Need help from the mathemeticians

I have some questions for anyone who wishes to respond. I have a hard time understanding standard deviation. Can someone please explain it for me in laymans terms. I think it means my fluctuation from one hour to the next. However I am not certain. I read Gambling Theory and Other topics, and I still have a hard time understanding standard deviation. Does it mean short term luck?


I just started playing $10-$20 and I have 12.50 total hours,my win rate is 36.24 an hour, my confidence is 14.11% and my std deviation is $99.39 an hour. I gathered this information with the use of Stat King.


The advisor points out that I have a low standard deviation. I just started playing at this limit, so I play much tighter than usual. I have played premium hands only and one night the deck seemed to hit me in the face. What kind of swings will I see? The advisor says fluctuations of up to 298. Does this mean I could lose or win 298 in an hour?


Thank you in advance for answering


Best Wishes


MK ---}}}

Standard deviation is a statistical measure of dispersion or fluctuation around the mean. To use the standard "bell-shaped curve" distribution, a standard deviation is an interval such that 68% of all results are expected to fall either one standard deviation to the right or to the left of the mean. Two standard deviations to the left or right of the mean would encompass 95% of all the expected results. Three standard deviations would encompass 99% of all the observed results.


Your results are taken over a very small time period so they are not really meaningfull. But to use your numbers, if your mean is $36.24 per hour and your standard deviation is $99.39 per hour than about 2/3 of the time you will end up either a $135.63 ($36.24 + $99.39) ahead or $63.15 behind ($36.24 - $99.39) from where you were in the previous hour. To capture 95% of your observed results you simply take the $99.39 number and multiply it by 2. To capture 99% of your observed results you simply take the $99.39 number and multiply it by 3.


Standard deviation can be used to compute bankroll requirements based on your estimated hourly earn and how many hours you intend to play. Standard deviation can also be used to compute the uncertainty associated with your computed hourly earn.

I believe Stat King uses the maximum likelihood estimator as presented in my Gambling Theory book. It turns out that even though this is a very good estimator to use, it is also a biased estimator, especially for small sample sizes. What that means is that your estimate of the standard deviation is too small for very small samples. But as the sample size increases the bias disipates. That's one of the reasons I recommend in the book at least 30 sessions of play for the estimate to be accurate.


It sounds like you have only played $10-$20 a couple of times, and I suspect your true standard deviation may be twice as large as the estimate you are currently getting. So, keep playing, you are off to a good start, and the maximum likelihood estimator for the standard deviation should come into line shortly.