standard deviation

  • sagefr0g

    standard deviation

    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?

  • Canceler

     

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

  • iCountNTrack

     

    Quote: sagefr0g said:
    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?

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

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

    Sandard_Deviation=SquareRoot(Variance)

  • sagefr0g

    lol, so a rehash

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

    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)
    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:

    Quote:
    Yes. First of all, there’s a question of how you’re calculating SD to begin with. If you’re playing on a computer which is tracking your results by hand, that’s probably okay. SD(total) = sqrt(SD(1)^2 + SD(2)^2 + SD(3)^2).

    But more often, SD is calculated from session wins, which means you calculate SD(total) = sqrt((ActualWin(1)-ExpectedWin(1))^2 + (ActualWin(2)-ExpectedWin(2))^2 + … (ActualWin(n)-ExpectedWin(n))^2).

  • sagefr0g

     

    Quote: iCountNTrack said:
    Assuming f and z are fractions rather than percents for simplicity.

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

    Sandard_Deviation=SquareRoot(Variance)

    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) ?

  • iCountNTrack

     

    Quote: sagefr0g said:
    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

  • sagefr0g

     

    Quote: iCountNTrack said:
    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!

  • blackjack avenger

    fixed is fixed

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

The BlackjackInfo Knowledge Base contains over 200,000 messages posted by the BlackjackInfo community.

Posting and replies to the knowledge base are no longer available, but comments and replies are welcomed on the blog.