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Polaris comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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Either box B is already full or already empty.
I'm not going to go into the whole literature, but the dominant consensus in modern decision theory is that one should two-box, and Omega is just rewarding agents with irrational dispositions. This dominant view goes by the name of "causal decision theory".
I suppose causal decision theory assumes causality only works in one temporal direction. Confronted with a predictor that was right 100 out of 100 times, I would think it very likely that backward-in-time causation exists, and take only B. I assume this would, as you say, produce absurd results elsewhere.
@Nick_Tarleton
Agreed, the problem immediately reminded me of "retroactive preparation" and time-loop logic. It is not really the same reasonning, but it has the same "turn causality on its head" aspect.
If I don't have proof of the reliability of Omega's predictions, I find myself less likely to be "unreasonnable" when the stakes are higher (that is, I'm more likely to two-box if it's about saving the world).
I find it highly unlikely that an entity wandering across worlds can predict my actions to this level of detail, as it seems way harder than traveling through space or teleporting money. I might risk a net loss of $1 000 to figure it out (much like I'd be willing to spend $1000 to interact with such a space-traveling stuff-teleporting entity), but not a loss of a thousand lives. In the game as the article describe it, I would only one-box if "the loss of what box A contains and nothing in B" was an acceptable outcome.
I would be increasingly likely to one-box as the probability of the AI being actually able to predict my actions in advance increases.