that one seems confusing but the math is actually quite simple. if you don't switch, it's a 1/3 chance of winning, no matter what. the host will always open the door that isn't the big prize, and so you perceive your chance of winning as 50/50 (it's one of the two doors that is left, therefore 50/50), but it's actually not, it's 2/3 if you switch, and 1/3 if you don't.
here's the permutations:
1 goat 2 goat 3 $
I pick 1, host opens 2, I switch: winner
1 goat 2 $ 3 goat
I pick 1, host opens 3, I switch: winner
1 $ 2 goat 3 goat
I pick 1, host opens either 2 or 3, I switch: loser
now, if the host doesn't have perfect knowledge of what is behind each of the doors, then the chances are different, because the host will randomly open the $ door some of the time, and that ruins the game.
make sense?