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Thread: Standard Deviation, How is it calculated?

  1. #1


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    Standard Deviation, How is it calculated?

    sd screenshot.jpg

    1. I'm working with BJA3 and trying to get a basic grasp of how SD is calculated.
    2. The rough and dirty formula on pg 16 is SD = 1.1 * (sq root of # of rounds of play).
    3. So if I want to find the SD for 1 round of play then is it just :
    SD = 1.1 * (sq root of 1) = 1.1 * 1 = 1.1 units
    1 unit = $8.04
    1.1 unit =$8.84
    4. CVCX tells me SD per round is $25.09 so obviously I'm not even in the ballpark.

    Help.

  2. #2


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    A standard deviation of 1.1 is a very rough estimate for the standard deviation if one round of blackjack in units. This is not the same as the global standard deviation of your system, which considers the frequency of each true count, the standard deviation at each true count, and how much you bet at each true count.

    CVCX does not display the standard deviation of your system in units, so you have no way of verifying the $25.09 manually. However, if you believe the $25.09 figure (and you should!), the standard deviation of your system in units is 25.09 / 8.04 = 3.12

  3. #3


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    Is there a formula for the global standard deviation that I can use that considers the frequency of each true count, the standard deviation at each true count, and how much you bet at each true count? Thank you.

  4. #4


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    Quote Originally Posted by MercySakesAlive View Post
    Is there a formula for the global standard deviation that I can use that considers the frequency of each true count, the standard deviation at each true count, and how much you bet at each true count? Thank you.
    See BJA3, bottom of p. 19, all of p. 20.

    Don

  5. #5


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    What do "Var" and "Cov" mean in the "Var + (h-1) * Cov" formula?

    I am pretty sure "var" is variance but "cov" ?

    I understand the h-1.

    Sent from my SM-G900V using Tapatalk
    Last edited by MercySakesAlive; 04-06-2018 at 03:53 PM.

  6. #6


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    Quote Originally Posted by Gronbog View Post
    CVCX does not display the standard deviation of your system in units,
    Actually, if you export you CVCX sim to excel it will provide the SD for each true count giving you the information need to calculate the same SD.
    Luck is nothing more than probability taken personally!

  7. #7


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    Cool, thanks, stealth. Anyone know what "cov" means in the BJA3 formula above?

    Sent from my SM-G900V using Tapatalk

  8. #8


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    Quote Originally Posted by MercySakesAlive View Post
    Cool, thanks, stealth. Anyone know what "cov" means in the BJA3 formula above?

    Sent from my SM-G900V using Tapatalk
    Covariance. About 0.50 for two blackjack hands played simultaneously. See the bottom of page 24. But, you bring up an interesting point. This explanation comes AFTER the chart I referred you to, and perhaps some allusion should be made to the explanation at the earlier point.

    Don

  9. #9


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    Quote Originally Posted by Stealth View Post
    Actually, if you export you CVCX sim to excel it will provide the SD for each true count giving you the information need to calculate the same SD.
    My fault for not being precise. I was referring to the global standard deviation that I had referenced in the preceding paragraph.

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  11. #11


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    I am trying to calculate the total standard deviation using the method on page 20 of BJA3.

    I'm doing something wrong because my math shows SD is 1.16 units but CVCX shows SD is 2.53 units.

    The sim is a simplified bet ramp just for the purpose of learning how to calculate SD.

    Any advice is appreciated.

    SD total CVCX Screenshot1.jpg

    SD total CVCX Screenshot.jpg

  12. #12
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    When you are backcounting the total frequency is not 1. You have to count rounds observed but not played as rounds. You may notice Don's charts on page 20 of BJA3 all divide the product of variance times frequency by frequency. Notice the frequency being divided is around 25 to 30 percent. You need the frequency of the counts you just watch and that plus the frequency of the hands you play is 1. The sim data implies you are playing 46% of the total rounds.
    Last edited by Three; 05-22-2018 at 12:47 PM.

  13. #13


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    Thanks, Three. I don't understand. I divided my variance by a total frequency of 1.00. (or rather I didn't divide at all)... I think I'm missing what you're trying to tell me?

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