Haseeb Qureshi

The Limits of Poker Theory

“Poker theory” is inherently seductive. In a game full of chaos and uncertainty, poker theory beckons to us, promising comprehensibility and control. But while theory is powerful, it is not a panacea. That’s not to say that theory in and of itself is flawed—rather, that we are.

Human beings are only boundedly rational. We are merely approximations of logical thinkers. And yet, we often take it for granted that in any situation, theory will show us a path to the answer.

In this article, we will analyze the limits of poker logic. First, we will look at the nature of heuristics and the function it plays in our cognition. Then we will begin to trace the boundaries of poker language, establish the difference between narrative and discrete poker logic, and lastly, deconstruct the way that poker arguments work in the real world.

It is critically important that we are attentive to our language, and the way we use concepts to guide our decisions. There is a temptation to think about theory in poker the same way one thinks of theory in physics, or some other hard science. By the end of this article, I will demonstrate that theory, for the most part, serves a profoundly weaker (and ultimately different) function in poker.

The Power of Heuristics

Most of our play in poker is unconscious. This is true even when we are playing our A-games.

We have spoken before of playing on “autopilot,” as though autopilot is a deviation from your normal poker game. To be more exact, autopilot is more like the skeleton of your normal game. Your “autopilot”—that is, your unconsciously competent skillset—is always running in the background when you’re playing poker. It’s just that when you’re on your A-game, there’s a lot of conscious activity buzzing on the topmost layer. But your unconscious autopilot is always running beneath it; that remains constant, even when you’re playing really well.

Our attention, then, is with that topmost layer—what is filled into the skeleton when we are consciously thinking about our play. Several things change when we are playing well, including our employment of skills that we haven’t unconsciously mastered, frequently accompanied by an increase in patience, but that’s not what we’re going to focus on now. Instead, we want to look at the stream of internal dialogue that is running through our head.

The chief characteristic of poker theory is that it is mediated through language. So any engagement with poker theory will almost always be processed through our conscious brain. (To be more exact, it is mediated by symbols, including mathematical and linguistic ones).

When we are on our A-game, we are constantly invoking heuristics. A heuristic is, to put it simply, a kind of rule of thumb. It is a not-quite-perfect-but-good-enough script that we follow and usually gives us good results. A practical (albeit rather specific) heuristic would be something like, “don’t check-raise bluff a board like A49r, just float it,” or “never c-bet air on QT7s,” or something more general, such as “in a SA/WB situation, try to minimize the pot size.” A heuristic is not a mental breakdown of a hand—it is merely a prefabricated rule to help you get to the answer to a hand that you don’t know on an unconscious level.

How do we know when we’re using a heuristic, rather than “just making plays”? After all, we are constantly making good decisions in poker when autopiloting. Most of those decisions are purely unconscious. The mark of using a heuristic rather than merely using our poker perception is that there will usually be some conscious, linguistic thinking involved. If the phrase “SA/WB” pops into your head, or “draw-heavy,” or whatever mental language that you happen to use to describe these situations—this is an indicator that you’re invoking a heuristic. They don’t always have to be explicitly linguistic; they may be merely symbolic. But for the most part, if you’re paying attention, it’s easy to spot when you’re using a heuristic.

Heuristics are ubiquitous in how we play poker. For every spot where we haven’t achieved unconscious mastery, it would take impractically long for us to fully process every scenario and figure out the best play. Heuristics are, in a sense, pre-formulated, simplified rules that help us quickly process many of these situations and approximate the best answer. They work pretty well most of the time. But because they are so widespread, we must be very attentive to how we use them. Bad, unexamined heuristics are often the source of some of our most consistent mistakes.

For example, one heuristic I inattentively used for a long time related to overbets. Whenever a good player overbet, I almost always assumed they were valuebetting. If you asked me why I assumed this, I likely would’ve cited the language that went along with my heuristic: “an overbet is a risky and unpredictable bet, so people usually make it when they’re sure of their hand.”

