Converting Hourly to Session Standard Deviation

My 2+2 books with the answer are on loan and I was hoping somebody could help me.


Let’s say you use StatKing to track results and your standard deviation is $400 per hour. How do you convert this hourly standard deviation to session standard deviation for session lengths of 4 hours, 6 hours and 8 hours?


One more question. My understanding is that you should be within one SD of normal results 67% of the time, within two SDs 93% of the time, and within three SDs 99% of the time. These numbers may be a little off. Does anyone know the correct numbers? Also, how often can you expect to be four SDs off normal results?


Regards,


Rick

Your standard deviation over an interval of time goes as the square root of the interval. If your standard deviation is $400 per hour, then your standard deviation over a 9 hour playing session would be $1200 ($400 x square root of 9).


In a normal distribution, I don't have the exact numbers but I believe one standard deviation covers 68% of the observations, two standard deviations covers 95% of the observations, three standard deviations covers 99% of the observations, and four standard deviations covers something like 99.9% of the observations. But I am just guessing based on statistics classes I took over 30 years ago.


I believe the odds are about 1000-to-1 that you will get an observed result which is more than 4 standard deviations off the expected result. Again, another guess.

Rick,


Here are the numbers, taken from Excel:


Stdev Probability within STdev

1 68.2689%

2 95.4500%

3 99.7300%

4 99.9937%

"My understanding is that you should be within one SD of normal results 67% of the time"


This is a true statement (approximately), but easy to mis-apply. If you looked into your history of sessions and drew one randomly then there would be a 68% probability of being within 1 s.d. of your mean. But not all sessions had the same distribution. If you are in a tougher than average game tonight, then you will have less than a 68% chance of being within one s.d. of your mean.

Steve,


There is no question that a loose aggressive tricky game will have a far higher SD than one's normal numbers, and a moderately loose and very passive game a smaller SD than normal .


Also note as a practical matter, those prone to tilt might hanve a massive SD during the tilted period of the session. Sometimes this helps them "get even" for the session, but slightly more often it can result in devestating losses we hear about or have seen.


Regards,


Rick