I've seen statements of Newcomb-like problems saying things like "Omega gets it right 90% of the time". In that case it seems like it should matter whether it's because of cosmic rays that affect all predictions equally, or whether it's because he can only usefully predict the 90% of people who are easiest to predict, in which case if I'm not mistaken you can two-box if you're confident you're in the other 10%. I'm sure this would have been thought through somewhere before.