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Alsadius comments on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 - Less Wrong Discussion
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Seems very clear at this point that Q. cannot predict Harry's actions, and that he was responsible for Hermione's framing. Truth is entangled, Harry is very clever, especially when not under a time crunch- this seems very likely to me.
I think the probability might be that high given narrative requirements(i.e., Harry will near-certainly figure it out, Potter books usually end at the end of school years and it's April, and we know that the series is in the homestretch), but I'd put an in-universe probability without reference to that data a vastly lower chance.