The interesting properties actually all exist in the original Newcomb's Problem, which if you're not familiar with it, has two important differences: First, Omega leaves the boxes, so they're both there. Second, Omega always, or nearly always in some variations, predicts what you'll do. (So the expected value is $1,000 versus $1,000,000).

The addition of these two properties result in some number of people insisting they'd two-box, and in at least one philosopher's answer, if for no other reason than to take a principled stand for human autonomy and free will. (Which, if this weren't all talk, would be rather an expensive principle that one has no choice but to stand up for...)