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MatthewW comments on Open Thread September, Part 3 - Less Wrong
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To get to the conclusion that against a 60% Omega you're better off to one-box, I think you have to put in a strong independence assumption: that the probability of Omega getting it wrong is independent of the ways of thinking that the player is using to make her choice.
I think that's really the original problem in disguise (it's a 100% Omega who rolls dice and sometimes decides to reward two-boxing instead of one-boxing). The analysis if all you know is that Omega is right 60% of the time would look different.
How exactly different?
It would become a mind game: you'd have to explicitly model how you think Omega is making the decision.
The problem you're facing is to maximise P(Omega rewards you|all your behaviour that Omega can observe). In the classical problem you can substitute the actual choice of one-boxing or two-boxing for the 'all your behaviour' part, because Omega is always right. But in the 'imperfect Omega' case you can't.