While figuring out my error in my solution to the Ultimate Newcomb's Problem, I ran across this (distinct) reformulation that helped me distinguish between what I was doing and what the problem was actually asking.
... but that being said, I'm not sure if my answer to the reformulation is correct either.
The question, cleaned for Discussion, looks like this:
You approach the boxes and lottery, which are exactly as in the UNP. Before reaching it, you come to sign with a flashing red light. The sign reads: "INDEPENDENT SCENARIO BEGIN."
Omega, who has predicted that you will be confused, shows up to explain: "This is considered an artificially independent experiment. Your algorithm for solving this problem will not be used in my simulations of your algorithm for my various other problems. In other words, you are allowed to two-box here but one-box Newcomb's problem, or vice versa."
This is motivated by the realization that I've been making the same mistake as in the original Newcomb's Problem, though this justification does not (I believe) apply to the original. The mistake is simply this: that I assumed that I simply appear in medias res. When solving the UNP, it is (seems to be) important to remember that you may be in some very rare edge case of the main problem, and that you are choosing your algorithm for the problem as a whole.
But if that's not true - if you're allowed to appear in the middle of the problem, and no counterfactual-yous are at risk - it sure seems like two-boxing is justified - as khafra put it, "trying to ambiently control basic arithmetic".
(Speaking of which, is there a write up of ambient decision theory anywhere? For that matter, is there any compilation of decision theories?)
EDIT: (Yes to the first, though not under that name: Controlling Constant Programs.)