standard deviation

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

  1. sagefr0g

    sagefr0g Well-Known Member

    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. Canceler

    Canceler Well-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. iCountNTrack

    iCountNTrack Well-Known Member

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


  4. sagefr0g

    sagefr0g Well-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) :confused::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. sagefr0g

    sagefr0g Well-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. iCountNTrack

    iCountNTrack Well-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. sagefr0g

    sagefr0g Well-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 avenger

    blackjack avenger Well-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.

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