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I've always used WoO's value of 1.16 s.d. on blackjack to find the standard deviation of 100 bets by doing 1.16*sqrt(bets). Does this 1.16 account for the covariance, or is it just an inaccuracy that we have to live with?
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That is the SD for one hand. Therefore it cannot have anything to do with covariance.
http://wizardofodds.com/blackjack/bjapx4.html
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I'm writing a simulator for solving the standard deviation of wagering X dollars on pontoon (a blackjack variant with a lower house edge than any form of BJ regularly offered).
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If you're simulating, I'm not really sure what the problem could be. Keep track of the total dollars won/lost on each round of play. Also keep a running total of the square of that number. At the end, variance is the sum of squares(*) minus the mean squared, and you're done. Maybe you didn't mean to say simulation?
alThor
(*) I'm intentionally ignoring the "n/n-1" factor.