Most of this interesting discussion doesn't help me with my original question, which is, what should I tell someone to read if they want an understandable (and correct!) discussion of the problem? Incidentally, since one of the things we're discussing is the impact that Monty's policy has on the conditional probability, it might be useful to broaden the discussion to include Monty's two evil twins (I guess that makes the three of them "evil triplets") who both look just like him. Evil Monty #1 has the policy that if the contestant guesses the right door on his first pick, he is summarily executed and the segment is never aired. But if the contestant guesses wrong, then Monty opens the other wrong door. Evil Monty #2 has the policy that if the contestant guesses a wrong door on his first pick, he is summarily executed and the segment is never aired. But if the contestant guesses right, then Monty opens one of the two wrong doors. If it so happens that you're on the show on one of the days when Evil Monty #1 is hosting, and you're still alive when he offers you the chance to switch, you should take it. But if Evil Monty #2 is hosting, and you're still alive when he offers you the chance to switch, you shouldn't. Jim Propp