who have had this hammered into them too many times already

这种方法他们应该遇到无数次了
so I apologize for them in advance.

提前跟你们道个歉吧
Backward induction.

逆向归纳法
Now it turns out there's precisely one controversial thing

关于逆向归纳法
about backward induction,

一直存在着争议
which is whether you should say backward induction or backwards induction.

是关于如何拼写的问题
So I'm going to leave the "s" off and call it backward induction,

在这里我用了去掉s的这种
but it's up to you which you think the correct English is.

你认为怎么写是对的就怎么写吧
Okay, so since we've got this game here let's talk about it a bit.

既然说到这了我们来进一步分析一下
This idea of the lender and the borrower,

这是有关借方和贷方的问题
it's not an unimportant situation.

它的重要性不容小视
We've simplified it down to a very simple choice here,

虽然我们这里把它简化成了几种选择