Hi,

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). However, I've tripped over a conceptual error that I'm unsure how to resolve.

The number of bets placed on a hand is not constant, because you can double or split. Since the pdf will end up being normal, I supposed that I could use the formula B*S*sqrt(WR/(B*M)), where:
B is the bet size, S is the s.d. of a single hand of pontoon, WR is the amount we are wagering, and M is the expected number of bets placed on a single hand of pontoon.

Unfortunately, there is a covariance between the number of hands played and the average bet size: the more we double and split, the less hands we will play. How do I resolve this problem? (Thanks to the person who pointed this out to me.)

I also wonder, as a result of this covariance, if this problem even has an exact solution at all. 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?

Thanks for any and all help!