The Nash equilibrium is a key concept of the game theory. It is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy.

This equilibrium is named in honor of John Nash, who is pretty well-known to everybody by the movie The Beautiful Mind. But actually, John Ford Nash, during those periods when he did not suffer from schizophrenia and delusions of persecution, which were colorfully shown in the movie, developed the theory of zero-sum games. And poker is a special case of it.

What is a Nash equilibrium in poker?

First of all, we have to say that it is almost impossible to reach the Nash equilibrium in poker because the set of choices is so big than even the most modern computers are capable of handling. That's why we talk about the Nash equilibrium only in the simplest poker disciplines, such as hyper-Turbo and heads-up. To simplify the game more, we reduce the solutions ranges to the push-or-fold.

To learn the Nash equilibrium is a great starting point for beginners. You'll start to understand the typical ranges of the push-or-call and what to do in the typical spots.

This happens before you learn how to build your own ranges for every situation, relying on your game skills and reading your opponents’ ranges. That's why the Nash equilibrium calculator is a very useful tool.

To learn more, read the full article "Nash calculator and Equilibrium Ranges in poker" in our blog.