Tag Archives: GTO Poker

Why

Why Think About GTO Poker?

I received a Facebook PM from a player the other day:

“How can working on your frequencies can be better than working your hands through CardrunnerEV and making the most +EV plays based on your assumptions?”

If you’ve followed my work through the years, you know I’ve said little about GTO/Balance. I’ve always focused on pounding away on my opponents’ weakness. If there are no/little weaknesses present, I find greener pastures.

Over the last eight months, I’ve spent much time on GTO ideas, and I think this focus is surprising to many of my readers. So…a public answer to this question.

Before I start with this answer, I want to provide a caveat. I’m still in my infancy with understanding GTO and what a balanced strategy looks like. So, my answer below doesn’t come from experience; simply what makes sense to me from my current understanding of theory.

I don’t think using words like “better” is the correct way to approach this topic. In a recent rereading of The Mathematics of Poker (MOP), this sentence popped. “We are searching for strategies that are near-optimal, or at least balanced, which can be profitably played against a wide range of opposition with little or no information.” So, we ask, “Why are we searching for such a strategy?” Simply put, there are benefits to the effort that often make it worth a player’s time. Here are a handful of benefits of attempting to find “at least balanced” strategies. MOP gives several great reasons on page 101. To simply list those ideas:

• We often deal with unknown opponents
• Game selection is not an option (think tourneys)
• Good games often still have a tough opponent or two.

However, I’d like to add a couple ideas.

1. Playing a fixed strategy is less-taxing at the tables and easier to mass-produce. Finding weakness in an opponent’s strategy is hard work and can be exhausting. A fixed strategy, while perhaps making less money, is less-taxing and easier to multitable.

2. Learning about balance shines a brighter light on weaknesses. It’s not necessary to understand a balanced strategy to spot glaring holes in an opponent’s strategy. However, as opponents patch the most glaring holes, we have greater difficulty understanding how to exploit. Being familiar with a balanced strategy gives us a better idea of when opponents stray from “safe zone” and what adjustments we must make.

In the meantime, an exploitive strategy makes more money than an unexploitable strategy, and many unskilled opponents remain in the player pool.

So, I don’t think “better” belongs in this discussion. However, I do think a player who puts effort in “attempting to find near optimal or at least balanced strategies” has the advantage in the game. I think it at least develops a deeper understanding of the game and perhaps provides this player with a mode not available to others who haven’t invested the time/effort.

Having said all this, the best of the exploiters have likely already approached something resembling balance. It seems clear to me that balance looks similar to playing exploitively versus your perceived range. And we know GTO is two players maximally exploiting each other. So, these ideas are connected…again, “better” just doesn’t seem to fit.

In any case, I’ll continue to dig and let my readers know what I find.

Enjoy the game.

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Pitfalls

GTO Mental Pitfalls

GTO mental pitfalls…I’m an expert in this topic as I think I’ve fallen in every mental pitfall available on my current, unfulfilled journey to understanding this topic.

In 2007, The Mathematics of Poker was published, and I’ve been confused ever since. Recently, a wave of poker literature hit the market about game theory and unexploitable poker strategies. I’ve read these books, discussed the ideas with others, and I’m making progress in grasping concepts.

Let’s get some semantics out of the way. When players say GTO, they typically mean playing an unexploitable strategy (specifically, the most +EV unexploitable strategy). That’s how I’m using the term here. Certainly, GTO could speak of a broader umbrella of the application of math to games, but this isn’t the typical meaning these days.

Pitfall #1: Exploitive VS GTO

Players tend to think about these words as an oxymoron; pitting GTO vs. Exploitive. Turns out, these terms are married: At equilibrium, GTO is Exploitive play.

Maximally exploiting your opponent means you’ve minimized his EV and therefore maximized your EV. Playing unexploitably means no strategy can lower your EV.

Let’s use two players, Bob and Mary.

At a game’s equilibrium, Bob and Mary are playing unexploitably. Neither player can lower the other’s EV. At equilibrium, both players are maximally exploiting the opponent.

Now, let’s say Bob decides to change his strategy. Equilibrium is broken. What has happened?

1. Bob is not playing a maximally exploitive strategy.
2. Mary is still playing an unexploitable strategy.

Bob cannot minimize Mary’s EV. However, Bob is not maximizing his EV. Bob hurt himself with this adjustment.

Meanwhile, Mary is unexploitable; Bob has not and cannot reduce her EV in this game. However, Mary is neither maximizing her EV nor minimizing Bob’s EV. Mary is not exploiting Bob. However, Mary has an option. She may remain at the safer, unexploitable strategy or she may adjust her strategy to maximize her EV and minimize Bob’s EV. If Mary leaves the safety of her part of the equilibrium pair, she exposes herself to exploitation…just as Bob already did.

