You can predict that water will boil when put on fire without simulating the movement of 10^23 molecules.
True but irrelevant. In order to make an accurate prediction, Omega needs, at the very least, to simulate my decision-making faculty in all significant aspects. If my decision-making process decides to recall some particular memory, then Omega needs to simulate that memory in all significant aspects. If my decision-making process decides to wander around the room conducting physics experiments, just to be a jackass, and to peg my decision to the results of those experiments - well, then Omega will need to convincingly simulate the results of those experiments. The anticipated experience will be identical for my actual decision-making process as for my simulated decision-making process.
Mind you, based on what I know of the brain, I think you'd actually need to run a pretty convincing, if somewhat coarse-grained, simulation of a good chunk of my light cone in order to predict my decision with any kind of certainty, but I'm being charitable here.
And yes, this seems to render the original formulation of the problem paradoxical. I'm trying to think of ways to suitably reformulate it without altering the decision theoretics, but I'm not sure it's possible.
...True but irrelevant. In order to make an accurate prediction, Omega needs, at the very least, to simulate my decision-making faculty in all significant aspects. If my decision-making process decides to recall some particular memory, then Omega needs to simulate that memory in all significant aspects. If my decision-making process decides to wander around the room conducting physics experiments, just to be a jackass, and to peg my decision to the results of those experiments - well, then Omega will need to convincingly simulate the results of those experim
This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.
Here's a diagram: