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For example, I could believe that it's twice as likely that the person's going to choose Left as Right.
比方说,我可能认为对手选左的可能性,是选右的可能性的2倍
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But obviously, you choose somebody that is going to say your work is great. Right.
当然了，你肯定要选择那些会夸奖你工作成绩的人来给你写推荐信。对吧。
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Something like this. That would be perfectly fine interpolation. All right, we choose to have a linear interpolation.
这种插值的方法也是完全可行的,好，现在我们决定使用，线性插值的方案。
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it's going to be: 1 minus the probability they'll choose Right times 1, plus the probability that they choose Right times 4.
方程是,1减对手选右的概率再乘以1,加上对手选右的概率乘以4
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But I would choose to sit down for these particular projects right around midnight so that when I woke up my program was giving me the results I wanted.
我可能会,为了这些特殊的项目一直等到半夜,这样我醒来时,程序就能给我想要的结果。
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Absolutely. The reason why we have a right to free speech is because we have a right to own ourselves, to exercise our voice in any way that we choose.
当然，我们之所以享有言论自由,是因为我们是自己的主人，有权用任何方式表达自己的观点。
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I also advocated it as a right for autonomous adults to choose if they are eternally ill.
我还主张将选择安乐死作为自主的成年人的一项权利,使他们在患有绝症的时候可以有所选择。
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What probabilities are associated with thinking it's twice as likely they're going to choose Left than Right?
那么在选左是选右的可能性的二倍时,选择每个策略的概率是多少呢
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So what's my expected payoff from choosing Up where I believe the other person's going to choose Left and Right, equally likely? It's what?
那么在我对手选择左或右,可能性相同的情况下,我的预期收益会是什么样的呢
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So this point here corresponds to my payoff if I choose Up and they choose Right.
也就是说这个点表示,我选上对手选右时我的收益
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If this probability is 0 that the other guy chooses Right, that's the same as saying that the other guy is going to choose Left.
如果对手选右的概率是0,也就是说我认为对手绝对会选左
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okay I chose Middle because I believed that the other guy was going to choose Right and Middle was the best thing for me to do against Right."
我选中是因为,我认为另一个人会选右,并且选中是右的最佳策略
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It could be, they're twice as likely to choose Left as Right.
这也可能啊,选左可能性是右的2倍
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It's the safer answer if you can't decide whether or not your opponent's going to choose Left or Right, so you don't have to worry about having a payoff of 0.
当你无法判断你的对手会选左还是右时,选下是较安全的答案,因此你不必担心收益变成0
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So if the other person's choosing Right with probability 0, that's the same as saying they're going to choose Left, and if I chose Middle against Left, I get what?
如果对手选右的概率是0,也就是说对手选左,此时我选中的收益是什么
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If I thought there was 2/3 probability they'd choose Left and 1/3 probability they'd choose Right, then I think it's twice as likely they're going to choose Left, and I could redo this calculation.
如果你觉得对手选左的可能性是2/3,而选右的可能性是1/3,即对手选左的可能性是右的2倍时,我们再重新计算一下
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So this isn't so hard, we know that if I choose Up and there's probability 0 that the other guy is going to choose Right, that's the same as saying I choose Up and the other guy chooses, let's try it again.
这不是很难得,我们知道如果我选上的话,我对手选右的概率就是0,也就是说我选上,我对手会选择,我说错了,重新来
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So this is a subtle thing because you think about the current election, there's a debate about whether Hilary Clinton, for example, can choose right now to be at the center of the democratic party given her past history of votes, for example, on the Iraq War.
这是个微妙的事情,因为你联想到现在的选举,举个例子,关于希拉里·克林顿能否选择,作为民主党竞选中间派参选就颇有争议,考虑到她的参选记录,例如在伊拉克战争中
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Conversely, if there was probability 1 that the other guy is going to choose Right, and I choose Up, then I get 0.
相反,如果对手,选择右的概率为1,并且我选的是上,那我的收益为零
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And we've already agreed that if I think it's equally likely they're going to choose right and left, that there's a probability ?
而且我们已经计算过了,如果我觉得对手,选左选右的概率相同,即他们选右的概率为1/2时
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And we know that Down does best if I think it was equally likely that the person was going to choose Left and Right.
我们还知道如果我们认为对手,选左或者是右的可能性相同的情况下,下是此情况下最好的策略
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It's my belief that the other guy's going to choose Right.
也就是我关于对手选右概率的信念
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What about my expected payoff from choosing Middle against , so in this case where I think it's equally likely that my opponents going to choose Left or Right?
那我在情况下,选中的预期收益是什么呢,在此情况下我依然认为,对手选左选右的可能性相同
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So it turns out that, as the gentleman out there said, if I thought it was equally likely that my opponent was going to choose Left or Right, then actually my best choice, my best response is to choose Down.
这个结果和刚才那位先生说的,如果我觉得我对手,选择左或右的可能性相同的话,这时候最好的选择,也就是说我的最佳对策是选下
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Or on the other side, there's a debate about whether Mitt Romney can choose to be, I guess he's trying to choose himself to be on the right hand wing of the republic party, given he has a record of governance, as being governor of Massachusetts when he provided state healthcare for example.
或者在另一派,争论米特·罗姆尼是否会选择,我猜他试图选择作为,右派共和党,考虑到他的政绩,在他作为马萨诸塞州州长期间,他提供了的州卫生保健
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if I think it's more likely than this crossing point Y I think it's very likely they're going to choose Right.
如果我觉得对手选右的概率,会在交点Y的右方
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If I think the probability that they're going to choose Right is less than X, then my best response is to choose Up.
也就是说如果我觉得,对手选右的概率小于X,那我的最佳对策是选上
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It's more likely than Y the probability that they're going to choose right is more than Y, then the highest line of these three is this one, which corresponds to my choosing Middle.
即比Y大,也就说对手选右的概率大于Y,那么这三条线中最高的是这条线,这条线表示我选中的收益
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