It was hard to picture looking at it in one direction for me as a kid, but after thinking about it for about 15 minutes I looked at it from the "opposite view" and for some reason it clicked. (Not from the players view, but rather the hosts view)

They give you the chance to open a door 1/3. Then ask if you would like to change after opening another door to show a goat. Your first thought is that, well it's a 50-50 chance the last door is the prize because there are only 2 left. so what would it matter, but really it is 2/3. As your chances of being right were 1/3 originally, and he knows where the car is, and has to eliminate one of the doors you don't have. Making it so now 2/3 of the options are out if you choose a new door, or it stays at 1/3 if you stay the same. So you say "thank you for the extra 33% chance at winning" and always change to the second door