When you pick a door, before the host does anything, there are three possibilities: a car; goat #1; goat #2. These are the same possibilities AFTER he reveals o

When you pick a door, before the host does anything, there are three possibilities: a car; goat #1; goat #2. These are the same possibilities AFTER he reveals one of the goats -- the goat he shows could be goat #1 or goat #2. Now of the three possibilities for your door, two are losers; by changing doors you have a 1/3 chance of losing (if the car is behind the door you first picked) and consequently a 2/3 chance of winning.