Great Answer
heihojin writes:
"If n < 1/2, then you should not switch.
If n = 1/2, then it doesn't matter, and this is the answer to the original question."
where
n = probability that the propositioner picks red after the player has picked a red.
heihojin's reasoning is great because it requires no assumptions about the motivations of the propositioner! In the typical monty hall question n = 1, so switch. In the random case, n = 1/2 so it does not matter.
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