You have a 50% chance to get the car. Because the host always opens the door WITHOUT a car, that door is completely removed from the equation. Just look at it.

No matter what door you pick first, he opens a door. That door will never have the car. The door he opens is removed from the equation. He asks if you want to change doors. He is asking you to pick one out of two doors. One of them has a car. One of them doesn't. 1/2 the time you will win, 1/2 the time you will lose. Whatever door you picked first is completely irrelevant because he will always remove a wrong choice after you pick your door. These are not sequential probabilities; they are independent. Your first choice has *zero* impact on the second choice. So instead of it being a [1/3 2/3] problem you have a [[1/3 1/3 1/3] problem. With one wrong answer removed, it is no longer in thirds. He asks you again: which door do you want? There are now two doors, not three, to choose from. One of two doors has a car, one does not. Your first choice doesn't matter at *all*, because whether or not you chose correctly, he will remove a door WITHOUT the car from the equation.

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"Oh how awful. Did he at least die peacefully? To shreds you say. Well, how's his wife holding up? To shreds you say."