Who is ‘Nash’, and why does he play so aggressively?

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Every poker player, throughout the course of their poker career, will experience a variety of what are commonly referred to as ‘A-ha moments’. Those times when you were studying a particular concept, trying to improve, struggling to get to grips with it…when all of a sudden, ding! The lightbulb appears above your head, and immediately your game jumps up a notch when you finally ‘get’ that one idea you keep hearing about online.

For me, probably my earliest ‘A-ha moment’ was the discovery that shoving all-in preflop with a wide range of hands was a perfectly viable option when short-stacked. I vividly remember playing 90-man turbo SNGs and feeling like poker was going to be easy from now on, since I had just discovered the key to success – just go all-in a lot!

Of course, things are never that simple, but you’d be surprised how sometimes the most straightforward of suggestions can actually be surprisingly profound. It’s been years since I played a 90-man turbo SNG, but it turns out that the mathematically appropriate solution to a preflop short-stacked situation is frequently the simplest answer in poker – just go all-in a lot!

The Nash equilibrium and how it works

If you’ve spent any substantial amount of time on poker forums or watching training videos, you might have heard reference to the phrase ‘Nash equilibrium’ at some point. You might have thought it sounded like a high-level concept dreamed up by someone more interested in the math of poker than the practical aspects – and you’d be exactly right.

In fact, it wasn’t dreamed up by a poker player at all. The concept is named for its creator, legendary American mathematician John Nash, who was famously portrayed by Russell Crowe in the 2001 film A Beautiful Mind. Until his death in May 2015 at the age of 86, Nash was a leading expert in game theory and decision-making logic, and was unwittingly responsible for many of the theories we now hold to be fundamental truths about the game of poker.

He proposed that for every non-cooperative skill game that exists, there must be a set of strategies in existence whereby neither player can feasibly improve their strategy in a way that allows them to benefit from a weakness on the part of the other. In other words, each player is playing perfectly, given that they know they’re playing against an opponent who is also playing perfectly. These strategies exist as an harmonious pair – they are in equilibrium.

Applying this concept to poker

It’s doubtful that John Nash had poker players in mind when he was working on these concepts back in the 1950s. In fact, the computing power necessary to perform equilibrium calculations with regard to hands of No Limit Hold’em (even if NLHE had existed back then) would not have been widely available, if at all. But nevertheless, Nash’s insights provide us with the backbone of many of our strategic poker decisions.

Let’s say we believe our opponents are playing a certain strategy. We’ll be broad and say we believe they’re playing ‘tight’. You’ve probably heard the old adage that says something like “at a tight table, play loose, but at a loose table, play tight” – so maybe we decide to play loose to exploit their tight play.

Are we absolutely certain that they’re playing as tightly as we assume? Not even close – after all, we can’t read their minds. Maybe they’re just getting bad cards. Do we expect them to change the way they play if we play looser? Maybe, maybe not. The longer it goes on, the more likely it becomes. Do we know how long it will take before they consider loosening up? No idea. Do we have a plan for how to protect ourselves in case they figure out how we’re playing? Nope.

All of a sudden, our strategy of playing loose has a lot of holes in it that these players could exploit if they knew about them. Do we simply play loose until it stops working? Well, maybe, but sometimes what we lose when it stops working is more than what we gained from doing it in the first place, invalidating the whole strategy.

The answer, of course, is moderation – a baseline strategy that forms a starting point for all our decisions, something that leaves no weaknesses in our own game while taking advantage of our opponent’s mistakes. This is the genesis of a ‘game theory optimal’ (GTO) or ‘unexploitable’ strategy, otherwise referred to as a ‘Nash equilibrium’ strategy.

What it means for us as players

You heard me refer earlier to a Nash equilibrium strategy as one designed to play against an opponent who is also playing perfectly. This is true, but it is commonly misinterpreted in poker. Many people’s response to this is, “but nobody plays perfectly!” – of course, this is true, but it’s missing the point. Nash equilibrium strategies guarantee us the ability to compete with a hypothetical perfect player, but against an imperfect player, we still benefit from their mistakes.

Let’s take the tight/loose broad analogy a step further. If we assume our opponents will eventually adapt to our loose play, and start playing looser themselves or at least folding less frequently, then a Nash equilibrium strategy would protect against this. We would not gain so much as before during the time where our opponents were playing tightly, but we would make up for that by continuing to profit during the time where they played loosely.

Many people also interpret Nash equilibrium strategies to be the same thing as playing ‘breakeven poker’ – this isn’t even slightly true. In almost every circumstance except for certain very obscure and uncommon postflop situations where one player’s range is exceedingly strong or weak, Nash equilibrium strategies guarantee you your share of the pot, no matter what. They guarantee you’ll never make a -EV decision – at least, not with your whole range. Some hands will lose you money, but you’ll make up for that with the others. If your opponent is playing anything other than their own GTO strategy, you benefit even further – the more mistakes they make, the more you win, and there’s nothing they can do about it. In fact, poker ‘bots’ playing GTO or Nash equilibrium strategies have been shown to compete toe-to-toe with some of the best (human) heads-up no-limit players on the planet.

Using it at the table

You might wonder how on earth you’re supposed to know these strategies or adhere to them in-game, but it’s easier than you might think. An early form of Nash equilibrium experimentation came in the form of ‘push-fold’ charts that were available from around 2008 onwards – these gave players an idea of what the Nash equilibrium preflop shoving ranges were from certain positions at certain stack sizes.

While many push-fold charts have since been proven to be somewhat inaccurate by the advent of commercially-available push-fold software like HoldemResources Calculator or ICMIZER, they gave tournament players an introduction to the idea that if they played a certain way, they could actually avoid needing to know much about their opponents’ playing styles at all. Nowadays, it’s simply not possible to compete at the highest level in tournament poker without a well-developed understanding of how to play a stack of twenty big blinds or less, even before you factor in potential adaptations to player dynamics or table images.

If you struggle with short-stacked poker and you’ve never done any significant work with a Nash equilibrium calculator like the ones mentioned above, I can promise you that those two things are correlated. If you’ve been working with a Nash calculator but you don’t quite ‘get it’ yet, keep at it – those really wide shoving ranges it’s telling you to use are, in fact, correct. If you consider yourself pretty good at push-fold poker already, then perhaps it’s time to take the next step and get yourself a postflop equilibrium calculator such as Simple Postflop – from there, it’ll be one ‘A-ha moment’ after another!

We should be thankful

It’s easy to assume that these things we learn about as poker players are immutable realities of the game that have always existed. This is true in a practical sense, but before John Nash’s work was applied to poker by a few intrepid theorists, none of these things were common knowledge. Nobody had any idea how to play short-stacked poker.

It took a sizeable amount of groundbreaking mathematical research for you to be able to say with certainty that that ten-seven offsuit shove you just made in a $2.50 180-man SNG was correct, so next time you hit that ‘all-in’ button, thank John Forbes Nash Jr. for making it possible.