At the moment you're staring at this, it's all a bit new,

刚开始你们可能觉得这些知识挺新鲜
and as well as being new, you're saying, okay but so what,

但你们可能也会有这样的疑问
why do I care about this seemingly mundane fact?

我为什么要关心这个很平常的结论呢
The reason we're gonna turn out to care about this seemingly mundane fact,

我们之所以要关注这个很平常的结论
is that this fact is going to

是因为懂了它
make it remarkably easy to find Nash Equilibria.

我们在寻找纳什均衡时会更容易些
This fact, this lesson,

这个结论
this idea that if I'm playing a pure strategy as part of the mix,

即我在混合策略中采用的纯策略
it must itself be a best response,

本身就是最佳对策的结论
that's going to be the trick we're going to use

它将是我们以后在寻找
in finding mixed strategy Nash Equilibria.

混合策略纳什均衡时的捷径
The only way I can illustrate that to you is to do it,

实践是检验真理的唯一标准