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Tuesday, May 18, 2004

Raw Data

In each hand of a game, I use my perception of individual players to follow the interactions between everyone at the table. All the while, I’m trying to manage other players' perception of my game.

With the blog, I’d like to start looking at groups of players. The goal is to explore the universe of poker “truths” with statistics. Ultimately I hope to help my sense of perception at the tables.

So, here’s a small sample of data:

-Limit-----Hands---Winners---Losers---%Winners
$.5/$1---197,308--------299------393--------43.21
-$1/$2---220,013--------369------426--------46.42
$5/$10----64,983--------101------117--------46.33


Now what do I do with that? First, I try to recognize the limitations. It's not a big sample and the size of the sample is smaller at the $5/$10 level. I resolve to collect more data before drawing too many conclusions. Also, there might be more short-handed data at the higher limits than the lower ones. I’ll have to control for that. This table was collected at one site on ten-seat tables. Also, I limited the sample to players with more than 100 hands. Increasing the number of played hands radically changes the data. I excluded myself from any statistics.

What kind of inferences do I want to make? I want to know if the percentage of winners is a function of the game itself, or if the number of skillful players in the game makes the difference. Do most winning players at the higher levels make their money by cutting losses and letting their winners run? Or do they consistently stay on the winning side of the ledger more often? I don’t think I’m anywhere close to answering that at this point. Surely, both types of winners exist. Which is the most actuarially sound strategy? Thus the quest begins.

Hand Histories Wanted: depbonus@yahoo.com

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Tuesday, May 11, 2004

Averages VS Large Numbers

Anytime I solely use pot odds to make a play I’m relying on the “Law of Averages.” Results are going to vary, but the more hands I play the closer that variance will be to the actual mathematical expectation. There is no uncertainty about that, just odds of one thing or another happening. If all I ever do is play the cards, there is not much uncertainty for my knowledgeable opponents either.

All of the uncertainty in a “honest” poker game comes from the players, not the cards or the dealer. I can’t know with moral certainty what laws, if any my opponents are operating under. The trick is to infer their psychology from the way they have played past hands. With Limit Hold’em on the Internet, I can use hand histories and the “Law of Large Numbers” for opponents I see quite a bit. Once I know their type, I can apply the law of averages and use the strategy that best suits the situation given what I “know.” Without enough hands in the bank to get some statistical certainty, it is best to determine the psychology that dominates the table and stick to playing the cards. Of coarse, you want to pick the tables that will yield the juiciest return from such a strategy (Loose and Passive).

But ideally, I’d like one or two known quantities at that table too, even if they are excellent players. It reduces the uncertainty for me in the game. I also prefer short-handed play for the same reason.

Usually, a player with a really self-destructive psychology will not be around long enough online to establish moral certainty by statistical methods, nor do you need statistics to spot the maniac. He’ll also attract enough attention that table psychology is still the most important factor. So, it is with the better players and at higher limit games that this approach is most useful.

Still, all the stats are just an adjustment to pot odds. They help me determine how strong my hand must be to win in the here and now. If you know that, there is no uncertainty about the odds of this hand holding up or of me drawing to hand that is good enough. The law of averages will work its magic. Instincts about relative hand strength are nice/mandatory, but the statistical method is definitely the fastest way to develop them online.

That is, it could be, IF it wasn’t so hard to get enough data. You see, to infer a law from incomplete information, you need independent observations. This means that your data has to be situational because other players are playing the players too. In fact, a big part of what you are trying to measure is how much are they playing the players. To get independent observations, you have to create a slew of general situations that combine starting cards, position and the previous action. Given X environment, generalize that a loose/passive acts like this 75% of the time and a tight/aggressive would act this way 75% of the time. Take score, determine what category the player fits in and make your game-time decisions with those collected results in mind. I’m having troubles with the model in a six-player universe. As far as after the flop, all I got is raise/call/fold stats with no hand strength or previous action factored in. I have just enough to see the players that see a lot of flops but play tight and aggressive afterwards. And I don’t think I have enough computer power to add much more that anytime soon.

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