>>12197130You have a 2/3 chance to initially pick a door with a goat behind it, if you in those 2/3 times switch, you will switch to a car. Therefore, switching gives you a 2/3 chance of getting the car. You change your win-condition from being picking the car to picking either of the goats, thus your chances are improved from 1/3 to 2/3.
Don't think of the revealing one of the goats as you getting to pick from one of two doors, but rather be a guess as to whether you initially picked a goat or a car. You have a 2/3 chance of initially picking a goat, and thus switching has a 2/3 chance of giving your a car.
