Jiro comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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When you say that player 2 "is obviously not going to pay out" that's an approximation. You don't know that he's not going to pay off. You know that he's very, very, very, unlikely to pay off. (For instance, there's a very slim chance that he subscribes to a kind of honesty which leads him to do things he says he'll do, and therefore doesn't follow minimax.) But in Pascal's Mugging, "very, very, very, unlikely" works differently from "no chance at all".