I'm not actually arguing, I know that counting the initial picked door, 2/3 is correct. What Pete and I are saying is after you pick, you essentially have a 50-50 chance. Which would be the chance you get no matter what (since they will always take a door away). The game show just makes it more interesting to the audience by adding the fact that they will take away one of three doors. (Actually it's a really bad game show, considering a game show probably doesn't want to give away 50-50 chances of winning a car every game).
You are correct in saying that it is 2/3 starting with the initial pick of one of three doors. It's just like those text problems in math books where you're like "WTF? This shit never happens."
The fact that you can even get 2/3 out of this is the same reason you have a 1/3 chance at the beginning if they didn't take the door away. Why the F would they take away a free door that wasn't the real one? I'd be the happiest game show person ever.
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