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So in the numbers game this is the spreadsheet -- or an example of this is the spreadsheet.
这就是数字游戏的电子表格,或者说这是其电子表格的一个样本
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We just understand that it's a numbers game.
我们知道那只是个数字游戏。
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So let's take those ideas and go back to the numbers game from last time.
那么我们带着这些方法,回到上次的数字游戏中
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So it's just a numbers game.
所以，这只是个数字游戏。
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The week after we implemented the so-called game of 15, this little party favor where you move the numbers up, down, left or right.
到第三周，我们要编一个叫做“15”的游戏，就是经常在派对上玩的,可以把数字上，下，左，右移动的小游戏。
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So in the numbers game what is this?
那么在数字游戏中它是怎样的呢
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In the numbers game "Ui" can be two things.
在数字博弈中Ui代表这两件事
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We also saw in that numbers game last time that in some games, but by no means all games, in some games this process actually converges to a single choice.
我们同样可以发现,在某些博弈中,不是所有的博弈,迭代剔除劣势策略,最终会导致唯一的选择
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In the numbers game, you'all, were the players.
我再强调下,你们都是参与人
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In that numbers game it converged to 1.
在数字游戏中最后就只剩1了
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But we also saw it's a dangerous idea to take too literally: that sometimes this can get you to over think the problem and actually, as in that numbers game last time, the best choice, the winning choice, might not involve so many rounds.
同时我们也发现过度照本宣科也不好,有时他会导致你,对于问题的过度探究,正如我们上次玩的数字游戏,最优选择,最后获胜的答案,有时不会绕那么多弯子
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How do we know that everyone choosing 1 is the Nash Equilibrium in the game where you all chose numbers?
我们怎么知道在那个数字游戏中,选择1就是这个博弈的均衡呢
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We handed out again the game with the numbers, but just in case, let me just read out the game you played.
再来介绍一下这个数字游戏,但是以防万一,我来介绍下游戏规则
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Even the game, when you chose numbers, you chose numbers 1, 2, 3, 4, 5, up to a 100, there were 100 strategies.
比如那个数字游戏,你能从1到100这100个数字中选择
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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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I chose 22 because I thought that most people would play the game dividing by two-thirds a couple of times, and give numbers averaging around the low 30's.
我选了22因为我想大多数人在游戏中,可能会多次求平均数的2/3,最后会得出30以下的数
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So I gave you some numbers I made up actually a long time ago, but since I've been using this game in class, somebody went out and checked.
我列举的数字都是我很久前编出来的,在我需要在课上引用数字的时候就有了,有人还为此做了调查
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Let's go back to the game we played with the numbers.
那我们回到之前玩的数字游戏
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This is a game where you get a little plastic device, it's got 15 plastic numbers on it and one hole in this little plastic board and you can move those numbers up, down, left to right, and the goal is to take what's a random assortment of tiles and arrange them in numeric order and that's one of these little things you can play sort of absentmindedly.
在这个游戏中，你会拿到一个可塑的装置，上面有15个数字和一个孔,你可以将数字上下移动，左右移动，目标就是,拿到一个随机的组合后,将其按数字顺序排列,这个你可以随便玩玩。
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