Now, certainly, this qualifies as a rationale. It is poker-logical, so to speak. But it’s important to note that I wasn’t thinking this through every time I folded to an overbet. I was simply consulting this heuristic that I had and applying it (or, after long enough, not even remembering the heuristic and simply unconsciously folding to overbets because I perceived them as strong). Consulting a heuristic is a mental shortcut; it simplifies the processing of a hand to conserve our mental energy, which is always limited when playing a long session, multi-tabling, or battling a difficult opponent. But such a lack of reflection makes heuristics an easy place to solidify bad play. In reality, good players were overbetting me with bluffs, but because my heuristic was so entrenched, it took me some time to realize this and discard it.

Every player has some of his consistent mistakes and biases embedded into his arsenal of heuristics. This is why creativity and defying your mental walls are so important: in order to break your suboptimal heuristics (which are usually quite old and deeply ingrained), you must go over them with a magnifying glass, to really see them for what they are, and then to systematically challenge them. To become a great poker player, you must constantly put your heuristics under assault, and replace old heuristics with newer and sturdier ones.

Not all Theory is Created Equal

We might say that heuristics are prefabricated molds of theory. They are not theory in and of themselves; heuristics are static. We don’t “do” heuristics, we merely remember them. But they usually derive from theory in some way. So now let’s turn to theory itself.

There are two fundamental types of theory. The first is discrete theory. Discrete theory is the type of theory that you likely think about when you imagine poker theory. It is discrete, mathematical, and involves things like delineating hand ranges, combinatorials, GTO analysis, breakdowns of stats, and so on. It’s the type of thing you do in PokerEV or PokerStove. It involves math, modeling, and explicit assumptions.

Contrary to the popular image, discrete theory is a miniscule part of the poker theory that we actually use.

By far, the largest chunk of poker theory we use is not discrete. It is rather what I call narrative theory. Narrative theory is not mathematical, but descriptive. It tells a story. It is not scientific, logical, or deterministic—it is literary. A narrative does not outline all of its assumptions or convert a hand into an analytical model. Instead, it uses established conventions to tell a narrative that leads toward the answer. Narrative theory lies somewhere between heuristic and discrete theory. And it is, by far, the most commonly used type of theory. I would conjecture that almost all of the theoretical thinking that we engage in is narrative. And yet, few acknowledge its role in shaping our approach to poker.

It is comforting to pretend that all theory is equally robust. But if it is true that the vast majority of poker thinking is narrative rather than discrete, then our faith in the comprehensibility of poker is unearned. It suggests that the vast majority of poker theory (and our understanding of this game) is not necessarily scientific, logical, or deterministic. Poker becomes more an art than a science. And that is a deeply uncomfortable thought for those who want to believe in the chess game of poker.

The Arc of Narrative Theory

Take this nugget of theory, taken from an actual explanation of a poker hand (the context is unimportant): “His range here is weak, and he just lost a couple big pots, so this is a good spot to bluff.” This seems on its face like valid reasoning, doesn’t it? This is a very typical example of what is going through our heads when we’re thinking about poker—and this is also very typical narrative theory.

Narrative theory has a few hallmarks:

To discretely analyze a spot involves complex math, the mapping of assumptions and forking paths through a hand. Narrative theory collapses these complexities. And, as it turns out, that is precisely where its strength lies.

Let’s go back to that original explanation. “His range here is weak, and he just lost a couple big pots, so this is a good spot to bluff.” But let’s say that perhaps the opponent knows his range is weak, and thus will be calling more. Or, what if losing big pots is going to make him more call-y? These are two possible counter-narratives that would directly challenge this one. The question is this: how do we decide between them? There are no numbers to compare, nothing to multiply or divide, no pot odds to analyze. How do we decide between the first narrative: “villains who just lost big pots tend to call more,” and “villains who just lost big pots tend to give up more”? In a very real way, both of these are valid. If the line of reasoning went, instead: “his range here is weak, but he knows that and he just lost a couple big pots, so he’s likely to call down light here,” this story would also sound rather convincing, wouldn’t it?

