When you pick a door, there's three possible scenarios: A) You picked the car door B) You picked a goat door C) You picked the other goat door. All three are eq

When you pick a door, there's three possible scenarios: A) You picked the car door B) You picked a goat door C) You picked the other goat door. All three are equally likely. But in B and C, the host only has one goat door available to open (because you already picked the other goat door) so since he has to show you a goat, he is effectively forced to tell you where the car is, since that must be the third door that has neither been picked nor opened yet - and switching doors is how you act on that information to get the car. It's only in scenario A that he gets a choice of which of the two doors to open. So there's a 2/3rds chance that he's telling you exactly where the car is, so you're better off acting on that info by switching.