The reasoning I've always used to understand this problem is to imagine that you and the host both choose at exactly the same time. Then 2/3 of the time you've

The reasoning I've always used to understand this problem is to imagine that you and the host both choose at exactly the same time. Then 2/3 of the time you've both simultaneously selected both boxes with goats, and therefore 2/3 of the time the unselected box is the car.