The Month Hall Problem has been discussed many many times on HN and elsewhere. I've read many of the discussions (but of course not nearly all of them. My obser

The Month Hall Problem has been discussed many many times on HN and elsewhere. I've read many of the discussions (but of course not nearly all of them. My observations: 1. The linked Wikipedia article is very extensive, and already covers usually all the points and insights that forum posters bring up. And a lot more. 2. Few people will probably bother to read the entire (or even most of the) Wikipedia article, because it's so extensive. 3. I'll copy and highlight the IMO most crucial part the article here: The most famous formulation, a column in Parade magazine in 1990, went thus: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? In this formulation the solution is ambiguous. Switching is *not necesarily* the optimal strategy (it depends on the precise strategy/behavior of the host, which is not well formulated). Under the unambigous "standard assumptions": - The host must always open a door that was not picked by the contestant. - The host must always open a door to reveal a goat and never the car. - The host must always offer the chance to switch between the originally chosen door and the remaining closed door. switching is the better strategy. But in this formulation the reason is also a lot more obvious.