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OK, here's a nice variant:

"You are playing the Monty Hall problem. However, you secretly know one of the goats is the former pet of an eccentric billionaire who lost it and is willing to pay an enormous amount for its return, way more than the car is worth. You really want that goat.

"The host is unaware of this. After you pick your door, as is traditional, the host opens one door, which he knows doesn't have the car. He reveals a goat, which you can tell is the ordinary goat and not the secretly valuable one. The host offers to let you switch doors.

"Should you?"

-- https://mathstodon.xyz/@shachaf@y.la/113777521149001723