We assume that Omega is powerful enough to simulate your brain and the environment precisely, and that quantumness is negligible.
In that case, you could still say that there's no way not to use a randomizer, but Omega would be using the same randomizer with the same seed.
If you use flipping a coin as a randomizer, Omega could simulate that too. But traditionally using coins doesn't fly while using brains is okay.
This is equivalent to Newcomb's Problem in the sense that any strategy does equally well on both, where by "strategy" I mean a mapping from info to (probability distributions over) actions.
I suspect that any problem with Omega can be transformed into an equivalent problem with amnesia instead of Omega.
Does CDT return the winning answer in such transformed problems?
Discuss.