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Alicorn comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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I'm pretty sure the logic is correct. I do make silly math mistakes sometimes, but I've tested this one on Vladimir Nesov and he agrees. No comment from Eliezer yet (this scenario was first posted to decision-theory-workshop).
It reminds me vaguely of Pascal's Wager, but my cached responses thereunto are not translating informatively.
Then I think the original Newcomb's Problem should remind you of Pascal's Wager just as much, and my scenario should be analogous to the refutation thereof. (Thereunto? :-)