Wikipedia says 1/3.Probably statistical clustering. Try it with more doors - if it were the same as the host-knows version, you'd win 9/10 times for ten doors.
Edit: no, sorry... it always ends up a 1/2 chance if you exclude those cases, yes, with any number of doors (assuming the host gets down to 2 doors without opening one on the car.) The point is that you don't gain anything by switching.
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Newington, Wed 27 Aug 2008, 11:42,
archived)
it's 1/3 overall, including the host fuck ups,but it's 1/2 for each of switching and not switching.
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Moon Girl Technologies horrendous beanbag, Wed 27 Aug 2008, 11:43,
archived)