I think most of the Monty Hall confusion comes from focusing too much on the question and the math and missing the important part: The confusing setup is part o

I think most of the Monty Hall confusion comes from focusing too much on the question and the math and missing the important part: The confusing setup is part of the game! Essentially it works like this: Host: Contestant, please choose one of the 3 doors Contestant: I choose door #1 Host: Confusing jibber-jabber to raise tension and keep this fun to watch Contestant: I don't know what to do! Host: Do you think the prize is behind your selection, door #1, or behind any of the others? Expressed this way there's no confusion but it's the exact same problem. The contestant first selected 1/3 doors and the host is offering to let Contestant keep that 1/3 or choose the other 2/3. Any obfuscation in between is intentional for the sake of the game.