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Thread: Session win %

  1. #14


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    I also pulled back a similar posting for a similar reason.

  2. #15


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    Quote Originally Posted by DSchles View Post
    The ? was supposed to be a square root sign. What you did above, while correct, is unnecessary. Why bother squaring, to get variance, only to undo the square by taking square root? Just take the square root of the number of rounds (sqrt 100 = 10) and multiply by the single-hand s.d.: 10 x 1.15 = 11.5.

    Then proceed as Dog Hand did. Get the z-statistic and refer to the chart to get probability of being ahead after specified number of rounds.

    Don
    Ah, you’re right! First time for everything, heh? j/k

    I’ve just always done it that way because....I don’t know why? Easier to keep it together in my head, I guess. Speaking of z-scores and whatnot, I figured out how to do the formula on wolframalpha and keep a bookmark to it on my phone. Change the (0.25) to whatever z-score you want.

    https://www.wolframalpha.com/input/?...%5E2)%2F2)++du


    Unless there’s an easier (but still accurate/precise?) formula?
    "Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]

  3. #16


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    Quote Originally Posted by RS View Post
    Unless there’s an easier (but still accurate/precise?) formula?
    It's that, without what you've done, you need a cumulative normal table, which is how most people get the final answer.

    Don

  4. #17


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    Quote Originally Posted by RS View Post
    Speaking of z-scores and whatnot, I figured out how to do the formula on wolframalpha and keep a bookmark to it on my phone. Change the (0.25) to whatever z-score you want.

    https://www.wolframalpha.com/input/?...%5E2)%2F2)++du


    Unless there’s an easier (but still accurate/precise?) formula?
    Unfortunately there is no simpler formula because the Gaussian normal distribution function cannot be analytically integrated because of the -u^2 square in the exponential function. Many functions can be analytically integrated by another function given as a short formula (the so-called anti-derivative function from Calculus), but not the Gaussian one.

    So you need large tables with function values or a computer in order to approximately compute the integral (= area under the curve), e.g. by the Simpson integration rule, which requires about 10 to 100 iteration steps in a loop to get sufficient precision in the results, depending on the desired number of precise digits.
    Last edited by PinkChip; 07-21-2019 at 05:39 AM.

  5. #18


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    Quote Originally Posted by DSchles View Post
    It's that, without what you've done, you need a cumulative normal table, which is how most people get the final answer.

    Don
    Quote Originally Posted by PinkChip View Post
    Unfortunately there is no simpler formula because the Gaussian normal distribution function cannot be analytically integrated because of the -u^2 square in the exponential function. Many functions can be analytically integrated by another function given as a short formula (the so-called anti-derivative function from Calculus), but not the Gaussian one.

    So you need large tables with function values or a computer in order to approximately compute the integral (= area under the curve), e.g. by the Simpson integration rule, which requires about 10 to 100 iteration steps in a loop to get sufficient precision in the results, depending on the desired number of precise digits.

    Thanks. That's pretty much what I figured, otherwise I'd have been able to find an easier formula. I'll just keep wolframalpha bookmarked.
    "Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]

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