If your choice to one-box or two-box is dependent upon some random factors, then Omega can’t predict what will happen because when he makes the prediction, he is up-branch of you. He doesn’t know which branch you’ll be in.
What Omega can do instead is simulate every branch and count the number of branches in which you two-box, to get a probability, and treat you as a two-boxer if this probability is greater than some threshold. This covers both the cases where you roll a die, and the cases where your decision depends on events in your brain that don’t always go the same way. In fact, Omega doesn’t even need to simulate every branch; a moderate sized sample would be good enough for the rules of Newcomb’s problem to work as they’re supposed to.
But the real reason for treating Omega as a perfect predictor is that one of the more natural ways of modeling an imperfect predictor is to decompose it into some probability of being a perfect predictor and some probability of its prediction being completely independent of your choice, the probabilities depending on how good a predictor you think it really is. In that context, denying the possibility that a perfect predictor could exist is decidedly unhelpful.
What Omega can do instead is simulate every branch and count the number of branches in which you two-box, to get a probability, and treat you as a two-boxer if this probability is greater than some threshold. This covers both the cases where you roll a die, and the cases where your decision depends on events in your brain that don’t always go the same way. In fact, Omega doesn’t even need to simulate every branch; a moderate sized sample would be good enough for the rules of Newcomb’s problem to work as they’re supposed to.
But the real reason for treating Omega as a perfect predictor is that one of the more natural ways of modeling an imperfect predictor is to decompose it into some probability of being a perfect predictor and some probability of its prediction being completely independent of your choice, the probabilities depending on how good a predictor you think it really is. In that context, denying the possibility that a perfect predictor could exist is decidedly unhelpful.