>>16633830
>monty presents me 100 doors
>i pick one door not to open
>1/100 to be right
>monty picks one door not to open
>if his choice was independent of mine, 1/100 chance to be right
>if his choice was changed by my choice removing an option, 1/50 chance to be right
>monty's choice is either twice as likely to be right as mine or half as likely to be right as mine depending on an unknowable variable, presenting two entirely separate mathematically correct answers
>a shell past this, is the separate logic problem of whether monty opening a car door is even a relevant part of the solution set at all or if his choice is just a 1/3 roll on simply ending the game, in which case it would be correct to treat it as a foregone conclusion that either monty was never going to open the car door or the question never mattered
See what I mean? Designed to make people argue. The correct answer is give me my goat.
>>16633831
Ah I see what you mean. My contention sort of poorly explained above would be that even the random choice scenario should be treated the same as a scenario where the host always avoids the car, because we are really only considering the scenario where he randomly did not choose the car to open. If he opens the car door your second choice didn't matter, it won't get made. So in situations where the choice to switch is relevant the car door was always going to be opened.

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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…