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AlephNeil comments on Does Solomonoff always win? - Less Wrong
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How about if we restrict attention to games where at any stage the players are allowed to choose a probability distribution over the set of available moves, rather than being forced to choose one move? Is it then possible for Solomonoff induction to lose (whatever 'lose' means) with non-zero probability, in the limit?
In other words, does Solomonoff induction win all variants of game 1 that use different proper scoring rules in place of log score? Nice question. I'm going to sleep, will try to solve it tomorrow unless someone else does it first.