[TNixon]

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It was a confused mess, and the method does not work. Sorry, I don't have time to explain why if my previous comments, and the comments of others, are not enough despite their relevance.

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Nobody else has commented on it at all, and your comments were not exactly self-explanatory.

My example was based on this very simple chain of logic:

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Is it not reasonable to say that, at any given point, the probability of your current progress being within one standard deviation of the mean is 68%? And if it is reasonable to say that, then it also seems reasonable to carry that probability across multiple hands, so that over a 2 hand span, the probability of being within one standard deviation for the entire span would be 46.24%?

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There are only two links in the chain there, but if they hold true, then the method I used would be a valid approximation (given that I'm willing to adjust the question slightly). If one of the links is bad, then it shouldn't be a great exercise in thought or time to point out which one and why.

I'm more than happy to admit I'm in over my head here, and would be very happy to be given some real direction, rather than just being told "that doesn't work, but I don't really feel like telling you why".