Practical Probability - Part VI

Here's a quick review of the discussion of sampling that started in my last column. There are certain statistical operations that you perform quite frequently in your daily life without really thinking of them in a statistical sense. Sampling Theory is a relatively complex division of statistics, yet it is something we routinely do. Basically, sampling is a technique designed to enable the sampler to draw conclusions about a "population" by testing a small group chosen from that population as a representative sample. There are two major types of errors that can be made in sampling. The first is choosing a sample that is too small. The second is choosing a sample that is not representative of the population.



When playing poker, every hand you play or observe becomes part of your sample. The more observant you are and the more often you play against someone, the more accurate should be the inferences that you can draw about him and what he will do in various situations. In general, when something happens frequently, a relatively small sample will be meaningful. When something is rare, you will need a very large sample to reach any meaningful conclusion. You will end up having the largest sample on yourself, and even this may be much too small to prove anything.



The situation is even worse when we try to draw conclusions about our opponents from the hands we play against them and the hands that we observe them play. Unless you play against a small number of opponents in a regular live game, it is completely impossible to see enough hands to form a realistic sample of the way your opponents play. In these cases, the population consists of how your opponent really plays. The hands that you played against him or observed him play are your sample. Your hope is to use this sample to determine how he plays, or even how he plays in specific situations. Earlier, I mentioned that there are two types of sampling errors. It is easy to see where you might have too small a sample to draw meaningful conclusions. There is also a grave danger of making the second type of error – choosing a sample that is not representative of the population.



Your opponents are not there to help you figure out how they play. In fact, they are probably doing everything they can to lead you astray. Here is an amusing example from the old days of draw poker high. Mike Caro used to be known as "Crazy Mike." (I guess that when he was promoted to "The Mad Genius," Mike Matusow inherited the sobriquet of "Crazy Mike.") High draw, jacks or better, was once the main game played in California cardrooms. Early in a session, Mike would make this play: After an opponent opened, he would raise. His opponent would usually draw three to a pair or perhaps one card to two pair. Mike would stand pat. His opponent would naturally check to Mike. Mike would check behind him, and then display five random cards. This play cost him at least two small bets. Seems stupid, right? Mike claimed that players, having seen this play, would be confident that he was totally insane, and throw their money at him for the next few hours. If it can be a winning tactic to make a play this stupid in order to deceive your opponents, there must be a variety of less costly things you can do to trick your opponents. Many tight players show a bluff or two early on, and then become much more solid. Likewise, some loose players start off playing a very solid style. Tournament structures very often reward this type of play. When the blinds and antes are small, it is usually reasonable to play a tight cash-game style. Later, when the blinds have escalated and the antes have kicked in, aggressive play is rewarded.



Even without making a deliberate effort to fool you, an opponent's play may be deceptive. A player may raise more often than average because he is an aggressive player or because he has been getting particularly good cards. A player who is normally fairly conservative may play rather wildly when he is losing a lot. I like to play sit-and-gos on Full Tilt. Lately, I've been a pretty steady winner, but occasionally I will play after having a few drinks at one of my bars. In these sessions, both my style and results are very different from normal. One more factor that may complicate things is the fact that some of your opponents will be improving over time. Don't make the mistake of thinking hands that you played against a beginner six months ago are a representative sample of how that person plays now.



Using the hands that you have played against a particular opponent and those you have watched him play as a sample of how he really plays is likely to produce both types of sampling errors: 1. The sample is too small. 2. The sample is not representative of the population. In an attempt to gather more data and assemble it more accurately, many online players have turned to tracking software. I must admit that I have been very negligent about installing and using some of these programs, even though I have tried a few. When using any software, make sure that you are looking at samples that are large enough to be meaningful. I have tried to take small sit-and-gos more seriously, and play them better. I can tell that this has been paying off when I use the advanced search feature on SharkScope software. I have played more than 5,400 sit-and-gos, with an ROI [return on investment] of -2 percent and a total loss of $10,500. The last 500 have had an ROI of 5 percent and winnings of nearly $5,000. The last 200 have shown even more improvement – an ROI of 17 percent and winnings of nearly $6,000. Note that even though 200 tournaments is a pretty big sample size, I have been quite lucky of late. Someone casually glancing only at my total stats, a huge sample of more than 5,000 tournaments, would be seriously misled into thinking I play much more poorly than I do. Someone who carefully focused on the last 200, to see how I'm playing now, also would be misled into thinking I'm better than I am.



In summary, be very cautious about making inferences about your opponents. Try to watch everything, especially hands in which you aren't involved. Try to get a feel for the basic level of skill and how they are playing at the moment. On the other hand, if someone seems to be playing badly and losing, go ahead and play some hands or try some maneuvers that you wouldn't consider against a tough opponent who is winning. My belated New Year's resolution is to get one of the tracking programs installed and start mastering it. Not only should it help to improve my results, but it will also enable me to write more accurately about them in columns.



Steve "Zee" Zolotow, aka The Bald Eagle, is a successful games player. He currently devotes most of his time to poker. He can be found at many major tournaments and playing on Full Tilt, as one of its pros. When escaping from poker, he hangs out in his bars on Avenue A – Nice Guy Eddie's on Houston and Doc Holliday's on 9th Street – in New York City.