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.
It’s still not clear to me why playing mind games is a better strategy than just one-boxing, even in the 60% case. But I do understand your point about independence assumptions.
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.
It’s still not clear to me why playing mind games is a better strategy than just one-boxing, even in the 60% case. But I do understand your point about independence assumptions.