RangeSharp
RangeSharp
Game theory optimal poker explained from scratch. Nash equilibrium, solvers, when to follow GTO, when to deviate.
You've heard people say "that's not GTO" or "I'm playing GTO here." You've seen solver output. Maybe you've run a spot yourself. But when someone asks you what GTO actually means, you're not sure. Here's the plain English version.
GTO stands for Game Theory Optimal. In poker, it usually means a strategy that's unexploitable. Your opponent cannot beat you by changing their strategy. No matter what they do, you're not giving away free EV. You're playing in a way that's mathematically balanced against a perfect opponent.
The concept comes from Nash Equilibrium, named after John Nash (the mathematician from the movie, though the real story was messier). In a Nash Equilibrium, no player can improve their outcome by unilaterally changing their strategy. Everyone is doing the best they can given what everyone else is doing. No one has an incentive to deviate.
In poker terms: if you're playing GTO, a perfect opponent cannot adjust to exploit you. They might play differently, but they won't do better. You're holding your own against the best possible adversary.
Rock-paper-scissors is the cleanest example. If you play rock every time, your opponent can play paper and crush you. If you play each exactly one-third of the time (and your opponent knows this), they can't exploit you. Paper beats rock, but you also play scissors. Scissors beats paper, but you also play rock. No matter what they choose, they're playing against a balanced mix. They can't gain an edge by picking one option.
Poker is more complex. There are thousands of decision points. Bet sizes, frequencies, hand ranges. But the idea is the same. GTO finds the balanced mix. How often do you bet? How often do you bluff? What hands do you call with? The solution is a strategy that can't be exploited. Your opponent can't say "I'll just fold more" or "I'll just call more" and print money. Your strategy is robust to whatever they do.
Poker solvers (PioSolver, GTO+, MonkerSolver, etc.) are computer programs that solve simplified poker games. You give them the rules: stack sizes, positions, action sequences. They compute the Nash Equilibrium. They output ranges and frequencies. "From this spot, raise 60% of the time, call 30%, fold 10%." Or "with this hand, bet 75% of the time, check 25%."
The math is real. The solutions are correct for the exact game you defined. The catch: real poker is messier. Solvers assume perfect play from the opponent. They assume no rake (or a fixed rake). They assume you'll always implement the strategy correctly. In practice, none of that is true. But the solutions are still useful. They're the best default when you don't know your opponent. And they're the reference point for when you do have reads.
A lot of low-stakes players say "GTO doesn't matter, my opponents are terrible." I disagree. GTO matters more when you don't know your opponents.
At low stakes, you're often playing against randoms. You have no history. No reads. No idea if they're a nit or a maniac. In that situation, what do you do? You need a default. GTO is that default. It's the strategy that doesn't assume anything about your opponent. It plays balanced. It doesn't leak. When you have no information, playing a reasonable approximation of GTO is safer than guessing.
The mistake is thinking GTO means playing robotically. It doesn't. GTO is the foundation. When you get a read (this guy never bluffs, this guy overfolds), you deviate. But you deviate from something. If you have no foundation, you're just making stuff up. GTO gives you the baseline. Reads tell you when to move away from it.
Some players hear "GTO" and picture a zombie who never adjusts. That's wrong. GTO is a starting point. It's what you do when you have no read. When you have reads, you exploit.
If your opponent folds too much to river bets, you bluff more. If they call too much, you value bet more and bluff less. If they 3-bet too often, you tighten your opens and 4-bet more. Those are deviations. They're exploitative. But they only make sense if you know what the baseline is. GTO tells you the baseline. Your reads tell you how to deviate.
The best players use both. They know GTO. They can run spots. They have a sense of what's balanced. Then they watch their opponents and adjust. GTO and exploitative play aren't opposites. GTO is the foundation. Exploitative play is the adjustment layer on top.
Solvers assume a perfect opponent. Real humans have tendencies. They overfold, overcall, underbluff. The GTO solution is optimal against someone playing GTO back. Against a human, the optimal strategy might be different. But you rarely know exactly what your opponent is doing. GTO is still the best default.
Rake changes things. Solvers often assume no rake or a simplified rake structure. In real games, rake is significant, especially at low stakes. It tightens ranges. Some spots that are profitable in a vacuum become marginal or losing after rake. Solvers give you the structure. You have to adjust for your actual game.
Implementation is hard. Even if you have the perfect solution, executing it is another matter. You have to remember ranges. You have to mix correctly. You have to do it under pressure. Most players can't. So the "GTO" they play is a rough approximation. That's fine. Rough GTO is still better than random.
"GTO means always checking." No. GTO has specific frequencies for betting and checking. Sometimes you bet. Sometimes you check. The mix depends on the spot. There's no universal "GTO says check."
"GTO means always betting small." No. Bet sizes vary by spot. Sometimes it's a pot-sized bet. Sometimes it's a third pot. The solution specifies. Don't assume small bets are always correct.
"GTO only works at high stakes." Wrong. GTO works as a default everywhere. At high stakes, opponents might exploit you if you play it badly. At low stakes, they usually won't. But the strategy is still a good baseline. You need something to do when you have no reads. GTO is that something.
"GTO and exploitative are opposites." They're not. GTO is the baseline. Exploitative is the adjustment. You need both. A player who only knows GTO can't adjust. A player who only knows exploits has nothing to adjust from.
The debate is mostly noise. Serious players use both. They study GTO to understand the structure of the game. They practice ranges so they have a solid default. Then they pay attention at the table. When they see a tendency, they deviate. The deviation only works because they know what they're deviating from.
I've met players who study only GTO and play like robots. They're easy to exploit if you notice. I've met players who "exploit" without understanding GTO. They're often exploiting the wrong thing. They think the guy who never bluffs is exploitable (true) but they don't know how much to bluff. They overbluff and lose. The sweet spot is knowing GTO and using it as a base, then adjusting when you have information.
If you're new to GTO, start with preflop. It's the simplest. Fewer decision points. Clear ranges. You can memorize BTN open, BB defense, 3-bet ranges. That gives you a foundation. You'll play better against unknowns. You'll have a baseline for when you start to get reads. Preflop is also the easiest to train. Each spot has a discrete set of hands and actions. You can drill it. Postflop has branching trees. Harder to memorize. Start where the structure is clean.
Then add postflop gradually. Run common spots. See what the solver says. You don't need to memorize everything. Just get a feel. "In this spot, I should bet about half the time." "With this hand, I should mix." The precision comes with practice. Most players never get to perfect implementation. That's fine. Rough GTO beats no GTO.
GTO isn't magic. It's a tool. It gives you a default strategy that doesn't suck. From there, you build.
There are times when GTO is the wrong reference. Against a player you've played 500 hours with, you have a detailed read. They never bluff the river. They overvalue top pair. They fold to 3-bets with everything except premiums. In that case, the GTO solution is less relevant. You should deviate significantly. Bluff less. Value bet more. 3-bet them wider. Your edge comes from exploitation, not balance.
Tournament spots are different from cash. Short stacks change the math. ICM changes the math. Solvers can run tournaments, but the inputs are more complex. Don't assume cash game GTO applies directly to a final table push-fold spot.
And sometimes the solver is wrong for your game. Rake structure, table composition, ante size. Small changes can shift the solution. Use GTO as a guide. Don't treat it as scripture.
Master your preflop ranges.