#4 - A Framework for Poker Study

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  A Framework for Poker Study Introduction  Recently I have put some thought into strategies for studying poker, in particular NLHE. It is frequently said that there are too many variables involved in the play of a hand for anything resembling a formulaic, component-by-component analysis to be practical. I agree with this, and agree that in even the simplest cases (short-stack push/fold calculations, for example), there is a significant margin for error in the final result which is due to necessarily imprecise assumptions about an opponent’s ranges. So even if a poker hand is one giant math problem, complete with game theoretic opponents who do a, b, and c x%, y%, and z% of the time, it’s an unsolvable problem. That said, I think a lot can be learned from thinking about poker hands in terms of their component variables, from thinking about the structure of that giant math problem and how it could be solved if it were solvable. This essay is my attempt to categorize and analyze those components. I call it a framework for poker study, because I think that one good approach to getting better is to spend time away from the table focused on these component variables one at a time, in order to be better prepared to think through all of the relevant information when faced with decisions at the table. Core Ideas  There are three core ideas with which I assume everyone is familiar – the concepts of pot equity and Expected Value (EV), Sklansky’s Fundamental Theorem of Poker, and what I will call “hand range calculus.” Pot equity and EV are functions of basic probability and govern every action in a poker game. Your hand has some % chance of winning the pot, the pot contains some amount of money, so you have a claim of some part of the pot. Every bet you make is an investment; you should bet when your expected return from the bet is larger than the cost of the bet. The FTOP formalizes how to maximize your return in the special case of complete information; every time you make a bet that maximizes expectation versus your opponent’s actual hand, you win, every time your opponent fails to maximize his expectation given your actual hand, you win. “Hand range calculus”, which is the form most analyses take on these forums, acknowledges that poker is actually a game of incomplete information, and attempts to define best actions in terms of maximizing expectation versus the range of possible hands your opponent could have, in light of the range of hands it is likely he thinks you have. Because in every case, both you and your opponent have a specific hand, the FTOP is still the final theoretical measure of what is profitable or unprofitable action. In practice, however, we work with incomplete information; thus poker skill is a combination of the ability to make best decisions within the context of “hand range calculus” and the ability to read your opponents’ ranges better than they read yours. Situational Factors  We all know that the proper play of a hand and the correct read on an opponent’s range depends on a lot of situational factors. I think we are accustomed to thinking about these factors in the context of whatever particular hand we are playing or analyzing, where many relatively small factors accumulate to a read and a decision. The framework for study that I  suggest in this essay (and which I am following myself) is to separate the most important situational factors and analyze them individually. The factors I want to talk about are position, board texture, betting patterns, betting frequencies, pot size in relation to stack size (there are two others I’m not going to cover but that I want to mention – table image, and bet sizing, table image because it is obviously so important, and bet sizing because I find it interesting. Maybe another time, this will be long enough as is). All of these factors are interrelated, but by isolating them I hope to get a better sense of the role each plays in the core goal we're all seeking - to maximize EV versus an opponent’s range and know his range better than he knows yours. Position  The most familiar, most analyzed, and easiest to understand situational factor is position. Hand ranges automatically widen with better position. Not only does someone in position have fewer people left to act and more information on that particular round, they and their out-of-position opponents have the knowledge that the player with position on this round will have position on future rounds. So CO and Button preflop raising ranges are much wider, and in-position bettors on the postflop streets usually have wider ranges. A 20/12 is 7/5 UTG and 40/25 on the button, or whatever; if you check the flop first to act in a three way pot, independent of any other knowledge, the Button is more likely to bet than the guy in the middle; etc. I don’t think much more needs to be said about this, as it is already built into every thought any of us has about the game. If position was all I had to talk about, this essay wouldn’t be very useful. Onward. Board Texture  This one is more interesting, and might make clearer what I’m getting at with the “isolating situational factors” idea. Imagine a heads up raised pot with a dry ace-high flop, Axy rainbow. You’ve probably played hundreds of hands that fit this description, thousands, maybe. What percentage of the time does one of the two players have an ace? How often can one of them beat AK? How often does someone bet this flop with less than an ace? If you are called the raise and are in position, what percentage of the time should you expect an honest opponent to bet into you? How much more frequently than honest does he have to bet before you can exploit him by representing the ace? There’s a whole game theory problem right here, on this simple board where the only hands people “should” have to continue are TPTK-TPGK, sets, pocket pairs, and the rare two pair. What about a medium two-tone flop, the kind with straight draws (T85 or 974). Now there are lots of draws, combo draws, still sets, there are always sets, but now if you get action that looks like a set, it might be a draw instead. What does a bet mean on this flop? How different is that from what a bet means on an A-high flop? How often does someone betting this flop have no pair? Compare a raiser betting this flop to the A-high flop – how often should he bet, how often should he get called, raised? Raised pot again, now K-high. Raiser is going to rep the K a lot, but have it less often than he has the A on the A-high flop. How often should an “honest” raiser bet the flop, allowing for bluffing as long as it isn’t done too frequently? How frequently is that? Paired board, like J88, or JJ8. Now there are only 5 cards that could have hit the board, instead of 9. Pocket pairs are stronger, the monsters are in plain sight. Same questions - how often should this flop be bet, by what hands, how easy or hard is it to push someone off a  mediocre