The Monty Hall problem is especially unintuitive if you've ever watched Let's Make a Deal, since the problem set up is oh so close to, but not exactly, the set up of the Big Deal in the show. It's too easy to conflate the rules of the show with the math problem, which will lead to confusion.
I think seeing the results of a simulation also elucidates the set up of the math problem vs reading a proof.
I think seeing the results of a simulation also elucidates the set up of the math problem vs reading a proof.