It can be infuriating, but such ambiguity is inherent to the nature of narrative theory. The strength of narrative theory is its ability to transform a hand into a story—a simplified narrative that efficiently organizes and condenses the information in a hand. Imagine if we laid out all of the assumptions behind something like “I’m going to slowplay my set here because a raise would look too strong.” We’d have to first say what his range is going into this hand, what our range is, how we think he’ll perceive a turn flat, the likelihood that he’ll bluff or valuebet any given river card, how he is going to react to a turn raise, and so on and so forth. Really, when it comes down to it, actually breaking down a hand is enormously complex. It involves a lot of paperwork. Narrative theory is, in a sense, a kind of deferral. A form of shorthand.

Behind narrative theory lies the claim, “there is some discrete theory that justifies this. I don’t have it on me, and I can’t show it to you now, but it exists somewhere.” Actually doing that discrete theory during a poker hand would be prohibitively taxing, in terms of mental processing and of time. We can’t discretely analyze every hand we play. So we must take shortcuts. Narrative theory is the only practical way that we, as human beings, can efficiently organize and recall our knowledge of poker theory.

But how do we actually generate a thread of narrative theory?

Narrative theory is composed of building blocks, which we might call poker memes. Things like “checking back for pot control,” or “maximizing stack-to-pot ratio,” or “extracting max value,” or “betting to induce a bluff.” These memes describe interpretations of events in a hand which we, poker theory users, view as valid. That is, these are things that really happen in a hand—they have a discrete theoretical basis. That does not mean that they happened in this particular hand you’re describing, but we all agree those are things that happen. They are valid memes. Here are some (usually) invalid memes: “I raised for information,” or “I bet because he was challenging me,” or “I folded because the hand might be tricky.” We don’t consider these reasons to be grounded in discrete theory, so we dismiss them. As you can imagine, the language of valid narrative theory has changed as poker has evolved.

Thus, narrative theory is a social phenomenon. It is created by the community of poker players who want to talk about poker, and it is through the poker community that we regulate what is valid narrative theory and what is not. They have a genetic quality—generally, very strong players (especially vocal ones who make videos or talk openly about their poker thinking) create new memes and foreclose less useful ones, and most other players tend to follow their example. Thus, changes in narrative theory disseminate through the poker community, not through poker itself, not through playing or changes in gameplay, but in social and linguistic changes that are amplified by prominent community members.

Narrative theory is, in a way, much more interesting and organic than discrete theory. Discrete theory should be the same for two people a world apart, even if they’re in totally different player pools. But narrative theory is always different. It is fluid and changing. It adapts to the needs and worldviews of its users. Reading a forum thread from top players just five or six years ago reveals just how much narrative theory has changed in recent years.

For my own part, one realization that came to me later on in my poker career was this: one of the most valuable things that is communicated through poker videos (and the reason why they’re invaluable for learning) is that they are so good at teaching narrative theory. In fact, most of what I think I gave away in all of the videos I was making was not actually my poker strategy, or the individual plays I made. I think the usefulness of my videos lay, instead, in how I talked about poker. Think about it. There are some videos that discretely analyze situations in hands, break things down into math and PokerEV and so on, but really, they are the minority—the majority of videos see a hand, quickly give a narrative explanation, and then move on.

Of course, once you start to see this, your instinct might be to think that you’re getting ripped off. Discrete theory is what you really want, isn’t it? On the contrary. One of the most powerful things we learn from videos is how better to apply narrative theory.

Narrative theory is much more important than discrete theory when it comes to regulating our play because we rarely have the time to apply discrete theory during an actual hand! If 95% of our play is regulated by narrative theory, then simply being able to listen to other people’s narrative theory, examining and regurgitating their language, and internalizing the rules with which they combine and chain together memes, we learn to become better at narrative theory. If Phil Galfond checks back top pair on a flop, his breaking down the math and discretely analyzing the hand is, actually, of little value. But what is immensely valuable is learning the memes, the rules of narrative theory that Phil Galfond is applying, and learning to apply them yourself. It is a curious thing—you take a bad player, teach him to simply talk about poker better, and he suddenly becomes a better player.

