A Nash equilibrium in poker is the point where every player's strategy is the best possible response to everyone else's, so no one can improve their winrate by changing how they play, even with full knowledge of their opponents' strategies. It's the game theory idea behind GTO poker, and it's what solvers try to calculate.
In practice, it describes players who are perfectly balanced against each other. Neither side has a profitable adjustment left to make.
Example of Nash Equilibrium used in a sentence -> A GTO poker solver is trying to arrive at a Nash equilibrium through iterative calculation.
Has Poker Been Solved?
No full version of No-Limit Hold'em has been solved, so a perfect Nash equilibrium strategy for the whole game isn't known. The closest case is heads-up Limit Hold'em, which researchers at the University of Alberta declared essentially solved in 2015.
Solvers get around this by calculating near-equilibrium strategies for game trees of a fixed size, using set bet sizes and stack depths. The output is a close approximation of Nash play for that spot, not the whole game.
Solver coverage also varies by game. Hold'em and PLO solvers are now widely used, while most other types of poker games have little or no solver support. The concept still applies to all of them. The tools just haven't caught up.
Does Nash Equilibrium Work in Multiway Pots?
Heads-up spots are where Nash equilibrium is best understood. Multiway pots are much harder: solvers can handle some of them, but only with heavily simplified trees, and more than one equilibrium can exist for the same spot.
With three or more players, an equilibrium strategy also stops guaranteeing that you won't lose. One opponent's mistake can shift value to another player at the table as well as to you.
Why Does Nash Equilibrium Matter to Poker Players?
Playing close to equilibrium makes you hard to exploit, but it only profits from your opponents' mistakes. To win more against weaker players, you deviate from it on purpose and target their leaks.
For worked preflop and push/fold examples, see our guide to putting Nash equilibrium theory into practice.
