[pzhon]

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I'm sure I must be missing something, but is it even possible to double to 1/3 the chips? If you doubled up again, then you'd have 2/3 the chips.

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That's not the point. With equal skill, the probability of reaching n times your stack before busting out is about 1/n. This doesn't require n to be a power of 2. He has a generalization to to situations where you assume that a player has a skill advantage.

His estimate of the probability of finishing in nth place is the probability of winning a tournament with 1/n times as many players minus the probability of finishing in higher places. This is a model which is only suitable for the start of a tournament. It's not clear whether this is a good model or a bad model.

I think he comes up with really bad conclusions using this model. His results are still much more conservative than from other models. I'm not sure why. I think he made a serious miscalculation.