I've tried that with people with limited success, though it could be that I've explained it badly. When you put the games in terms of "you and a friend playing

I've tried that with people with limited success, though it could be that I've explained it badly. When you put the games in terms of "you and a friend playing the game simultaneously", most people get it. You and a friend are playing the game simultaneously; you both decide ahead of time to: a. always pick the same initial door b. no matter what Monty does, you ALWAYS switch, your friend NEVER does. The possible outcomes before the reveal are: * Monty wins, because he shows you the car. We agree ahead of time that this never happens. Now, since you know one of you is going to win, since Monty didn't, who has the better chance? Your friend started with a 1/3 chance, and he hasn't switched; does his chance suddenly change because Monty opened a door? Most people (not all!) will agree that it has not. Since one of you MUST win, and friend has 1/3 chance, what's left?