Wednesday, November 29, 2006

Number Crunching (1 of 4)

Just got off the 6-max, $0.50/$1.00 limit hold ’em tables. Was playing one on PokerStars, the other on Full Tilt Poker. I played exactly 100 hands -- 50 on each site. Ended up ahead $4.70 on Full Tilt, and just $1.45 ahead on Stars. Was as much as $12 down on FTP, and as much as $9 or so ahead on Stars, before settling back to where I ended up -- a total of $5.15 gain for the 100 hands I played.

Is this typical? A post over on Simon’s Poker Blog a couple of months ago got me interested in this “standard deviation” business and so I’ve been diggin’ around, trying to figure out what to make of it. As Simon tells us, if you use Poker Tracker you can click on the “More Detail” button under “Session Notes” (in the ring game stats) and you’ll see your “standard deviation” neatly calculated for you. Should this number be meaningful?

Since the beginning of the year, I have played around 80,000 hands of 6-max, $0.50/$1.00 limit hold ’em. Only about half of ’em are here in my database, unfortunately, as I suffered a computer meltdown in the early summer and lost a few months’ worth of stats. Those of you who use Poker Tracker, avoid Shamus’s misfortune and backup your databases on a disc or external drive! It’s only a matter of copying a few .mdb files -- click here to read Pat’s instructions about backing up your data.

For the 36,000 or so hands (of the 6-max limit game) that I currently have in my database, I see that I currently enjoy a win rate of just over 2.5 BB/100 hands. (Here, BB = “big bets,” not big blinds, so we’re talking about $2.50/100 hands.) Now I know that rate has fluctuated between 2 and 3 during the entire run, but for the most part the rate has hung around the 2.5 mark pretty much throughout. I also know that before the crash, I had just about the same rate for the 50,000-odd hands I had in there before. (Reading around I see that 2 BB/100 hands is generally considered a decent rate for micro/low limit games, so I’m doing okay there, I suppose.)

Poker Tracker tells me my current “standard deviation” when playing this particular game at this particular limit is just a hair under 18 BB/100 hands. (That’s about where I was before the crash, also.) If understand it correctly, my “standard deviation” indicates the likelihood that I will in fact win my “average” 2.5 BB in the next 100 hands I play. (Please, if anyone knows better about any of this stuff, correct me mercilessly.)

Of course, I usually don’t earn exactly $2.50 for every 100 hands. Sometimes I earn $5.15 (like today). Sometimes I lose $12. Sometimes I win $20. Having a standard deviation of 18 BB/100 means that I will usually (but not always) land in a range anywhere from 20.5 BB up to 16.5 BB down. In other words, the number indicates the degree of “variance” I should expect when playing this particular game. In fact -- as my old statistics textbook explains -- “variance” is precisely the square of “standard deviation,” so these two terms are directly related to one another.

Now if I had literally made or lost no more than 2 or 3 BB for every 100 hands I played, my statistical deviation would have been much lower. But I didn’t. Obviously my wins and losses during those individual 100-hand segments were much greater, and thus my standard deviation is 18 BB/100. From reading around, I see that my number here isn’t necessarily that unusual. (Keep in mind I am playing 6-max games, where one tends to experience more variance than at full tables.) I could be wrong, but I’d venture to guess that my win rate (2.5 BB/100 hands) and my standard deviation (18 BB/100 hands) are both fairly typical for moderately successful players who spend most of their time at this limit.

The more hands a person has played, the more representative stats like win rates and standard deviations become. There is a lot of disagreement about how many hands constitutes a meaningful sample, but for the sake of argument I’m going to assume that my 80,000-hand sample is enough to ensure that these numbers mean something.

I thought I’d use the next three posts to “think out loud” and explain (to myself and to anyone else who is interested and who might help me) what these numbers -- my win rate, my standard deviation, the number of hands I’ve played -- might help me as I try to assess myself as a player. Here are the questions I thought I’d try to answer over the next three posts:

(1) How might I use these stats to predict how my next 100 hands (of 6-max, $0.50/$1.00 limit hold ’em) will go?

(2) How might I use these stats to determine what kind of bankroll is suitable for me to be playing this particular game at this particular limit?

(3) How might I use these stats to help decide whether or not it might be time for me to make the move (seriously, not just occasionally as I am doing now) to a higher limit game?

Before I do, though, I think I’ll head back to the tables for another hundred or two. Not sure yet what these stats are going to tell me, but I am pretty sure they ain’t gonna tell me math is more fun than poker.

Photo: “Chinese Abacus,” Dave Fischer. CC BY-SA 3.0.



Anonymous Anonymous said...

Shamus my friend

Interesting stuff as always.

80000 hands is pretty sick dude lol ;-)

Having just moved up to the $0.50 and $1.00 and played 2500+ hands I have noticed that the variance or as I put it (The rollercoaster ride) becomes more of a bumpier one. You can win more and you can lose more of course.

I spoke about going up to the next rung on the ladder but until I have 300 x the BB ($600)then i will stay. Hopefully I will get there, If I don't then i will be quite happy grinding away where I am.

I think that only you can decided
when it's time to move up. I don't know what bankroll you have nor have I seen your stats. Perhaps you could email them to me??

Good luck whatever you decided and thanks for sharing.

11/30/2006 8:10 AM  
Blogger Short-Stacked Shamus said...

Yes, that's part of what I'm gonna try to think about here -- given my expectations/abilities/etc., how much should I have at the ready to move to $1/$2? (My "bankroll" per se is never more than a few hundred, since I routinely try to cash out.)

11/30/2006 2:09 PM  

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