Gnu, I feel your pain.

The key is that there's a distinction between the odds of where the car *is* (1 in 2 for either of the two final doors, regardless)

AND

the odds that you, the contestant, will *find* the car.

It's too easy for a non-mathematician (like me) to confuse the two. You're thinking of where the car *is* in the final setup. It's got to be behind one of the two doors (odds for either door, 1 in 2). But the real issue is the odds of your *finding* the car when there were three doors, Monty knowingly eliminated one, and you get to stick or switch. A more complicated situation (odds if you switch, 2 in 3).

Remember, the 2 in 3 probability is still no guarantee that you'll win the car. It isn't anything tangible like a door or a goat. You just have a better chance of finding the car if you switch.

It still feels weird, but I'm now convinced. It's almost as though something spooky must be migrating from your first choice to your second, but that's not what's happening at all. All that changes is the intangible mathematical relationship among the choices. You can't detect it without having worked out the possible results one by one. The mathematical relationship is real even if not detectable by straight observation.

Check out Jim Dixon's chart last week of all possible results. It will take a while to absorb all the permutations, but the 2 in 3 odds are right there.