In any decision involving an Omega like entity that can run perfect simulations of you, there wouldn't be a way to tell if you were inside the simulation or in the real universe. Therefore, in situations where the outcome depends on the results of the simulation, you should act as though you are in the simulation. For example, in counterfactual mugging, you should take the lesser amount because if you're in Omega's simulation you guarantee your "real life" counterpart the larger sum.

Of course this only applies if the entity you're dealing with happens to be able to run perfect simulations of reality.