I answered in the 99% confidence bracket. The intuition pump that got me there is talking about submitting computer programs that output a decision, rather than simply making a decision. Omega gets to look at the program that makes the decision before filling the boxes. It's obvious in this situation - you submit a program that one-boxes, open that box, and get the million dollars (since Omega knows that you are going to one-box, since it's in the computer code).

Now, the real Newcomb problem has people making the decision, not code. But, if you assume determinism, the state of the universe and the laws of physics at the time Omega makes their prediction is the submitted computer code. One-boxing has a higher payoff, so you should be the sort of person who one-boxes.