Narrative theory is not deterministic. By learning the language of a better player, such as a coach or a videomaker, you won’t necessarily play like him. But listening to and engaging with such a coach may teach you how to tell stories like him—a concept known in psychology as scaffolding. Your coach’s style of narrative theory emphasizes the a particular hierarchy of concepts—embedded within his language is his idea of what concepts are most important in a hand, which things to look for first, and which patterns should trigger which responses. In the same way our parents engage in scaffolding to teach us how to tell stories as children (e.g., “and why did Billy do that? How did that make you feel? And then what did you do?”), getting coaching and watching videos guides us toward constructing good poker narratives in much the same way.

It would be incorrect to claim, however, that narrative theory is all that we’re doing when we’re playing poker. There is also some discrete theory involved, especially as your game improves to a high level. Estimating pot odds, analyzing how to optimize against a given hand (given certain assumptions about his play), logical hand-elimination to narrow down his range, or even holistically strategizing on how to allocate your hand range in a certain spot—these things may well fall under the purview of discrete theory, which strong players are continually applying during their play. But no matter what level you’re at, narrative theory is always the dominant mode of theory we employ in poker hands. There is simply no other method as efficient at encoding the large swathes of information contained in poker. Narrative theory is, in a very real sense, the human answer to complexity.

Arguing over Stories

So let’s say that you begrudgingly accept the validity of narrative theory as I’ve presented it. Okay, you say, maybe this is how it works. So what?

I’ve been very steadfast in claiming that narrative theory has many advantages, and is essential to our ability to parse the complexity of poker. But, of course, narrative theory has its drawbacks.

Inherent to its nature, narrative theory cannot be logically argued. There are some narrative disputes that can be resolved verbally, such as demonstrating two inconsistent memes were strung together, breaking the rules of narrativity. For example, there might be a narrative that includes both “he couldn’t’ve had a draw on the flop, because he loves to checkraise them” and “on the river he never bluffs big, so he had to have hit his draw.” The rules of narrative theory disallow this combination, and others. Inconsistencies like this, however, are not terribly common once you reach a certain level of mastery over poker theory.

More often, when people are arguing about a poker narrative, it is not resolved by the narratives themselves. After all, narratives are incommensurate—they cannot be evaluated objectively, and each participant believes their own narrative (it should be no surprise that when we share hands, we always label ourselves the hero and our opponent the villain).When such disputes arise, they are often resolved by an appeal to authority—the players will go to a third party, another trusted poker player, to decide which narrative is best aligned with authority.

In fact, once you start seeing this phenomenon, you will start seeing it everywhere—especially in poker forums. What is a typical strategy thread, after all? An opening poster shows a hand, and then every subsequent poster takes a shot at communicating their own narrative of what’s going on in the hand. This should seem like chaos, and yet usually when we read such a thread, we have an idea of which narrative “won.” How do we decide that?

There are three ways. First, if there is no consensus, we tend to ally ourselves with the narrative that most closely resembles our own. Second, if there is a consensus, then we choose the narrative that is most popular with the best players (which is a sign of fitness). This is often the way that narrative theory works. We observe a narrative somewhere in the wild, and from the fact that it’s alive and well—by the evolutionary principle—we assume it must be strategically fit.

This is the basis of what I call ecological learning. There are three fundamental modes of learning in poker: learning through theory, learning via experience, and learning through observing others—ecological learning. Through this type of learning, you learn from “what’s out there” or “what people are doing” (under the presumption that weak strategies would be culled out from the population). Thus, through ecological learning, popularity is an effective measure of a theory’s fitness. Going back to the forum thread—the third possibility is that a poker authority weighs in to choose among these narratives, or possibly offer his own (which, if he does, we take as an even stronger sign of fitness). Let’s say, for example, that Sauce or Jungleman weighs in. If they say something like “this is a definite fold,” this doesn’t really qualify as narrative theory, it’s simply a stand-in for a statement like this: “this is a fold, and I’ve done (either explicitly or intuitively) the data analysis that tells me on average, folding is better than calling/raising.” But if they offer their own explanation of the hand, then their narrative inevitably becomes the dominant one that later posters accept.

