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Thread: Calculating N0

  1. #1


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    Calculating N0

    Can someone help explain what N0 means, and how to calculate it?

    I see the formula is N0= variance ÷ (EV×EV)

    What exactly do i use for my EV numbers?

    I just want to know how many hands it would take to get to the "long run" in a blackjack game where the variance is known and the game pay back is 100.1% flat betting.

    Im a bit confused as to what to input as my EV numbers, and should it be calculated as 4×N0 to be considered the "long run"?

    Im trying to look up info on my own but am kind of stumped.
    May the Variance be with you.

  2. #2


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    https://www.blackjacktheforum.com/sh...-from-a-Newbie

    See #2 of the above thread. It is the better post from T3.

  3. #3


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    Quote Originally Posted by BJGenius007 View Post
    https://www.blackjacktheforum.com/sh...-from-a-Newbie

    See #2 of the above thread. It is the better post from T3.
    So if this game is flat bet $50 would i use the number $0.05 as my EV per round, or use the edge so my ev number is 0.001 ?

    N0= variance/(0.001×0.001) ?

  4. #4


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    Im actually starting to understand now..

    It would be N0= variance/(0.001×0.001)

    So now i need to figure out variance..

  5. #5
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    EV and SD for 1 round.
    N0=(SD/EV)²

    Why ?

    N0 is another strategy scoring technique developed by Brett
    Harris. It is defined as "the number of rounds that must be played,
    with a fixed betting spread, such that the accumulated expectation
    equals the accumulated standard deviation As such, it is a
    measure of how many rounds must be played to overcome a
    negative fluctuation of one standard deviation with such a fixed
    spread
    .

    N0*EV=SD*SQR(N0)
    etc ...

  6. #6


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    And i understand how N0 means youll be in profit x% of the time for 1N0 4N0 and 9N0, but now how do we figure out how many hands is needed to be at our actual EV? If i play a bagillion hands, i better be up exactly $0.05× 1 bagillion

  7. #7


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    1N0 is where EV = 1SD.
    "Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]

  8. #8


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    Quote Originally Posted by Three View Post
    Since n0 is exponentially related to SD, the number of rounds where EV = 2SD is 4*n0, EV =3SD is 9*n0, etc. Remember SD increases as rounds accumulate.
    Ok so let's see if i got this right.

    Variance is 1.2
    Edge is 0.14%

    1.2÷(0.0014×0.0014)

    n0= 610,000 hands

    So after 610,000 hands i should be up 854 units (EV), but my results should fall 85% of the time from 0 to 1708 units

    After 2,440,000 hands i should be up 3416 units but 97.7% of the time fall between 0 and 6832 units

  9. #9


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    blue

    N_0 = Var / EV^2 = (1.2) / (0.01)^(2) =12000 or 12K rounds

    SD = root(Var) or s^2 = Var(X)
    Last edited by lij45o6; 03-03-2018 at 03:11 PM. Reason: Maths error.

  10. #10


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    Quote Originally Posted by dogman_1234 View Post
    blue

    N_0 = SD / EV^2 = (1.2)^(0.5) / (0.0014)^(2) = 558900.568882823 or 550901 rounds

    SD = root(Var) or s^2 = Var(X)
    Your formula for N0 is wrong. You don't use standard deviation; you use variance.

    Don

  11. #11


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    Quote Originally Posted by dogman_1234 View Post
    blue

    N_0 = SD / EV^2 = (1.2)^(0.5) / (0.0014)^(2) = 558900.568882823 or 550901 rounds

    SD = root(Var) or s^2 = Var(X)
    The SD is 1.1 the variance is 1.2

    The meanings of n0 i am understanding correctly too right?

  12. #12


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    Quote Originally Posted by DSchles View Post
    Your formula for N0 is wrong. You don't use standard deviation; you use variance.

    Don
    Thanks for pointing out my egregious error, Don.

  13. #13


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    Quote Originally Posted by blueman View Post
    Ok so let's see if i got this right.

    Variance is 1.2
    Edge is 0.14%

    1.2÷(0.0014×0.0014)

    n0= 610,000 hands

    So after 610,000 hands i should be up 854 units (EV), but my results should fall 85% of the time from 0 to 1708 units

    After 2,440,000 hands i should be up 3416 units but 97.7% of the time fall between 0 and 6832 units
    Are all of these statements correct by me?

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