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And it has never made sense to me, for a simple reason:
I pick Door #1. Monty opens Door #2, and Rosie O'Donnell is standing behind it, so obviously I didn't want that one. He offers me the choice of keeping Door #1, or switching to Door #3.
What I do not, and probably will never understand is how the second choice is not _independent_ from the first one. Yes, Monty has information that I do not as to which door has the prize -- but the mere fact that I do not have that information makes it irrelevant to my choosing process. I don't know whether Monty is trying to help me or screw me over by making his offer, and I have no way of finding out short of making a blind choice; all I _do_ know is that between my first choice and my second, the situation has changed and my options are different.
When I make my second choice, I am making an independent choice between two doors. One has a prize. One has a goat. A third door has a goat, but that door is _no longer an option_, so I don't grasp why it is figured into the odds when I choose again. (Really, if Monty always offers you the choice to switch, the first choice is irrelevant; he will always open a goat door, so you'll always have a final choice that narrows it down to two.)
I've taken math courses through Calculus 3. I've taken Probability and Statistics courses. I've read lots of explanations of the "real" odds for each door... and I _just don't get it._
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