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.