lukstafi comments on Counterfactual Calculation and Observational Knowledge - Less Wrong
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Vladimir says that "Omega doesn't touch any calculator". If the counterfactual is entered at the point where the computation starts and Omega tells you that it results in Odd (ETA2: rereading Vladimir's comment, this is not the case), then it is a second observation contributed by Omega running the calculator and should affect both worlds. If on the other hand the counterfactual is just about the display, then the counterfactual Omega will likely write down Odd (ETA3: not my current answer). So I agree with your analysis. I see it this way: real Omegas cannot write on counterfactual paper.
ETA: -- the "counterfactual" built as "being in another quantum branch of exactly the same universe" strikes me as being of the sort where Omega does run the calculator again, so it should affect both worlds as another observation.
ETA2: I've changed my mind about there being an independent observation.