Quote:
Originally Posted by Dirty F
No, because there is a 2 in 3 chance it's behind door 2 or 3. So by picking the door that is left from those 2 (he eliminated one of them) you still have a 2 in 3 chance.
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Your title is right but probability of winning by always switching is a distinct concept from the probability of winning by switching given the player has already picked door 1 and the host has already opened door 3. The title and the example you gave are two slightly distinct propositions. If you announce before a door has been opened you plan to switch you'll get 2/3 not if you already made your pick and host already opened door 3. Anyway yeah better to just always switch.