What do you mean?

I mean that as part of the specification of the problem, Omega has all the information necessary to determine what you will choose before you know yourself. There are causal arrows that descend from the situation specified by that information to (i) your choice, and (ii) the contents of the box.

why almost no one here seems to see the point of 2-boxing, and the amazing overconfidence is beyond me.

You stated that "the game is rigged". The reasoning behind 2-boxing ignores that fact. In common parlance, a rigged game is unwinnable, but this game is knowably winnable. So go ahead and win without worrying about whether the choice has the label "rational" attached!

Yes, that's true. Now chase "however obtained" up a level -- after all, you have all the information necessary to do so.

No. The method's output depends on its input, which by hypothesis is a specification of the situation that includes all the information necessary to determine the output of the individual's decision algorithm. Hence the decision algorithm is a causal antecedant of the contents of the boxes.

It's better for the thief to two-box because it isn't the thief's decision algorithm that determined the contents of the boxes.

You have the same choice as me...

If Omega fills the boxes according to its prediction of the choice of the person being offered the boxes and not the person who ends up with the boxes, then the above statement where your argument breaks down.

My point of view is that the winning thing to do here and the logical thing to do are the same.

If you want to understand my point of view or if you want me to understand your point of view, you need to tell me where you think logical and winning diverge. Then I tell you why I think they don't, etc.

You've mentioned 'backwards causality' which isn't assumed in our one-box solution to Newcomb. How comfortable are you with the assumption of determinism? (If you're not, how do you reconcile that Omega is a perfect predictor?)

Imagine a simple but related scenario that involves no backwards causation:

You're a 12 year old kid, and you know your mom doesn't want you to play with your new Splogomax unless an adult is with you. Your mom leaves you alone for an hour to run to the store, telling you she'll punish you if you play with the Splogomax, and that, whether there's any evidence of it when she returns, she knows you well enough to know if you're going to play with it, although she'll refrain from passing judgement until she has just gotten back from the store.

Assuming you fear punishment more than you enjoy playing with your Splogomax, do you decide to play or not?

Edit: now I feel stupid. There's a much simpler way to get my point across. Just imagine Omega doesn't fill any box until after you've picked up one or two boxes and walked away, but that he doesn't look at your choice when filling the boxes.

Yes. But it was filled, or not, based on a prediction about what you would do. We are not such tricksy creatures that we can unpredictably change our minds at the last minute and two-box without Omega anticipating this, so the best way to make sure the one box has the goodies in it is to plan to actually take only that box.

By rational, I think you mean logical. (We tend to define 'rational' as 'winning' around here.*)

... and -- given a certain set of assumptions -- it is absolutely logical that (a) Omega has already made his prediction, (b) the stuff is already in the boxes, (c) you can only maximize your payoff by choosing both boxes. (This is what I meant by this line of reasoning isn't incorrect, it's just unproductive in finding the solution to this dilemma.)

But consider what other logical assumptions have already snuck into the logic above. We're not familiar with outcomes that depend upon our decision algorithm, we're not used to optimizing over this action. The productive direction to think along is this one: unlike a typical situation, the content of the boxes depends upon your algorithm that outputs the choice, only indirectly on your choice.

You're halfway to the solution of this problem if you can see both ways of thinking about the problem as reasonable. You'll feel some frustration that you can alternate between them -- like flip-flopping between different interpretations of an optical illusion -- and they're contradictory. Then the second half of the solution is to notice that you can choose which way to think about the problem as a willful choice -- make the choice that results in the win. That is the rational (and logical) thing to do.

Let me know if you don't agree with the part where you're supposed to see both ways of thinking about the problem as reasonable.

* But the distinction doesn't really matter because we haven't found any cases where rational and logical aren't the same thing.

I deny that 1-boxing nets more money - ceteris paribus.

Then you're simply disagreeing with the problem statement. If you 1-box, you get $1M. If you 2-box, you get $1k. If you 2-box because you're considering the impossible possible worlds where you get $1.001M or $0, you still get $1k.

At this point, I no longer think you're adding anything new to the discussion.