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BT_Uytya comments on Circular belief updating - LessWrong
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If I were a Dark, I would try to rearrange the cards so they look random to an unsophisticated observer. No long runs of same color, no obvious patterns in numbers (people are bad random number generators, they think that random string is string without any patterns, not string without big patterns, 17 is the most random number, blah blah blah).
(It's possible that the variation of it can be a good strategy even against more sophisticated agents, because if by a pure chance string of cards has low Kolmogorov complexity, agent is going to take this as evidence for Bright, and I don't want him to believe in Bright)
I think I have a proof that the only Nash equilibrium strategies for Dark playing against a perfect reasoner are those that lead to a uniform distribution over observed decks. K-complexity doesn't seem to come into it. What Dark should do against an imperfect reasoner is a different question, which we can't solve because we don't have a good theory of imperfect reasoning.