re: Marilyn vos Savant and the history of the Montel Hall question

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She was pretty good-looking back in the day.

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Indeed she was.

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Doesn't it matter more whether the opened door was chosen at random or picked specifically because it did NOT have the car?

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Yes. The reason this works is that Monty Hall knows which door has the car, and will only open doors that don't have one.

To make it more obvious, suppose that instead of 3 doors you have 100. You open one - you have a 1% shot at this point. Monty (who will never open a door with the car) opens 98 of the remaining 99. Don't you think you should switch now?

ETA: Monty's opening all the other doors does not change the chance you originally picked the right one. It does change the chances that the other unopened door is correct because he showed you all the others that were wrong.