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.
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.
Like this post? Receive free tips and articles from QTipPoker.