扑向左路,你最好选择从右路射门,其次是从中路射门,最差的选择是从左路射门
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So the goalie is going to shoot to the right with the probability less than a ?, sorry he's going to dive to the right with the probability less than a ?, you should shoot to the right.
如果门将从右路射门的概率,小于?的话,抱歉,是门将扑向右路的概率小于?,你应该从右路射门
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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%
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So the thing that I hope jumps out at you from this picture is no great guesses about figuring out this is a ?, so if the probability that the goalie's going to jump to the right is less than a ?, then the best you can do is represented by this green line, which is shoot to the right.
我希望大家都能从图中看出来,得出这一点的横坐标是?不难,如果门将扑向右路的概率,小于?的时候,此时你的最佳策略用这段绿线表示,即你应该从右路射门
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I'm going to put down two different definitions of best response, one of which corresponds to best response to somebody else playing a particular strategy like left and right, and the other is just going to correspond to the more general idea of a best response to a belief.
我写出最佳对策的两种不同形式定义,一个是参与人针对对手策略的定义,比如这里的左路右路,另一个强调的是,最佳对策的广义上的定义
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Conversely, if you think the goalie's going to shoot to the right with probability more than a ?, then the best you can do is represented by the pink line, and that's shooting to the left, or if you think the goalie's going to dive to the right with the probability more than a ?, the best you can do, your best response is to shoot to the left.
相反如果你认为门将扑向右侧的概率,大于?的情况下,此时你最佳策略用粉线表示,即从左路射门,也就是说如果你觉得门将扑向右路的,概率大于?的话,你最好选择从左路射门
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