say: we have two games one game has SD = X and is played f% of the time the other game has SD = Y and is played z% of the time mathematically what is the proper way to calculate the 'combined' standard deviation?

I would start with this thread, which seems like it was active only a couple months ago, but is actually two years old, WTF?

Assuming f and z are fractions rather than percents for simplicity. Variance=(f*X^2+z*Y^2) Sandard_Deviation=SquareRoot(Variance)

lol, so a rehash lol, thanks as always, Canceler but yeah, two years old, good reason i guess for not being able to remember how to do it, but hazily suspecting it had something to do with taking a square root before adding.... edit: (geesh, yeah two years, took that much time to realize how much i care about standard deviation) :whip: some stuff you can just add, like i think EV is additive, other stuff, like standard deviation, errhh a bit trickier, lol so this looks key here to me:

ok, thank you ICNT. so digressing a bit...... say you have in the case of blackjack SD = Z for a hand of blackjack so to get the standard deviation for N hands would it be: Z*SQRT(N) ?

yep that is why accumulated expectations overcome accumulated standard deviations as the number of hands increases, because the former (expectation) is proportional to the number of hands, while SD is proportional to the square root of the number of hands

heh, heh, funny you should mention that, cause that's what i just noticed fooling around in excel with this stuff. kewl!

fixed is fixed Those formulas are for fixed bets right? If you resize bets on wins and losses the long run is longer.