# Optimal Win Rate Standard Deviation

I've been tracking my live sessions for some time now. After 35 sessions (about four hours a session) my win rate is 34.42 an hour. My win rate standard deviation is 157.67. This seems high to me. I play pretty TAG at the 1/2 NL game. Is this high standard deviation just an expression of the volatility of low limit cash games, or is this my problem?

• It's been brought to my attention that you haven't denoted what measurable unit your win-rate and StDev figures represent. e.g. Are they in \$USD/100 hands or bb/100 hands? If you could update it, that would be great, otherwise i'll just assume you meant bb and do it soon myself. Thanks. – Toby Booth Jul 11 '12 at 1:18

Typically, live play will mean you're seeing between 30-50 hands per hour. In your case, this will mean that you've seen somewhere in the region of 7,000 hands. This is an incredibly low number to make any significant, reliable assumptions about the StDev of your win-rate. The data set simply isn't large enough to be approaching what we'd consider a normal distribution yet.

As for your question, `"Is this high standard deviation just an expression of the volatility of low limit cash games, or is this my problem?"`...It's just too early to tell!

Commonly...

• 6max, your StDev will be about ~90bb/100 hands.
• FullRing, your StDev will be about ~80/100 hands.

Check out this post for some helpful Statistical Tools for analysis of your game.

• Fair enough. About how many hands would you say is a good sample size? – k to the z Jan 30 '12 at 18:13
• Not to put you off but we're talking 100,000's to truly feel comfortable with the StDev volatility measure. It's not impossible to gain insight into your game using this stat, but it's genuinely difficult as the games change periodically. Thus one sample of hands and the corresponding StDev represent more of a snapshot in time, rather than a linear progression of an attribute of skill. – Toby Booth Jan 30 '12 at 18:21
• 100,000s was really easy back in the day with online poker. At a live game it's going to take me playing full time for a year. One final question, when playing in a live game how do you determine your bb/100 stat? Do you just estimate the amount of hands you played? – k to the z Jan 30 '12 at 18:25
• Yes, other than actually counting the hands you could do that. Also, consider determining your profitability in a game by Money Won Per Hour (or \$Won/Hr). I find this a useful measure alongside bb win-rate to gauge my success. – Toby Booth Jan 30 '12 at 18:32
• The money won per hour was actually the stat I gave in the question. – k to the z Jan 30 '12 at 18:33

Disclaimer: All of what follows applies only to winning players. For non-winning players, none of this matters a whit.

I'm not going to discuss actual, hard numbers as most people familiar with StdDev in poker will declare something that can be interpreted as "StdDev is completely useless until you have 100k+ hands," -- a sentiment I disagree with in principle. You can gain some insight with far fewer hands.

What I'll discuss is the relevance of StdDev in poker. So, what does StdDev tell you about your game? StdDev is an indicator of your variance. Your variance, in turn, is effected by many things. Two of the most important are:

1. Your skill relative to your opponents
2. Your long-run winrate at a given stake/structure.

As your skill increases relative to your opponents, you'll win more. As you win more, your long-run winrate increases. Simple. As your winrate increases, your variance decreases. The best .05/.10 player in the world might have a huge winrate measured in tens of BB/100 online, and a very low variance.

But skilled players tend to move up in stakes. As you get better at poker and move up in stakes, you'll find that your skill relative to your opponents actually decreases. You may still have an edge, but your edge will be smaller. This will reduce your winrate, thereby increasing your variance and your StdDev.

That is not to say that when your StdDev is high you need to work on your game. I mean, yes -- you need to work on your game, all the time, but it has nothing to do with your StdDev. The best online \$25.00/\$50.00 player in the world is probably going to have a long-term winrate that is much lower, probably measured in the low single digits in terms of BB/100. They have an edge, but their edge is smaller. So their variance and StdDev are going to be higher than the world's best \$0.05/\$0.10 player. Does that mean that the .05.10 player is better than the 25/50 player? Hardly.

Variance is also dependant on your game style. Set-mining nits will have a lower variance than a loose-aggressive player. That also doesn't mean that the set-miner is better than the LAG. Nor does it mean the opposite.

In other words, StdDev has no direct relation to your absolute skill at poker. Other variables do. StdDev only has an indirect (at best) relation to your skill.

My advice is to forget about StdDev as a diagnostic tool, and look at it as a mathematical curiosity.

35 sessions at 4 hours each is only 140 hours. That's a fairly small sample size to me. Which means your standard deviation could easily be "high" (or low).

The other issue is that it's low limit, \$1/\$2. As such, you'll get a wider range of outcomes than at higher stakes, because this represents "play money" to most people.

It's not really a "problem" as far as you're concerned. Most people would be glad to be doing as well as you.

• Ha. I suppose problem is the wrong word. – k to the z Jan 30 '12 at 18:13