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Looking at standard deviation in poker

I often write articles about a part of Texas Hold em poker that many players find the most difficult and this is the fluctuations within the game. There is a large volume of material written these days with regards to earn rates but yet many people shy away from mentioning standard deviation. The two are linked and basically need to be discussed in unison rather than in isolation. What you find though is that players and especially novice and intermediate player’s only focus on earn rates.

There are two main measurements when it comes to earn rates and this is dollars per hour and ptbb/100 which means PokerTracker big bets per one hundred hands. But most players like to look at the dollars per hour figure and even users of tracking software like to know how much they are making per hour. However unless you have an absolutely massive sample size then your hourly rate is never constant and you can never really say that you are earning X dollars per hour!

But even if you have a huge sample size then you still cannot take your earn rate as gospel. If you are earning say $50/hr over a very large sample size of say 1 million hands then what really does that mean? Well firstly let us say that your standard deviation which is a statistic measurement of a dispersal of results within specified barriers is say $250/hr. This means that you will win or lose $250 per hour a total of 66% of the time which is one standard deviation. Two standard deviations would be $500/hr and would happen 95% of the time and three standard deviations would be $750hr and would happen 99.7% of the time which is close to being all the time.

So you would almost never win or lose more than $750/hr but this breaks down to the following. If your EV is truly +$50hr then you could win up to a maximum of $800 in any one hour which is your earn rate plus the $750 standard deviation. However you could also lose $700 in an hour which is your earn rate minus $750. The chances are though that it wouldn’t get this bad and would fall within one standard deviation. Very few players understand what their standard deviation is and it is often difficult to estimate for numerous reasons.

If you change your style of play then you are changing your standard deviation. If you move up or down in levels then you could be changing your standard deviation. If you are playing stronger players or if the playing dynamic of your level alters then your standard deviation along with your earn rate changes. I have known players who were doing very well at their level and even turned pro who probably thought that their earn rate and standard deviation was pretty accurate with a high confidence level. However there were subtle and almost invisible changes within their playing environment that led to the level that they were playing becoming far tougher.