There are Only Three Concepts in Poker

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Introduction

Given the speed at which poker education has progressed over the last five-to-ten years, you could be forgiven for thinking that the title of this article was somewhat ridiculous. I mean, come on, aren’t there dozens of different concepts in poker? Well, yes, of course there are. But what I aim to highlight here is that all of these concepts that we talk about are, for the most part, simple ways to explain mathematical ideas and make them easily intelligible, and that if we can really master the core concepts that generate all these different aspects of the game, we can eliminate the need to ‘reverse engineer’ our poker game from the outside in, and start exploring it from the inside out.

Language, signifiers and signifieds

I’ve written about this before. Poker is as much a game of language as it is of math and theory, because language is the only tool we have at our disposal to facilitate discussion and communicate our ideas about the game. We can’t ‘talk math’ to each other, and I couldn’t write this article purely in math form. I’m sure an expert mathematician could give it a go, but it wouldn’t be useful to many people.

In linguistics – more specifically, semiotics – which I studied a fair amount in college, there are two concepts known as the signifierand the signified. Developed by linguist Ferdinand de Saussure in the late 1800s and early 1900s, the simple explanation of these concepts is that the word or name assigned to something is the signifier, and the thing itself is the signified. This idea has helped linguists to understand language for over 100 years, and I believe it can help us to understand poker as well.

For the purposes of this article, the signifiersare the many and varied strategies and concepts that have become a part of poker over the last ten years or more – things like 3-betting, bluffing, preflop raising, floating, check-raising, and anything else you can think of. The signifieds, or the specific mathematical ideas that these concepts attempt to explain, are three simple things – ranges, equities, and odds.

Ranges

The reason ranges are the first concept that needs to be addressed is simple. Everything we do when analysing a poker hand, every statement or assertion we make, every note we take on another player, every bit of past experience we draw on, every bit of research we do, every training video we watch – all of it is done with the end goal of being able to correctly ascertain our opponents’ ranges, our ranges, and our perceived ranges in every spot. If we knew their ranges, our ranges, and our perceived ranges, and we knew the mathematical implications of them, every decision would be easy.

Imagine knowing your opponent’s exact calling range when you raise his or her continuation bet on a dry flop. Imagine knowing their exact 3-bet bluffing range and the frequencies with which they slowplay their strong hands. If we could dissect our opponents’ ranges down to the tiniest detail, and provide accurate mathematical estimates down to the nearest fraction of a hand combination (in order to account for frequencies), then we wouldn’t need to ask ourselves, “how aggressive is this player?”, or “what are the table dynamics like?” – the language we use and the questions we ask are a way to get to the root of the math. The math of our opponents’ ranges is the signified, and the language we use to describe it is the signifier.

Equities

Now, I said above that every decision would be easy if we knew our opponents’ ranges. That’s not strictly true, because we’d still need to know how our own ranges interact with theirs, and who stands to win the hand in any given spot. For that, we’d need to know our equities. Once we know exactly what our opponent’s range is, and how not just our hand, but our entire range plays against that range, we’d be able to determine exactly the right play in order to maximise our chances of winning the hand.

If we knew how exactly how much fold equity we had in every spot, or the exact equity our flush draw had versus the ranges of our three opponents in a multi-way pot, or whether to call or fold to a preflop shove in every single instance, things would get a lot easier. Questions like “how often does he fold to our 3-bet here?” or statements like “I think we’re pretty much flipping against his range” are nothing but the signifiersfor the mathematical concept that is equity, and the different types of equities that exist mathematically as the signifieds. If we could instinctively understand the math, we wouldn’t need the language to explain the concepts.

Odds

Odds are the final piece of the jigsaw. I almost didn’t include them, until I realised that we wouldn’t be able to decide what the optimal decision was in any given situation, even if we knew our ranges and equities perfectly, unless we knew what kind of pot odds we were getting. Odds drive the profitability of our plays, because they determine the mathematical aspects that actually relate to pot sizes and bet sizes and the practicalities of each hand we play, rather than simply the hand each player holds at any one time.

If we knew the ranges of our opponents and ourselves (folding ranges, calling ranges, raising ranges, bluffing ranges, value betting ranges, perceived ranges, etc), and we knew the equities of each range against the other (preflop all-in equity, fold equity, draw equity, bluff equity, etc), then all we would need to complete the puzzle would be to know the odds we were getting (direct odds, implied odds, reverse implied odds, etc), and making a decision based on the other factors would be easy. We’d be able to play mathematically perfect poker. So in this instance, the signifiersare the shorthand ways that we calculate pot odds or try to estimate our reverse implied odds, and the signifiedsare the specific numbers that those pot odds generate.

Conclusion

So, we’ve established that these three mathematical concepts are central to all of poker theory, and that the other ideas we’ve created to help us understand them are simply linguistic ways of getting us closer to determining the math of specific situations. What does this mean? How can we use this?

Well, what it means is that we can use it to drastically simplify our thought processes, and eliminate some of the ‘white noise’ that tends to cloud the thinking of players who are looking to progress their game. Instead of thinking extensively about all kinds of esoteric ideas we half-remember from a training video we watched a month ago, we can always bring it back down to thinking about the ranges involved in the hand, the equities of those ranges, and the odds given by the pot. Every concept in poker and every decision we make is a function of those three elements, and the inner monologue that goes through our head when playing is simply our brain trying to make sense of incredibly complicated mathematical concepts.

Work on estimating and shortcutting the math where you can, because it’s important. But when language is necessary, make sure the signifiers that you use are referring to the right signifieds. If you know a villain is aggressive and it’s the final table bubble, think about how that affects his ranges, because other information is useless if you don’t know what mathematical effect it has. If you know you have a strong draw, think about how that affects your equities, and what different kinds of odds the pot is offering you. Sometimes, the best thing you can do is get back to basics.