Understanding the mathematics of poker

By: STUDstood
Published: Sep 21st, 2009

As I mentioned in my last blog, over this past year we have covered many items to hopefully enable you to become a more successful poker player, such as per game money management (how much bankroll is necessary for a given limit), per session money management (how much bankroll is necessary for a given session), game selection, table persona, table demeanor, etc. We have explored these for both cash games and tournaments. These concepts should neither be underemphasized nor underestimated in their importance. They are truly building blocks necessary for you to succeed. In fact, without these concepts, I feel that no matter how well you play your poker hands, you will still likely come up short unless you add them to your arsenal. That said, it is just as important to know and employ the mathematics of every hand situation you are faced with. And, when I use the word “mathematics”, I am referring to all three types of odds that take place in any given hand, which are: • Real odds – the actual hand vs. hand(s) odds at a given time (or street) in a specific hand • Pot odds – the odds that the pot is offering at that moment • Implied odds – a calculated estimate of the return you could get as the hand progresses, relative to your current investment There are various computer programs which can be used to calculate the real odds by entering given hand match-ups. You should review and understand the math of the most common types of match-ups. One of my favorite software programs is called Poker Probe, written by Mike Caro. Poker Probe calculates the “QPR” of hands, which stands for “Quick Power Rating”. Caro’s calculation (I do not know if this type of analysis can be found on other types of software), gives you a measure of the actual “power” of a given hand at that time. My interpretation of the QPR is that it somewhat simulates the implied and pot odds. I say that because there will be instances in Mike’s analysis where the value of real odds for one side of a match-up does not agree with its QPR. Even knowing the actual real odds of a given hand, it can be hard to calculate its pot and implied odds. That is because it is impossible to truly know what is going to transpire as the hand progresses. After all, we can’t know what cards will be dealt into our hand or our opponents’ hands, nor do we know how our opponents will act as the hand unfolds. Nevertheless, trying to predict a given hand’s pot and implied odds is at least as important as knowing the current odds. To make an assessment of implied odds requires understanding your opponents, making an educated guess, based on experience, as to whether they will pay you off if you make your hand, and how much. This is a very important skill, which you should work on constantly. This is a very difficult skill to master, since it is hard to “practice” many scenarios without actually being in them in “real time”. While you play, whether you’re in the hand or not, you should always be trying to categorize your opponents, trying to get a feeling for how they play. To some extent, an athlete can simulate an actual scenario which might take place at some point in a competition. A basketball player can shoot countless free throws, lay ups and jump shots. Many times, doing this prepares you for when a specific scenario happens in a “real” game. This is harder to do in poker. How many people can you get to sit around a table with you and simulate hand after hand under realistic conditions, for real money? What I used to do to try and get a better handle on how to estimate the odds and probability of these types of scenarios was to take a deck of cards and deal out a hand to some (1-7) fictitious opponents around the table. Of course I was able to see all their cards, both up cards and hole cards, but I would try to “play” their cards as I thought they might play them, and then try to calculate the pot and implied odds of the hand under those conditions. Although this was very time consuming, I found that it did help me. There may actually be some computer software that does this, which you can purchase, and if so would save you a tremendous amount of time and effort. The computer can simulate hands at high speed, but you should take the time to do the situational calculations, so when they come up in a real live game, you’ll be ready. There are many other factors which have to be accounted for in making correct decisions during a hand. Some are: Reading your opponents’ cards accurately. This is huge, because there is such a wide range of hands your opponents can have. How accurately you assess their hands will obviously affect your calculations of all three types of odds for a given hand. Knowing what cards have been shown. This applies more with games such as Stud (and its variations) as opposed to Hold’em. Who your opponents are. Based on your read of his/her cards and your knowledge of their tendencies, what is this person going to do on that street and subsequent streets? With each decision you face, you again have to know what cards are available based on your knowledge of the discards, evaluate your read of your opponents’ hands, assess your hand’s possibilities, and make the best possible decision. How your opponents are doing in that session. Remember, as we discussed in past blogs, when you are losing and your opponents are winning (or vice versa), certain strategies will be more or less successful based on the changing situation. What your opponents think of you. This is somewhat similar to the last point, but assuming you have all just started playing, and everyone has equal chips, you should try to get a feeling for what your opponents’ perceptions are of you, and act based on those expectations. As the game progresses, be aware of how your image has changed, and adapt your play accordingly. The limit and type of the game. For example, is this a higher or lower limit than your opponents are used to? Is this your opponent’s best or worst game? Is this a tournament or a cash game? These are some of the factors that must be taken into consideration within a split second of every hand you play. Pretty intense, huh ? We’ll discuss this more in upcoming blogs. In the meantime, you can find me in the $10/$20 and $30/$60 limit games in our Stud section, as well as in our weekend $215 buy-in tournaments for Stud games. Please check the starting times of each of those events under Tourney > Special in the PokerStars lobby. Feel free to contact me with any questions, suggestions or thoughts at adamr@pokerstars.com. See you at the tables!
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