Ed - Exactly! thanks for clkearing it up.

Lighter - I am not calling anyone stupid. There are people who do enjoy playing the curmudgeon, and I simply don't want to argue with such. But if someone really wants to understand, there are many really good explanations in this thread. I will try one more, and if it is still not clear, it is my fault.

The contestant's initial choice has a one in three chance of being correct.

This never changes at any point for any reason, and does not depend on anything Monty does. The initially-chosen door has a one in three chance of being correct. Period.

Now focus on the other doors.

Once a door is opened to reveal a goat, that door has a zero in three chance of being correct.

There is a three in three chance that there is actually a car behind one of the doors.

Your initial choice has an unchanged one in three chance of being correct.

So, the other two out of three chances must (I repeat *must*) lie behind the remaining unopened door (not the revealed goat door, not your initial choice, but the remaining unopened door).

So please switch - it doubles your odds!