This is fun... Let's explore the second possibility: the announcer doesn't know which door is the winner. After you pick a door, he shows you what is behind one of the other two doors (with equal probability). If he reveals the prize, you lose. If not, you may switch to the other door.
You switch:
You pick: He shows: Result:
Loser (2/3) Loser (1/2) Win! (1/3)
Loser (2/3) Winner (1/2) Lose (1/3)
Winner (1/3) Loser (1/1) Lose (1/3)
You don't switch:
You pick: He shows: Result:
Loser (2/3) Loser (1/2) Lose (1/3)
Loser (2/3) Winner (1/2) Lose (1/3)
Winner (1/3) Loser (1/1) Win! (1/3)
So, if the announcer doesn't know where the prize is, but just reveals one of the other doors randomly, no matter what you do you have a 1/3 chance of picking the winning door.
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