Rarely are these things decided by application of discrete theory, comparing mathematical models of the hands and assumptions and so on. Really, once you look at it this way, the art of poker argument can seem almost simplistic.

As a student of poker, if you were anything like I was, you will get into many arguments about poker. When you find something you disagree with, or which doesn’t seem to make sense to you, it is good to challenge it. Debating poker theory will nourish your mind. But, especially as a developing player, you should be wary of arguments that begin and end in narrative theory.

At its core, all of narrative theory carries with it an implied warranty. The warranty is: “somewhere out there, someone did some discrete theory to prove this works.” Usually, this warranty goes unquestioned. But if you are engaged in a debate about poker, it is time for you to call this out. When someone makes a narrative claim that you deeply disagree with—challenge them to prove it. Don’t accept it at their word! Or, if you have good reason to trust their authority, then take the time to prove it to yourself. As much as I’ve been stressing narrative theory as essential to our development, the ability to do discrete theory is important as well. Especially now, as poker evolves and games get more and more rigorous, the precision in strategy that can be captured by narrative theory is often not enough.

To reach the highest levels, you must gain a mastery of both discrete and narrative theory. And the only way to do that is to practice them. Learn how to run simulations. Learn how to use PokerEV, or StoxEV. If you don’t know how to run basic programs like PokerStove, or how to do fold equity calculations, or how to calculate a GTO river strategy—learn them. Knowledge of discrete theory only bolsters your narrative theory, and helps you to know which structures in your poker game are sound, and which are more suspect.

Discrete analysis is the bedrock of theory, always. In the end, narrative theory is merely a stand-in, and so you must be willing to not only call others out when their stories don’t add up, but also to scrutinize the concepts you employ in your own game. Narrative theory is merely the roadmap we sketch atop the true terrain of discrete theory.

But there are some situations which, no matter how hard we try, are insuperably complex, and cannot be broken down by discrete theory. PLO has many such situations. When you have a pair and a mediocre draw on a flop, is it better to lead out, or check/call? Is it better to flat it in a 3-bet pot, or raise the flop? What if stacks are deep? All of these variables will certainly affect the answer—but we don’t know how. We have no idea where any of the cut-offs are for these variables, because PLO is such a combinatorially complex game, which makes mapping out a decision tree effectively impossible.

I remember once getting into a very tricky PLO flop situation. I couldn’t figure out how to analyze the hand, so I took it to a number of world-class PLO players I knew. To my surprise, I kept getting different answers from anyone on the best way to play it—on the flop, one of the earliest streets, it baffled me that there could be so much disagreement! I was frustrated, but also fascinated. In reality, nobody who I took the hand to could actually break down the hand either—mathematically, it would be overwhelmingly complex to even try. The only way to defend a particular way of playing the hand was narratively. Essentially, I realized I was being told two different stories—and the only way I could decide between them was to pick one and go with it.Even with all its complications and imperfections, we need narrative theory. Although it can seem hopelessly convoluted at times, we have no alternative but to engage in the circus of narrativity, debate, and reason-giving. You must embrace the way that poker works. Only then can you navigate the world as it is, and develop your skills as a poker player.

You could say that, in a sense, it’s incidental that math can model poker. After all, you can mathematically model the physics behind tennis, but physics has little to do with the process of learning tennis. I suspect that the same is largely true of poker. Most of the learning that we do in poker has little to do with the chess match. What we are playing is something vague and large, it is played in large strokes of thoughts, it is not transmitted through equations and proofs, but through stories and emulation. If poker couldn’t be modeled by mathematics, then storytelling would be all we’d have to make sense of the game. Perhaps that’s closer to reality than we think.

In the end, poker theory tells us about a lot more than just poker. It tells us about ourselves, the way our minds work, and the way that we interact with other members of our community. In the next article, we are going to look at this latter phenomenon, with an eye toward the practical. What kind of relationship should we have with the poker community? Poker is an intensely isolating and isolated profession, and yet, we would be helpless without a community of peers to guide our learning in the right direction. In the next article, I will discuss the poker community, and how to successfully develop and foster a poker network, and how to stay sane in a less-than-sane culture.

