Broggly comments on Is That Your True Rejection? - Less Wrong
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Presumably the Predictor would be smart enough to calculate the result of that coin flip.
If it was an actually random bit, then I don't know. In the real universe, as you require, then the Predictor would have a 50% certainty of being right. Probably if the Predictor thought you might do that it wouldn't offer you the challenge, in order to maintain its reputation for omniscience.