Nash Equilibrium

Also known as: Nash, equilibrium strategy, Nash EQ

A strategy profile where no player can improve their EV by unilaterally changing strategy — the formal basis of GTO.

A Nash Equilibrium is a set of strategies — one per player — where each player's strategy is a best response to the others, so no player can raise their EV by deviating alone. This is the formal definition underneath GTO: a GTO strategy is one half of a Nash Equilibrium pair.

Poker is a zero-sum game (one player's win is another's loss, minus rake), and for heads-up zero-sum games the equilibrium has a strong property: every equilibrium strategy guarantees at least the game value regardless of what the opponent does. That's why a GTO strategy is unexploitable.

The equilibrium is built from indifference: at a well-constructed equilibrium, players are made indifferent between their options at key decision points, which is exactly why mixed strategies appear — a player only randomises when several actions share the same EV.

Multi-way pots (3+ players) are messier: multiple equilibria can exist and they're not guaranteed to be unexploitable the way heads-up equilibria are. This is why solvers are most trusted in heads-up range vs range spots, and why multi-way solver output is treated as a guideline, not gospel.