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If the host doesn't know, and just opens a door, then it creates a 3rd outcome where he picks the right one (depriving you of the prize). Whereas before, when you picked wrong and switched you were guaranteed the prize (2/3 of the time) now in this case the host takes the prize off you half the...

The easiest way I can explain this is this If you picked the right one, you'll swap and lose your prize. That'll happen 1/3 of the time. If you picked the wrong one, you'll swap to the right one, since the other wrong one was removed. That'll happen 2/3 of the time. So this strategy gives you...