I'm going to look at a game and we're going to go through this game.

我列举一例然后一起来仔细研究一下
We'll discuss it a little bit because it's a fun game,

这个博弈饶有趣味我们要深入讨论
and we're going to find the mixed-strategy equilibria of this game.

而且要寻找出它的混合策略纳什均衡
Everyone know where we're going?

大家都知道我们的任务了吧
I want to make sure before I go on,

在开始之前我来确认一下
are people looking very sort of deer in the headlamps?

大家是不是头脑有点乱啊
That was a lot of formality to get through in a short period of time.

我们短时间内接触了很多正式定义
Does anyone want to ask a question at this point?

你们有没有什么疑问啊
Are you okay? Okay to go on?

都懂了是吗那我们继续吧
So just remember that the conclusion here comes from this very simple idea.

记住这个结论是从简单道理中总结出来的
The simple idea is, the payoff to a weighted average must lie

结论就是加权平均数的收益
between the best and worst thing involved in the average,

一定介于最好和最差的收益之间