Pitfall #2: No Money in GTO

I could understand unexploitable play best through the game rock, paper, scissors (called Roshambo). Unfortunately, this example provided a pitfall.

In Roshambo, I may perfectly randomize my choices so I pick rock, paper, or scissors each 33.3% of the time. This is unexploitable Roshambo. My nemesis is left with no winning strategy. We break even over the long run regardless my opponent’s decisions.

Imagine Mary and Bob are playing Roshambo. They are at equilibrium, both randomizing decisions at 33.3%. Suddenly, Bob decides to play rock every time. The results do not change. Bob’s EV is still the same as when he was at equilibrium; Bob is not losing. Mary can work hard to ensure she plays unexploitably, Bob can be a monkey, and Mary gains nothing from her hard work. Certainly, Mary could change her strategy to an exploitive strategy of all paper and crush Bob.

Why would I want to create such a situation in poker!? I want to win! Why would I work so hard to ensure Bob can act like a monkey and have the same results regardless his decisions?

Turns out, while poker and Roshambo share a theoretical equilibrium, the effect of one opponent leaving the equilibrium is different in the two games. In Roshambo, only one of the equilibrium pairs need satisfied to ensure both players’ EVs are minimized and maximized. To get this effect in poker, both players must be at equilibrium.

In poker, when Bob left the equilibrium and Mary stayed, Bob lost EV and Mary gained EV. Mary works hard to stay at the unexploitable strategy, Bob plays like a monkey and Mary wins money!

Yes, Mary can win even more money by maximally exploiting Bob’s altered strategy, but she has a risk in doing so (she opens herself up to exploitation).

In summary, staying with an unexploitable strategy is a defense plan. You can’t be hurt, you’re not attempting to hurt your opponent, and you’re simply hoping they hurt themselves…and they can…and likely will.

Pitfall #3: GTO Doesn’t Apply

I often read comments in forums where players are saying GTO will not work in their games because players are so bad. If you’ve followed me to this point, you’ll know this thinking is incorrect. I’ve never been in this pitfall, but I’ve been in something similar.

All I’ve ever done in poker is work to exploit my opponent’s strategy. If I felt I couldn’t exploit well for whatever reason, I leave the game…I find a situation I feel I can exploit my opponents. With good games available, why bother working to understand GTO. There are valid reasons:

1. Better games are not available.
2. Game selection is not an option (think tournaments).
3. Your opponent is unknown.
4. Your opponent’s play is virtually random.
5. Understanding the equilibrium helps you identify exploitable strategies as well as how to exploit those strategies.

Pitfall #4: GTO is King

I’ve never been in this pitfall either, but I’ve seen others here. “Exploitive play is dead, GTO is the future of poker.”

A poker player staying at an unexploitable strategy regardless Villain’s decisions makes money when Villain is not at equilibrium. However, if your goal is to maximize your winnings, staying at the unexploitable strategy after Villain has left equilibrium will not make the most money. GTO is not king.

I’m reminded of a sentence in The Mathematics of Poker on page 47. “Virtually every player uses exploitive play in one form or another, and many players even some of the strongest players in the world, view exploitive play as the most evolved form of poker.”

Seems apparent to me exploitive poker is the most evolved form. In Bob vs. Mary, exploitive poker always produces at least the same money as the unexploitable strategy. And because the goal in poker is to win as much as possible, choosing to exploitive your opponent is always the most evolved decision.

Certainly I can imagine reasons why someone would remain at an unexploitable strategy when they have the option to exploit. And I understand arguments can be made to say one could make more money staying with an unexploitable strategy because of mental fatigue, etc.

Further Questions

Now that we’ve worked those pitfalls out, I’ve still plenty of core issues to resolve.

First, I don’t know how much money playing an unexploitable strategy produces. Say you’re playing in a 25nl game with decent opponents. If you played an unexploitable strategy, would you beat the rake? I tend to think this strategy would perform well in today’s environment, but I’m not sure.

Second, the small problem of application. ;) Poker is so complex, those on the cutting edge realize they’re dealing with approximations. How close are those approximations? What’s the impact of our best estimation’s deviations from equilibrium in typical game environments? When we do find some decent approximation, how feasible is it for a human to employ the strategy?

To me, these are huge questions. I’m more intrigued than I’ve ever been in this topic, and I’m starting to dig on my own with these ideas. In my recent research, I’ve tripped over a few more pitfalls I’ll share another time.

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