I first saw this problem on "The Royal Institution Christmas Lectures for Young People a few years ago (always worth a watch).
They way they demonstrated the solution was this. Imagine instead of three doors it's a pack of cards, face down. You pick one and if it happens to be the ace of spades you win. Out of the 51 remaining cards, the host turns over 50 of them to show that none of them are the ace of spades leaving one face down. Do you swap now?
~iw
