In the classic Newcomb's Problem Omega moves first before I can do anything. Step 1 happens before I made any choices.

This is true both for the 99% and 100% accurate predictor, isn't it? Yet you say you one-box with the 100% one.

I can make a choice only after step 1, once the boxes are set up and unchangeable. And after step 1 everything is fixed so you should two-box.

Please answer me this:

What does 99% accuracy mean to you exactly, in this scenario? If you know that Omega can predict you with 99% accuracy, what reality does this correspond to for you? What do you expect to happen different, compared to if he could predict you with, say, 50% accuracy (purely chance guesses)?

Actually, let's make it more specific: suppose you do this same problem 1000 times, with a 99% Omega, what amount of money do you expect to end up with if you two-box? And what if you one-box?

The reason I am asking is that it appears to me like, the moment Omega stops being perfectly 100% accurate, you really stop believing he can predict you at all. It's like, if you're given a Newcomblike problem that involves "Omega can predict you with 99% accuracy", you don't actually accept this information (and are therefore solving a different problem).

It's unsafe to guess at another's thoughts, and I could be wrong. But I simply fail to see, based on the things you've said, how the "99% accuracy" information informs your model of the situation at all.

I can make a choice only after step 1, once the boxes are set up and unchangeable.

It's common to believe that we have the power to "change" the future but not the past. Popular conceptions of time travel such as Back To The Future show future events wavering in and out of existence as people deliberate about important decisions, to the extent of having a polaroid from the future literally change before our eyes.

All of this, of course, is a nonsense in deterministic physics. If any part of the universe is "already" determined, it all is (and by the way quantum "uncertainty" doesn't change this picture in any interesting way). So there is not much difference between controlling the past and controlling the future, except that we don't normally get an opportunity to control the past, due to the usual causal structure of the universe.

In other words, the boxes are "already set up and unchangeable" even if you decide before being scanned by Omega. But you still get to decide whether they are unchangeable in a favourable or unfavourable way.

If Omega is a good predictor, he'll predict my decision, but there is nothing I can do about it. I don't make a choice to be a "two-boxer" or a "one-boxer".

Well, if that's true -- that is, if whether you are the sort of person who one-boxes or two-boxes in Newcomblike problems is a fixed property of Lumifer that you can't influence in any way -- then you're right that there's no point to thinking about which choice is best with various different predictors. After all, you can't make a choice about it, so what difference does it make which choice would be better if you could?

Similarly, in most cases, given a choice between accelerating to the ground at 1G and doing so at .01 G once I've fallen off a cliff, I would do better to choose the latter... but once I fall off the cliff, I don't actually have a choice, so that doesn't matter at all.

Many people who consider it useful to think about Newcomblike problems, by contrast, believe that there is something they can do about it... that they do indeed make a choice to be a "two-boxer" or a "one-boxer."

I don't make a choice to be a "two-boxer" or a "one-boxer".

If you said earlier in this thread that you would two-box, you are a two-boxer. If you said earlier in this thread that you would one-box, you are a one-boxer. If Omega correctly predicts your status as a one-boxer/two-boxer, he will fill Box B with the appropriate amount. Assuming that Omega is a good predictor, his prediction is contingent on your disposition as a one-boxer or a two-boxer. This means you can influence Omega's prediction (and thus the contents of the boxes) simply by choosing to be a one-boxer. If Omega is a good-enough predictor, he will even be able to predict future changes in your state of mind. Therefore, the decision to one-box can and will affect Omega's prediction, even if said decision is made AFTER Omega's prediction.

This is the essence of being a reflectively consistent agent, as opposed to a reflectively inconsistent agent. For an example of an agent that is reflectively inconsistent, see causal decision theory. Let me know if you still have any qualms with this explanation.