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I don't think 40 sessions is enough, but it has been too long since I've done the math to determine what would get you to a high enough confidence level.
Still, I'm very intrigued, especially by the way he's varying his bet size. Normally, that kind of thing makes sense as the probabilities shift and don't have much to do with whether you won or lost the last bet. I would focus on the pattern between which side he's on and the bet size variation. There must be a pattern there somewhere, but I don't know the game at all.
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"Unlearning is the highest form of learning"
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