Exactly the way I like to think of it. When he opens the goat door there are now two possibilities: you were right the first time, or the remaining door has th

Exactly the way I like to think of it. When he opens the goat door there are now two possibilities: you were right the first time, or the remaining door has the car. By selecting the other door your are now betting against your initial choice, which was a 1/3 chance. Thus your new odds are 2/3.