[fixermark]

It's much easier to understand when you realize that Monty never reveals that one of the closed doors contained the car.

That asymmetry of action leads to the asymmetry of probabilities; your initial choice constrained his choices when he takes action.

[cptvideo2]

Well, Monty doesn't know (or care about) your choice. He's 'constrained' by the fact that his 'probability' is 100%: he knows where the goats and car are.

[jjnoakes]

What? Of course his action is based on your choice.

If a has the car and b and c have goats, and you pick b, he opens c. And if you pick c, he opens b...

[cptvideo2]

You’re right. I forgot that you had to tell him which door you wanted to open (instead of just saying that you've decided on a door - like the FBI as just SAID that they've cracked the iPhone5). But it doesn’t matter because Monty was always going to open one of the two goat doors, and the one that he opens doesn’t matter to the 1/3 probability that you picked the car door. Your probability of getting the car ALWAYS doubles when you switch (even though you still may not get it).

[function_seven]

He does care. 2/3 of the time, your choice forces his. If you choose a goat, Monty doesn't have a choice. He can only reveal the other goat.

The other 1/3 of the time, you're right, he doesn't care, because he can choose any of the remaining doors at random.