This was the problem as stated in the Marilyn vos Savant column that started the controversy: > Suppose you’re on a game show, and you’re given the choice of t

This was the problem as stated in the Marilyn vos Savant column that started the controversy: > 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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors? Diaconis is in fact correct that given just that information the problem cannot be solved. What is missing is a statement that the host will always reveal a goat and always offer you a chance to switch doors. If the host can chose whether or not to make the offer then if you you happen to receive the offer when you are on the show you cannot say anything about whether or not switching is to your advantage. For instance suppose the show has given away a lot of cars earlier in the season and the producers ask the host to try to reduce the number of cars given away during the rest of the season. The host might then only offer switching when he knows the contestant has picked the car door. He will still open a goat door first because that's more dramatic. He just won't offer to let you switch before going on to open either your door or the remaining door.