Consider 3 doors. Behind one door is a prize (a 'Let's Make a Deal' scenario) and behind the other two is nothing. Naturally, you wish to claim the prize. You are told to select a door. After selecting a door, say door number one, someone who knows where the prize is tells you it is not behind door number two and there is no chance he is attempting to deceive you. He then tells you that you may stick with your initial choice of door number one or switch your decision to door number three. Do you stick or switch? Does it make a difference at all? Why?

My friend swears up and down that it is correct to switch but he has, as yet, been unable to provide me with a solid, mathematical reason. My intuition is that it makes no difference, but I am slowly convincing myself, after thinking through the situation a while, that perhaps it is correct to switch.