standard deviation

Discussion in 'Skilled Play - Card Counting, Advanced Strategies' started by sagefr0g, Oct 26, 2011.

1. sagefr0gWell-Known Member

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?

2. CancelerWell-Known Member

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

3. iCountNTrackWell-Known Member

Assuming f and z are fractions rather than percents for simplicity.

Variance=(f*X^2+z*Y^2)

Sandard_Deviation=SquareRoot(Variance)

4. sagefr0gWell-Known Member

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:

5. sagefr0gWell-Known Member

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) ?

6. iCountNTrackWell-Known Member

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

7. sagefr0gWell-Known Member

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

8. blackjack avengerWell-Known Member

fixed is fixed

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