1⁄2 is a reasonable answer because it was decided by a coinflip, and no new information has been given. For some possible behaviors of the guard, this is true—say “the guard flipped a coin, and made a statement about vulcan or earth based on that coin”. For other possible behaviors (“the guard equiprobably picked one of the three non-true options to eliminate”), information _WAS_ revealed, by the unequal planetary weighting of possible guard statements. For still different others (“the guard eliminates the vulcan desert if you are elsewhere, and says nothing if you are there”), the information revelation is also in the distribution of making a statement or not.
I have no clue how a prisoner can distinguish between these guard-information mechanisms. Intentionally ambiguous situations are ambiguous, I guess.
1⁄2 is a reasonable answer because it was decided by a coinflip, and no new information has been given. For some possible behaviors of the guard, this is true—say “the guard flipped a coin, and made a statement about vulcan or earth based on that coin”. For other possible behaviors (“the guard equiprobably picked one of the three non-true options to eliminate”), information _WAS_ revealed, by the unequal planetary weighting of possible guard statements. For still different others (“the guard eliminates the vulcan desert if you are elsewhere, and says nothing if you are there”), the information revelation is also in the distribution of making a statement or not.
I have no clue how a prisoner can distinguish between these guard-information mechanisms. Intentionally ambiguous situations are ambiguous, I guess.