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I don't understand why the given solution doesn't fall prey to the same problem of "her logic would make it unnecessary to consult the guard". By this solution

I don't understand why the given solution doesn't fall prey to the same problem of "her logic would make it unnecessary to consult the guard". By this solution, if the guard says "B" (as in the original story), the probably of A being condemned goes up. But if the guard says "C", the probably also goes up by the same amount, because the graph is symmetric! Going by this logic, if the guard is not allowed to say "A", then their answer doesn't matter. So why isn't the final probability still 1/3?

strangecasts 9y ago
The final probability of A being released is indeed 1/3. The second part of the article just attempts to nail down the specific fallacy in A's reasoning, which is also helpful in explaining the Monty Hall problem (which makes the guard's orders implicit rather than explicit)
shardo 9y ago
I think it's the author's fault for switching between probabilities and odds and the readers for not recognizing the switch. "Thus A’s chance of being condemned remains twice that of being pardoned." When he says this, he is talking of odds of 2:1 and therefore, the probability of not being condemned is 1/1+2 = 1/3 Also when he says "Because, unlike in Monty Hall, the intuitive judgment is the correct one in Mosteller’s puzzle." He means the intuitive judgment that 1/2 is incorrect. I was extremely confused the first 2-3 times I read it and kept trying to understand the author's viewpoint because everything other than these two statement seemed to make sense. At least I wasn't the only one.