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Kindly comments on Harry Potter and the Methods of Rationality discussion thread, part 23, chapter 94 - Less Wrong Discussion
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A more perfectly isomorphic variant of Newcomb's problem is the following. Both boxes are transparent, and Omega acts according to the following rule: if you two-box when box B is empty, then box B is always empty, while if you one-box, box B is empty with a 50% chance.
If you one-box in this variant, you win half a million dollars in expectation. If you intend to two-box should you see that box B is empty, then you only win a thousand dollars.
... Perhaps, but that's no longer isomorphic to the actual problem. We are past the point of Omega's influence; in Newcomb's problem, it'd be as if Omega grabbed your mind state, ran it forward until it confirmed that you would not initially two-box, and then stopped. Omega itself has been removed from the problem, and you're left with one empty box that you've already claimed a million dollars from (or negative one million, in this case) and one closed box.
Near as we can tell, history can't change in the MoRverse: what's done is done, so Harry might as well exploit it.