Solving for standard deviation

[alThor]

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My problem is that I'm solving for the standard deviation of one HAND, but then trying to use that to find the standard deviation of a hundred WAGERS

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Yes, and that's what cannot be done (if I understand your use of those terms). So can't you incorporate all of this extra uncertainty (# hands, wager size, etc.) into your simulation engine? If so, you can estimate all kinds of things regarding the risk per ROUND of betting.

alThor

[Izverg04]

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If so, you can estimate all kinds of things regarding the risk per ROUND of betting.

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He doesn't want to calculate risk per ROUND of betting, he wants to calculate risk per BET.

He's got a dataset with 2 columns. Column1 has NBETS (bets put in on a round), Column2 has RESULT. He wants to use this dataset to calculate the variance on 1 bet, not 1 round.

A simplistic method to do this is to calculate Var(Column2)/Ave(Column1). This is wrong though (although not by much to be important in practice). To get the right answer, you also need to incorporate Var(Column1) and Cov(Column1,Column2) which is non-zero.

I'd have to spend a bit of time to give the OP the right answer, but I hope the problem is now made clear.