[zephyrfalcon]

But if he doesn't know where the car is, how can he be sure that the door he opens is going to have a goat?

[yen223]

The scenario is the host doesn't know which door has the car, opens some random door, and that door happens to have a goat behind it.

If you were in this scenario, your odds of getting the car doesn't change whether you switch or not

[auggierose]

That would indeed be annoying, but I doubt it is the case. If you only consider this scenario, it cannot be distinguished by conditional probability from the case that the host knows, and so the math should stay the same.

As usual, the problem is not an incredibly difficult problem, but just a failure to state the problem clearly and correctly.

Try to write a computer program that approximates the probability, and you'll see what I mean.

[CRConrad]

Nobody said he can be sure.