[plikan13]

I've been wondering about another somewhat intuitive way to see the problem: suppose a third person enters the room and he is allowed to finish the game, knowing nothing of what went on before. In particular, he doesn't know your initial choice. Now it is obvious that his chances of winning are 1/2. It is also obvious that if you stick to your first choice, your chance of winning is still 1/3. Now it is odd that somebody who has LESS information about the problem has a better chance of winning than you. Meaning that you must have some way of getting at least the odds of the other guy. But there's only one thing you can do other than sticking to your first choice: taking the other door. So that seems the correct thing to do.