Congratulations, you have stumbled on a problem we were researching pretty actively a month ago or so. See this post of mine and the links from there, especially the discussion between Eliezer and Wei in an old mailing list thread.
The current status of the problem is that the Solomonoff prior is not sufficient for playing all games, and in fact any prior (computable or not) can be beaten by a suitably chosen “epistemically lucky” ordinary human. Here’s a MathOverflow thread with a proof. Be warned, it may be rather hard to understand.
Congratulations, you have stumbled on a problem we were researching pretty actively a month ago or so. See this post of mine and the links from there, especially the discussion between Eliezer and Wei in an old mailing list thread.
The current status of the problem is that the Solomonoff prior is not sufficient for playing all games, and in fact any prior (computable or not) can be beaten by a suitably chosen “epistemically lucky” ordinary human. Here’s a MathOverflow thread with a proof. Be warned, it may be rather hard to understand.