I meant that something takes the functional equivalent of Omega. There is a dissimilarity, but not enough to make it irrelevant. The point that Psychohistorian and I are making is that the problems have subtly contradictory premises, which I think the examples (including modified TSL) show. Because the premises are contradictory, you can assume away a different one in each case.

In the original TSL, TDT says "hey, it's decided anyway whether I have cancer, so my choice doesn't affect my cancer". But in Newcomb's problem, TDT says, "even though omega has decided the contents of the box, my choice affects my reward".