# Nash Equilibrium

### From PokerAI

For any multiplayer game, a **Nash Equilibirum** is a set of strategies so that no player can increase his or her expected return by unilaterally changing his or her strategy. It is named after John Forbes Nash, who proved that equilibrium always exist in every multiplayer game. In 1994 he received the Nobel prize in economics for his work in Game Theory as a graduate student.

Nash Equilibrium and pseudo-optimal play for poker is both interest of academic research as well as is profitable approach for practical pokerbot decision-making implementation. In a field dominated by weak players, however, other techniques (exploitative play) are more profitable.

While determining a Nash Equilibrium strategy even for simple cases of heads-up limit hold-em is computationally intractable, good Nash Equilibrium approximations exist. Nash Equilibrium can also be calculated for certain poker games (variants, or game abstractions) in which the search tree is smaller than the original one, for example HeadsUp Push-Fold Equilibrium.

## See also

- Computer Player Strategy
- Alex Selby's optimal preflop holdem

## Links

- Wikipedia's Nash Equilibrium
- John F. Nash "Equilibrium points in n-person games" Proceedings of the National Academy of Sciences 36(1):48-49, 1950 [1]
- Michael Bradley Johanson, "
*Robust Strategies and Counter-Strategies: Building a Champion Level Computer Poker Player*" [2]