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
and therefore if I'm including things in there as part of a best response,

而且如果该混合策略是最佳对策
they must all be good.

则其所含纯策略也一定是最佳对策
That's the simple idea, this is the dramatic conclusion.

这个扣人心弦的结论其实是个常识
So the only way to prove this to you and

为了证明它确实是个很有效的方法
to prove to you that this is useful is to go ahead and do it.

接下来我们就用它实践一下
So what I'm going to do is I'm going to clean these boards

我先把这几块黑板擦干净
and I'm going to start showing an example.

然后列举一例
Again don't panic,

大家不必慌张
I think a lot of people at this part of the class have a tendency to panic,

我觉得有些人总是惊慌失措
because it's a new idea, it seems like a lot of math around.

因为这个新概念好像需要很多数学知识