Assume no "future peeking" and Omega only correctly predicting people as difficult to predict as you with 99.9% probability. One-boxing still wins.

Newcomb's Problem is silly. It's only controversial because it's dressed up in wooey vagueness. In the end it's just a simple probability question and I'm surprised it's even taken seriously here. To see why, keep your eyes on the bolded text:

Omega has been correct on each of 100 observed occasions so far - everyone [on each of 100 observed occasions] who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars.

What can we anticipate from the bolded part? The only actionable belief we have at this point is that 100 out of 100 times, one-boxing made the one-boxer rich. The details that the boxes were placed by Omega and that Omega is a "superintelligence" add nothing. They merely confuse the matter by slipping in the vague connotation that Omega could be omniscient or something.

In fact, this Omega character is superfluous; the belief that the boxes were placed by Omega doesn't pay rent any differently than the belief that the boxes just appeared at random in 100 locations so far. If we are to anticipate anything different knowing it was Omega's doing, on what grounds? It could only be because we were distracted by vague notions about what Omega might be able to do or predict.

The following seemingly critical detail is just more misdirection and adds nothing either:

And the twist is that Omega has put a million dollars in box B iff Omega has predicted that you will take only box B.

I anticipate nothing differently whether this part is included or not, because nothing concrete is implied about Omega's predictive powers - only "superintelligence from another galaxy," which certainly sounds awe-inspiring but doesn't tell me anything really useful (how hard is predicting my actions, and how super is "super"?).

The only detail that pays any rent is the one above in bold. Eliezer is right that one-boxing wins, but all you need to figure that out is Bayes.

EDIT: Spelling

I have found that the logical approach like this one works much more rarely than it doesn't, simply because it appears that people can manage not to trust reason, or to doubt the validity of the (more or less obvious) inferences involved.

Additionally, belief is so emotional that even people who see all the logic, and truly seem to appreciate that believing in God is completely silly, still can't rid themselves of the belief. It's like someone who knows household spiders are not dangerous in any way and yet are more terrified of them than, say, an elephant.

Perhaps what's needed in addition to this is a separate "How to eschew the idea of god from your brain" guide. It would include practical advice collected from various self-admitted ex-believers. Importantly, I think people who have never believed should avoid contributing to such a guide unless they have reasons to believe that they have an extraordinary amount of insight into a believer's mind.

I have found that the logical approach like this one works much more rarely than it doesn't, simply because it appears that people can manage not to trust reason, or to doubt the validity of the (more or less obvious) inferences involved.

Additionally, belief is so emotional that even people who see all the logic, and truly seem to appreciate that believing in God is completely silly, still can't rid themselves of the belief. It's like someone who knows household spiders are not dangerous in any way and yet are more terrified of them than, say, an elephant.

Perhaps what's needed in addition to this is a separate "How to eschew the idea of god from your brain" guide. It would include practical advice collected from various self-admitted ex-believers. Importantly, I think people who have never believed should avoid contributing to such a guide unless they have reasons to believe that they have an extraordinary amount of insight into a believer's mind.

I can understand 'supernatural' in the context of the Game Of Life: the user ('God' if you like) violates the laws of physics (in this case by anomalously switching some cells on or off).

Can't we give pretty much the same definition of 'supernatural' in the real world? (Relative to the 'true laws of physics' whatever they are.)

Perhaps we could say that a supernatural event is one that "increases the algorithmic information content of the universe", though formulating this precisely would require some care.

It's also often used to mean "not material," or "not obeying the same laws as most stuff we see." So the stuff we see around us is the "natural," and things that don't follow natural law are "supernatural."

I suspect most supernatural beliefs are non-reductable just because they're made up by people and people don't generally think in terms of reductionism. I prefer "magic" form for complicated human-interacting ontologically basic things.

I didn't downvote and it's not an inappropriate topic, but the post is a bit rambling. More thought and editing could allow you to figure out what you're really trying to say, and hence tighten up the post.

So from the negative votes I'm guessing that this is not something you guys find appropriate in "discussion"? It would help me as a newcomer if you also suggested what makes it bad :)