The role of probability in solving the Monty Hall problem

[robvalue]

Here's the important point, I'll say it again once more:

We know he will open one of the other two doors. We know it will be a goat. Whether we picked right or not, he will do the same thing. It gives us no more information about whether we picked right, because he can't pick our door and he can't pick the car.

This is the crucial part. If you miss the significance of this, then you misunderstand the whole thing. He knows where the car is, and he can't pick my door. These are not meaningless details.

I tell you, I could make a lot of money out of this. I'll bet £4 against £5 that I will find the prize. I'll clean you guys out. Promise me. You have to promise... Never go to a casino!