Whatever the experiment, you can't expect the results to shift your beliefs (on average!) in a particular direction.
P(H) = P(H|E)*P(E) + P(H|~E)*P(~E)
prior probability = expected posterior probability
(<a href="https://www.lesswrong.com/tag/conservation-of-expected-evidence">https://www.lesswrong.com/tag/conservation-of-expected-evidence</a>)