So I would imagine everyone has heard of the game show theory as it has been in various tv/movies including 21 and numb3rs. But to refresh your mind. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? I have heard some people say yes you do have an advantage because you start with a 1/3 chance and when the card is flipped you have double the chance of winning if you swap choices. But I have heard other people argue the other way. Just curious to hear what you all have to say about it.