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Stuart_Armstrong comments on My Fundamental Question About Omega - Less Wrong
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"Perfect predictor" leads us somewhat astray. "Bloody good predictor" would be enough (same reason to avoid probabilites 1 and 0, except as a shorthand).
Then if Omega shows up and predicts you will give it $5, and you don't feel like it, then don't. Omega made a mistake - which is possible, as he's only nearly perfect.