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Jiro comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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The problem, as stated, as far as I can tell gives Omega three options:
It is likely that Omega will try to correctly predict what the person will choose; that is, Omega will strive to ignore the first option. If Omega offers the choice to this hypothetical person in the first place, then Omega is not taking the second option.
That leaves the third option; to cheat. I expect that this is the choice that Omega will be most likely to take; one of the easiest ways to do this is by ignoring the spirit of the constraints and taking the exact literal meaning. (Another way is to creatively misunderstand the spirit of the rules as given).
So I provided some suggestions with regard to how Omega might cheat; such as arranging that the decision is never made.
If you think that's outside the problem, then I'm curious; what do you think Omega would do?
The constraints aren't constraints on Omega; the constraints are constraints on the reader--they tell the reader what he is supposed to use as the premises of the scenario. Omega cannot cheat unless the reader interprets the description of the problem to mean that Omega is willing to cheat. And if the reader does interpret it that way, it's the reader, not Omega, who's violating the spirit of the constraints and being hyper-literal.
I think that depending on the human's intentions, and assuming the human is a perfect reasoner, the conditions of the problem are contradictory. Omega can't always predict the human--it's logically impossible.