The role of probability in solving the Monty Hall problem

[Excited Penguin]

Lets say you have a billion options. You make a choice and the moderator takes away 999.999.998 of them, thus leaving you with the one you chose and one other one. I think it's an illusion to think that this alone makes the other one any more likely to be true than the one you already chose, even if the ones he took out of the equation are all false. And this is because no matter what(that is, even if you made the right choice to begin with) the moderator is going to take away 999.999.998 of them away. So just the fact that you "made it this far" and that all of the ones he eliminated are the "bad ones" doesn't tell you anything. And that's because the game wouldn't have ended even if you made the right choice at first - and you know this. No matter what you chose, right or wrong, the moderator is going to take away the same number of options leaving you with a 50/50 chance of being right in the end. To assume that now it's more likely you're wrong is to assume that the moderator would end the game if you made the right choice at first, and that's a wrong assumption to make.