I'm currently on a miserable run and noticed that my hourly standard deviation (through this run) has dropped from 12BB/hr. to 8BB/hr. I thought SD was supposed to go up when running bad, since the lower the SD, the more likely it is your win rate is accurate? Should I be concerned that my standard deviation is lower when losing than when winning?


btw- bad run involved limit hold'em of two different limits. One of which I'm stuck almost 2BB/hr thru 88 hours, and one where I'm break even thru 124 hours.

There is no reason to believe that SD would go up if you're running bad.

Consider, for example, if you got all in with 80/20s 10 times in a row for 1 buyin each time, and somehow lost them all. Your standard deviation would be 0. Standard deviation is just a means of how far each of your samples is from the mean, as an aggregate. If each sample is equivalent to the mean, then your SD is 0.

Thanks that makes sense. It's also a measure of consistency, right? If you're losing consistently then it makes sense SD would be low. I just thought I read somewhere (from Mason Malmuth) that SD should be higher for a winning player when losing, because he is experiencing abnormal results. So if normal results = your win rate, then anything severely above or below that win rate should increase SD.

Sorry, I'm very unfamiliar with the math involved.

Well, now you're talking about 2 different things, I think.

Let's expand my example. Let's say that usually you win an average of 1bb/100, with a standard deviation of 10bb/100. Let's say this is calculated over the course of a year. Then you have a week where you lose 1bb every hand for some reason.

Your standard deviation FOR THAT WEEK is 0, because your results on average are the same as each specific result.

Your standard deviation for one year plus that week will go up, because each new sample is deviating greatly from the combined average. Does that make sense?

Like say you had taken the heights of 10,000 people and found that the average was 5'7" with a standard deviation of 3". Then found another group of 100 people that were all exactly 4 feet tall. The stdev of the 100 people is 0. If you add them to the larger group, your averge goes down a bit, and also your standard deviation goes down.

Thanks again. All I know is that I'm normally a .9BB/hr winner and have been losing at 1BB/hr for the last 200 hours and am pulling my hair out. I have looked at every conceivable stat I know to try and make sense out of it. The best I can tell is that I'm running +2.25 standard deviations below the mean for the past 200 hours. I suppose I can live with that, but this is the 2nd such bad run within a 12 month period. My overall win rate is still +.9BB/hr, but I'm starting to question both my skill and what I thought I knew about variance. I really appreciate your response. Thanks.

I know you probably don't want to hear this, but 200 hours is really not a big sample. If you're seeing 30 hands/hour that's 6000 hands. I am a low-volume player - I've never played more than 4-5 tables at a time online - and I have personally had single sessions totally over 2000 hands. A multi-tabling reg sees more than 6000 hands/day.

It's quite brutal live because a 10k hand downswing can just go on FOREVER. I've been there.

Your SD will go down if your sessions (aka data points) become more consistent. If you're looking at just your downswing data, your SD will be calculated based upon that downswing WR (~ -1BB/hr).

Here is a random example of what results look like for SD ~ 8BB/hr and SD ~ 12BB/hr for a $10/$20 player over 200 hours. Both have an average WR of -1BB/hr. In general the 2nd column is more swingy than the first.

Session Length (hrs)	Result (SD=8BB/hr)	Result (SD=12BB/hr)
4	-500	-700
7	500	1000
4	-380	-580
6	450	450
8	300	800
3	50	350
6	400	400
4	200	-100
7	-500	-500
4	-420	-420
6	600	600
8	100	500
3	-350	-550
6	-400	-200
4	-400	-400
7	-300	-500
4	300	500
6	-200	600
8	-300	-300
3	-100	-500
6	-100	-500
4	500	-500
7	100	700
4	-500	-200
6	-300	-800
8	-550	-550
3	-200	200
6	200	1000
4	-300	-300
7	-500	-500
4	200	600
6	-500	-500
8	-600	-600
3	500	-500
6	-600	-600
4	-100	-700
6	-300	-700