[Note: this is adapted from the rough draft of my first book, How to Be a Poker Player: The Philosophy of Poker. If you like what you read, consider buying the completed book—it’s tightly edited and contains new material! Hope you enjoyed. :) ]

-Haseeb
  • Andy

    I like your insights about narrative theory and discrete one- art versus formula.
    “Narrative theory is, in a very real sense, the human answer to complexity.”
    I will say that typical day-trader is like typical poker player who utilizes mostly narrative theory .
    An reality of financial markets shows that narrative theory loses badly against discreet? theory implemented by quants and executed by computers. The art is defeated big time by coded formula.It looks that day-trades and on-line poker pros share the same destiny-the extinction in nearest future.

  • Kenny

    Andy, I disagree with your analogy. There still exist successful traders/investors who employ “narrative theory” in their day-to-day transactions (read: Steve Cohen, Warren Buffet, et.al.). Furthermore, the financial markets, unlike poker, is so inherently complex that you cannot define a set of rules that allow you to track the odds — note that financial market theory is heavily fragmented across people who espouse the Markovitz theory, the Keynesian theory, the Mandelbrotian theory, etc. There’s absolutely no way for us to “put it in a box” like poker and hence a lot of these nerds actually lose a lot of money when exposed to “black swan” events. Trading heuristics like “ride the trend”, “keep a 3:1 RR”, “never bet beyond 2%”, “go where the market is”, etc are proven to be robust that it serves beginners well and is pretty much a mantra for advanced traders.

    That aside, I do agree that there is still merit to learning discrete theory in that it allows you to avoid big mistakes (ie. shoving AAxx in a two-tone board with 2 connecting cards). But if we plan to excel, augmenting that foundation with heuristics is essential.

    • Andy

      Kenny – I agree there are plenty differences.
      My point was about a trend.
      The pool of successful day-traders and online poker pro is shrinking.
      In case of financial markets overall trading volume grows fast.
      The volume executed directly by humans are shrinking dramatically.
      We do not have reliable info about poker.
      My point is: about a lower probability to be successful day-trader or online poker pro.
      The trend tells me that it will be much more demanding task to accomplish in the nearest future.That’s all.

  • Greg

    Really good article.

    “Through this type of learning, you learn from “what’s out there” or “what people are doing” (under the presumption that weak strategies would be culled out from the population). Thus, through ecological learning, popularity is an effective measure of a theory’s fitness.”

    Not sure if I totally agree with this part. I do agree that it’s important to know “what people are doing,” but not necessarily because “what people are doing” is what we always should want to do ourselves. Because of reciprocality we must do some (or many) things differently than the player population in order to have an edge. If we are starting with a strategy that is inferior to “what people are doing” (for example, if we are a relative beginner or new to a given stake), then perhaps jumping on the bandwagon will stop some bleeding, but to make money we have to play differently than the population in a lot of spots (although knowing what the population is doing is still useful in that we can then develop a counter strategy).

    • You raise a very fair point, but I think both my point and yours can coexist as part of a healthy poker strategy. In reality, you are *not* going to be better than everyone at your table at every part of their game. And in reality, many parts of other people’s games are already optimized or GTO (especially trivial parts), such that there is no reciprocal edge that can be gained. I absolutely agree with you that in order to be a strong player, you must actively engineer stronger strategies than your opponent. But you won’t be doing that everywhere–only in certain places. And no matter how good you are, there is always going to be need to play catch-up somewhere (i.e., to plug holes in your game that are reciprocally weaker than your opponents’). For that, ecological learning is invaluable.

      I should add, ecological learning doesn’t necessarily have to be in your own player pool. Observing what people are doing at 10/20 or 25/50 with their 3-betting strategies can inform your 3-betting strategy at 2/4, even if your understanding of it is naive or superficial. You may still gain a reciprocal edge over your own player pool that way.

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