Okay, how about this: Reverse the problem and talk about Monty's behaviour. Let's assume he wants to help you win the car because he's a nice guy. His goal is t

Okay, how about this: Reverse the problem and talk about Monty's behaviour. Let's assume he wants to help you win the car because he's a nice guy. His goal is to give you the best signals he can. His constraints are: (1) He has to open exactly one door, (2) he can't open the door you chose, and (3) he can't open the door with the car behind it. If you've picked the car then he can't do anything for you (2), so he opens a door at random. If you've picked the wrong door, he can help you out by showing you the other wrong door, leaving you with only one remaining option - an easy win! So assuming you understand Monty's intentions, you can see that there's a 1/3 chance you've picked the right door and should do nothing, and a 2/3 you've picked the wrong door and should listen to what Monty's telling you. (Monty's intentions are of course irrelevant because his behaviour is completely described by the constraints, but he doesn't know that and it's not polite to point it out.)