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Thread: Please explain standard deviation

  1. #1


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    Please explain standard deviation

    Please explain standard deviation. I googled it, looked it up in the dictionary, yet still cannot implement it into blackjack calculation. When reviewing simulations in a blackjack program I purchased there is a section that shows the standard deviation of the simulations I ran (SD#1, SD#2, SD#3). Is this what could be won or lost? How much bankroll fluctuates while the allotted time of hands are played? And why is there 3 different levels of it?

    Thanks for any info related to this matter. These are the questions you'll get from a "ditch digger" trying to learn math again twenty years after leaving high school a bit too early without that favorable diploma...

  2. #2
    Senior Member Bodarc's Avatar
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    Hi Jacks

    SD is just a measure of how spread out numbers are.

    Here is a link that will explain it to you in easy to understand terms if you don't have the book Blackjack Attack. There is a full explanation in BJA.

    http://www.mathsisfun.com/data/standard-deviation.html

    The reason you have SD#1 etc is because your results should be within +or- one SD 66.3% of the time. That is if your expected results are 50, you should be within 50 - 1SD to 50+1SD 66.3% of the time and within 50-2SD to 50+2SD 95.4% of the time and within 3SD or 50-3SD to 50+3SD 99.7% of the time.
    Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson

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    Look up bell curve on google. Standard deviation will define the likelihood of being within certain ranges of your expectation.
    1 standard deviation range on either side of the mean contains 68% of your possible results (34.13% in either direction from the mean). So you have a 68.26% chance of being in that range for the number of hands the SD is for. 2 standard deviations adds another 13.59% on each side of the mean for a total of 95.44% chance of being within 2 SD's of the mean. 3 SD's adds another 2.14% to each side of the mean. So there is a 99.72% chance of your results being within 3 SD's of the mean for the number of rounds the SD was calculated for.

    Your N0 (N-zero, a very important statistic) is the point were your EV equals 1 SD. At this point you are about 84% chance you are out of the red (have not lost money) for all your N0 rounds. SD is the square root of variance so your EV would equal 2 SD's (97% chance of being out of the red) at 4 times N0. At EV equals 3 SD's you are at 9 times N0 rounds and a 99.9% chance of being out of the red.

    SD = square root of (sum of the (difference from the mean squared for each data point)/(sample size))
    Variance = sum of the (difference from the mean)/(sample size) = SD*SD = SD^2
    N0 =Var/(EV^2) = (SD/EV)^2
    N0 is a linear function of variance but an exponential function of SD.

    Important stats are explained here:
    http://www.blackjackapprenticeship.c...dvantage-play/

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    JacksAces,

    For a typical BJ game with a flat-betting player, the Standard Deviation (SD) is 1.15 units per round. The actual value varies a bit with different sets of rules, but 1.15 is a pretty fair average value. The SD varies TREMENDOUSLY if the player varies his bet (as card counters do, for instance).

    Now, what does this mean?

    Let's assume you're flat-betting $10 per round on a BJ game, so your SD per round is $11.50 (1.15 times $10). Note that this calculation takes into account that you will sometimes split or double down, as the 1.15 value is the SD per round.

    The total SD for a session is proportional to the SD per round times the square root of the number of rounds you play. Thus, if you play 100 rounds in a session (roughly an hour), then the SD for that session is $10*1.15*sqrt(100) = $115. If your per-round EV is, say -0.5% (since you're flat-betting, you'll almost certainly be playing at a disadvantage), then in 100 rounds your total EV is 100*$10*(-0.5%/100) = -$5.

    Since your total SD is $115, that means that, roughly two-thirds of the time, your actual result will be within one SD of your EV: thus, you'll end up somewhere between -$120 and +$110 about 2/3rds of the time (actually, closer to 68%).

    Hope this helps!

    Dog Hand

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    Senior Member Nikky_Flash's Avatar
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    good info guys , thanks

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    I think this is an excellent video on Standard Deviation. It's part of 11 minutes from Semyon Dukach talking about EV.

    https://onedrive.live.com/redir?resid=1124C09E80343E96!222&authkey=!ALHQ DFgcFaScEMg&ithint=video,m4v

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