hand? Etc. etc. How many flop textures are there? Dozens, hundreds even, and they all blend into each other, but questions like “how often should the preflop raiser bet the ace”, and “how fast should JJ play on a T85 two tone board” are things that are partly determined simply by the kinds and number of hands that can like a given flop. Betting Patterns  Because NLHE is a game where you can bet any amount at any time, it could feel like there are a ton of ways to build a pot. In fact, especially among decent players, the same patterns repeat themselves over and over. Think about how often a hand plays out like this: preflop raise, call. Raiser bets, call. Raiser checks, caller bets, raiser folds. Or, raiser in position, checked to the raiser, bet/call, turn goes check/check, OOP bets, raiser folds. Or, raiser OOP, bet/call, check/check, bet/fold. Or bet/call, check/check, bet/call. Or bet/raise/call, check/bet/fold. Or, checked to raiser, raiser bets, check-raise, raiser folds. It’s easiest to categorize headsup pots this way, but patterns repeat themselves in multiway pots also. Some patterns are more common than others. What I suggest is that thinking about these patterns and the frequency with which they occur is instructive, for two reasons. One, the patterns that occur most frequently are also the patterns that match the most frequently occurring situations (weak to moderately strong hands building and contesting a small to medium-sized pot). Two, the majority of profit comes from creating large pots with big hands, which is easiest to get away with if done quietly. Especially against good players, this can be very difficult. Betting Frequencies  Under “betting patterns” I was talking about an observer’s view of all participants in a hand, here I’m referring to the frequency with which individuals bet, call, fold, and raise. There are big meta-theory questions here, like what % of the time should a preflop raiser bet the flop (or optimal frequencies for any action sequence), but I am more talking about things like “what % of the time do I (or this opponent, or that opponent) bet the turn after having bet the flop and being called? What % do I bet three streets in a row? What % do I bet two streets then check/fold? What % of the time do I check-raise the flop, then bet the turn? Do I ever check-raise the flop, then check the turn? How often do I call three barrels? How often do I follow up my turn bet with a river bet? Clearly, the board often changes from flop to turn and turn to river. If the draw hits, and you know 100% that your opponent was drawing, you should check/fold, and no frequency mumbo-jumbo changes that. But since some of the time you should bet the flop with that obvious draw and some of the time your opponent is calling without it, then some of the time, you should follow up when it hits on the turn (whether you have it or not). Etc. These are the things you start thinking about when you think about action frequencies. Are there optimal frequencies for all of these? Maybe, sort of, in a game-theoretic, perfectly-playing opponent sense. Pots grow exponentially, so maybe in theory we should bet the flop 75% of the time we raise, bet the turn 25% of the times we’re called and 50% of the time the flop checks through, and bet the river 10% of the time the turn is called and 20% of the time the turn checks through, all with appropriate bluffs mixed in. In practice, we set these frequencies to exploit specific opponents, but I think analyzing these questions in general can  help us understand how to do that. Pot Size/Stack Size Dynamic  100xBB stacks. Limpy McLimper limps in front of you. He does this with 20% of his hands and he never raises. You have two cards and raise. He calls and you see a flop with 9 BB in the pot. How strong a hand do you need to play for 100BB? For 50? For 25? Too broad a question? Dependent on too many other factors? Yes, of course. But contrast: Same 100xBB stacks. Raisy McRaiser raises in front of you. He does this with 20% of his hands and he never limps. You reraise with the same two cards, he calls (he calls raises as often as Limpy). 27 BB in the pot. Now how strong do you have to be to play for it all? What size pot should you play, on average, with one pair? With a big draw? The only difference is that the pot is a bigger percentage of the stack. With more to fight for, people’s ranges for postflop actions necessarily should change toward being more aggressive. If your opponents don’t make this adjustment, exploit them – reraise a lot, then play aggressively, let them fold too much. If they do make this adjustment, you have to adjust with them in reraised pots. Go broke with AA against Limpy, you’re usually a fish, against Raisy, probably not. The point is not that there is a formula for proper size pot with xx on flop abc in terms of preflop pot size “AA is worth 3x preflop pot size”. Clearly there isn’t. There may be times to fold a set in a reraised pot and times to felt middle pair in a limped pot. But on every flop, you should be able to look at the pot size, look at the stack sizes, and have some general idea of what kind of hands should be willing to play for how much. Sure, that general idea has to be adjusted based on all of the other situational factors, but it plays its role too. Obviously, in MTT’s, pot/stack dynamic is always present because of increasing blinds and variance in the size of opponent’s stacks. I find the 30-40xBB range particularly interesting, because it is a time when raisers with one pair have a hard time folding, but callers with speculative hands still have odds to call and try to outflop (also because allin reraises are too overaggressive in this stage and easily exploitable). This generates a cat-and-mouse game where you have to accompany the raising hands you do plan to go broke with hands you don’t plan to go broke with in order to deny implied odds to speculative hands. But do too much of this, and you become vulnerable to preflop reraises. Also, in MTT's, a significant shift in pot size/stack size ratio happens when antes are introduced. There is more to fight for, so ranges change and more aggressive play is rewarded. In cash games, where stacks are usually 100x and there aren't antes, this dynamic shows up more in the differences between limped pots, raised pots, and reraised pots. All this theory in practice  A short, simple example. Someone raises UTG+1, Button calls, you call in the BB with 55. The flop contains a 5. Before you say “lead” or “check,” you have to consider -the range the raiser raises from that position -how likely the particular flop is to have hit that range (AQ5? T85? 522?) -what betting pattern is most likely to create a large pot without tipping anyone off that you want a large pot -how likely the raiser is bet the flop if checked to, raise if bet into, how likely the other caller is to be trapped with a marginal hand, how often the raiser will follow up on the turn with a
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