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MoreOn comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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You're essentially engaging in arbitrage, taking advantage of the difference in the probabilities assigned to both boxes being full by different people. Which is one reason rational people never assign 0 probability to anything.
You could just as well go to some one-boxers (who "believe P(both full) = 0") and offer them a $1 bet 10000000:1 in your favor that both boxes will be full; then offer the two-boxers whatever bet they will take "that only one box is full" that will give you more than $1 profit if you win. Thus, either way, you make a profit, and you can make however much you like just by increasing the stakes.
This still doesn't actually solve newcomb's problem, though. I'd call it more of a cautionary tale against being absolutely certain.
(Incidentally, since you're going into this "fully intending" to take both boxes, I'd expect both one boxers and two boxers to agree on the extremely low probability Omega is going to have filled both boxes.)
Yes, nshepperd, my assumption is that P << 0.5, something in the 0.0001 to 0.01 range.
Besides, arbitrage would still be possible if some people estimated P=0.01 and others P=0.0001, only the solution would be messier than what I'd ever want to do casually. Besides, if I were unconstrained by the bets I could make (I'd tried to work with a cap before), that would make making profits even easier.
I wasn't exactly trying to solve the problem, only to find a "naively rational" workaround (using the same naive rationality that leads prisoners to rat each other out in PD).
When you're saying that this doesn't solve Newcomb's problem, what do you expect the solution to actually entail?
Yes, arbitrage is possible pretty much whenever people's probabilities disagree to any significant degree. Setting P = 0 just lets you take it to absurd levels (eg. put up no stake at all, and it's still a "fair bet").
Maximizing the money found upon opening the box(es) you have selected.
If you like, replace the money with cures for cancer with differing probabilities of working, or machines with differing probabilities of being a halting oracle, or something else you can't get by exploiting other humans.