I’m finding "correct" to be a loaded term here. It is correct in the sense that your conclusions follow from your premises, but in my view it bears only a superficial resemblance to Newcomb’s problem. Omega is not defined the way you defined it in Newcomb-like problems and the resulting difference is not trivial.

To really get at the core dilemma of Newcomb’s problem in detail one needs to attempt to work out the equilibrium accuracy (that is the level of accuracy required to make one-boxing and two-boxing have equal expected utility) not just arbitrarily set the accuracy to the upper limit where it is easy to work out that one-boxing wins.

First, thanks for explaining your down vote and thereby giving me an opportunity to respond.

We say that Omega is a perfect predictor not because it's so very reasonable for him to be a perfect predictor, but so that people won't get distracted in those directions.

The problem is that it is not a fair simplification, it disrupts the dilemma in such a way as to render it trivial. If you set the accuracy of the prediction to %100 many of the other specific details of the problem become largely irrelevant. For example you could then put $999,999.99 into box A and it would still be better to one-box.

It’s effectively the same thing as lowering the amount in box A to zero or raising the amount in box B to infinity. And one could break the problem in the other direction by lowering the accuracy of the prediction to %50 or equalizing the amount in both boxes.

We must disagree about what is the heart of the dilemma. How can it be all about whether Omega is wrong with some fractional probability?

It’s because the probability of a correct prediction must be between %50 and %100 or it breaks the structure of the problem in the sense that it makes the answer trivial to work out.

Rather it's about whether logic (2-boxing seems logical) and winning are at odds.

I suppose it is true that some people have intuitions that persist in leading them astray even when the probability is set to %100. In that sense it may still have some value if it helps to isolate and illuminate these biases.

Or perhaps whether determinism and choice is at odds, if you are operating outside a deterministic world-view. Or perhaps a third thing, but nothing --in this problem -- about what kinds of Omega powers are reasonable or possible. Omega is just a device being used to set up the dilemma.

My objection here doesn’t have to do with whether it is reasonable for Omega to possess such powers but with the over-simplification of the dilemma to the point where it is trivial.

I don’t think Newcomb’s Problem can easily be stated as a real (as opposed to a simply logical) problem. Any instance of Newcomb’s problem that you can feasibly construct in the real world it is not a strict one shot problem. I would suggest that optimizing a rational agent for the strictly logical one shot problem one is optimizing for a reality that we don’t exist in.

Even if I am wrong about Newcomb’s problem effectively being an iterated type of problem treating it as if it is seems to solve the dilemma.

Consider this line of reasoning. Omega wants to make the correct prediction. I want Omega to put the million dollars in the box. If I one-box I will either reward Omega for putting the money in the box or punish Omega for not putting the money in the box. Since Omega has a very high success rate I can deduce that Omega puts a high value on making the correct prediction I will therefore put a correspondingly high value on the instrumental value of spending the thousand dollars to influence Omega’s decision. But here’s the thing, this reasoning occurs before Omega even presents you with the problem. It is worked out by Omega running your decision algorithm based on Omega’s scan of your brain. It is effectively the first iteration.

You are then presented with the choice for what is effectively the second time and you deduce that any real Omega (as opposed to some platonic ideal of Omega) does something like the sequence described above in order to generate it’s prediction.

In Charlie’s case you may reason that Charlie either doesn’t care or isn’t able to produce a very accurate prediction and so reason he probably isn’t running your decision algorithm so spending the thousand dollars to try to influence Charlie’s decision has very low instrumental value.

In effect you are not just betting on the probability that the prediction is accurate you are also betting on whether your decision algorithm is affecting the outcome.

I’m not sure how to calculate this but to take a stab at it:

Edit: Removed a misguided attempt at a calculation.