P(guessed right) isn’t exactly 0.5 (most likely). We expand it as
P(experience helped (prior)) P(guessed right | experience helped) +
P(experience didn’t help (prior)) P(guessed right | experience didn’t help).
Of these, only P(guessed right | experience didn’t help) should be 0.5; P(guessed right | experience helped) should be higher. So on average P(guessed right) is somewhere in between depending on your priors.
P(guessed right) isn’t exactly 0.5 (most likely). We expand it as
P(experience helped (prior)) P(guessed right | experience helped) + P(experience didn’t help (prior)) P(guessed right | experience didn’t help).
Of these, only P(guessed right | experience didn’t help) should be 0.5; P(guessed right | experience helped) should be higher. So on average P(guessed right) is somewhere in between depending on your priors.
Right, thanks. Pushing the uniform approximations to the point of silliness I get 4⁄7 for a rough value (with the prior then being 2⁄7).