A tough variance problem (at least for me)

[TNixon]

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Having a downswing of a particular size is very different from losing that amount in a fixed number of hands.

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Did you read my example? I *think* I'm calculating a close approximation of what I'm trying to get at there. If the example doesn't work, can you explain why, and how to get a real approximation?

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Losing $x starting at hand 1 is far from independent from losing $x starting at hand 2.

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Again, I'm not sure I understand what you're saying here. I mean, I understand what you're saying, I'm just not seeing how it's relevant.

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%?