New Standard Deviation Stat

[9ball]

I play limit holdem 6max, 2/4 and 3/6. I have ~70K hands, and according to PT3 I have a sd of ~29 Big BETS/100, playing a 24/17 style.
Since the generally accepted sd for this style is <20BB/100, i downloaded hm trial and imported all the hands. It shows a sd 14Big BETS/100.
Who is right?

Thanks.

[WhiteRider]

SD in poker isn't something I've personally done much with, and I'm yet to find anyone who knows what they actually want the SD of.
PT3 takes the standard deviation of the BB/100 of each session, and from a mathematical point of view it seems to be giving the correct values.
Until we find out what these other applications are taking the SD of we can't say which is correct.

[Dan_Jazz_Man]

I also noticed something strange about SD values. It seems to give a reasonable value for FR games (around 30-35 PTBB/100) but
for 6-max games it's way off (around 130 PTBB/100).

[WhiteRider]

I would expect the SD to be higher for 6-max tables since they play looser.

[brone]

Alright, first things first. PT3 SD values (in BB/100) are, as several of us have mentioned, roughly four times higher than they were in PT2, so there is definitely some kind of a problem in one of the two versions (or both).

Secondly, for the games I play, and my extensive experience with calculating SD in both online and live poker, I am fairly certain that PT2's numbers are far closer to what the SD should be than PT3's numbers.

Now let's define SD (in Big Bets per 100) to be sure we're on the same page:

Your inputs to the SD formula should be:

1. The BB/100 number for EACH session
2. The total number of sessions
3. The number of hands played in each session.
4. The BB/100 number for the player over ALL sessions.

The formula needs to first compute the Variance, then the square root of that variance gives you the desired Standard Deviation.

How to compute Variance? You SUM, over all sessions, the SQUARE of the quantity (Session's winrate - Player's winrate) multiplied by the number of 100 hand blocks played in that session. After summing, divide by the total number of sessions minus 1. This is called the unbiased maximum likelihood estimator of the Standard Deviation and is going to be the best estimate of what the player's true standard deviation is.

In math: Variance = [1/(N-1)] * SUM_1_to_N { [ (BB/100_for_session - BB/100_for_player)^2] * (H_for_session/100)}

Where N is the total number of sessions played, and H is the number of hands played for each session.

And, as mentioned, the square root of the above formula gives you SD/100.

Just to clarify, each term in the sum requires you to subract, square, then multiply by (H/100). You do those 3 operations for EACH session.

Similarly, for the SD/hour number, you need the analogues of the above inputs that have the per hour inforrmation for inputs (1), (3), and (4): BB/HR for each session, number of hours played in each session, and BB/HR for the player's winrate. The multiplicative term in the sum in this case would just be the number of hours played in the session.

Hope this helps.

[brone]

Just to give you some rough numbers of what SD SHOULD be:

For limit holdem, for 9 max, it should be roughly 12-15 bb/100
For 6-max, it should be roughly 14-18 bb/100
For HU, it should be roughly 23-29 bb/100

For No Limit 6-max, it should be roughly 40-55 bb/100

Anything considerably outside of the ranges I gave above is probably wrong, and if it's more than double, it's *definitely* wrong.

[WhiteRider]

Thankyou brone - that looks really useful and I will make sure that our lead developer sees this.

I've put your formula through Excel on the same set of hands I tested the built-in STDEV function, and I get 24 with yours instead of 81 with the built in formula. Quite a small sample, so I wouldn't read too much into the figures, but I guess you would say that was more reasonable.

[brone]

WhiteRider,

After reading your earlier post, it occurred to me what the problem is.

Computing the Standard Deviation of the BB/100 values, as PT3 is doing, is NOT THE SAME as computing the SD/100.
This is because when you just feed the BB/100 values into the SD formula, you are IGNORING the length of the sessions.
You are assigning an equal weight to a BB/100 value from a session of 1 hand and the BB/100 value from a session of 1000 hands. Intuitively, if you are way above the mean over 1000 hands, that is a MUCH more meaningful indicator of high SD than if you are way above the mean in just 1 hand.

If you guys want to do it this way, where you just feed a list of bb/100 numbers, then you need to use the hand results from the HANDS TAB instead of the session results. Then you can just feed the list of winnings for the hands into a STD formula like the one in excel. No modification for session length would be necessary since each hand is the same length (1 hand). This would actually be more accurate than using sessions, in the sense that it would converge to the right SD/100 value more quickly. However, you wouldn't be able to get the SD/hr this way. SD/hr would still require using the Sessions tab and normalizing by the session length, in hours, like I explained in the formula in my previous post.

Finally, since sessions of short length tend to have very high or very low BB/100 values compared to sessions of greater length, the result when you just compute the STD of the BB/100 values will be that you will inflate the SD/100 number well beyond what it really is, which is what we're observing.

[WhiteRider]

Yes, agreed. I figured it was something like that, but until your post we haven't found anyone who actually knew what the calculation should be.
I have passed this information on to our lead developer, but I haven't heard back from him yet. (I don't always get immediate responses, though, because he's a busy chap.)

[9ball]

brone ,good post. thanks for the explanation.