# The Nash Equilibrium

• Bronze
Joined: 19.01.2011
A little background to start, I'm a decent heads-up player, I can turn a profit from heads-up sitngos and do reasonably well in the heads up phase of tournaments when I get there. I don't play heads up cash as I haven't got the roll to deal with the variance swings entailed in heads up play when playing for stakes that make heads up worth playing.

I have only just heard of the Nash Equilibrium in an article I read elsewhere, ive never came across it before and I've never used it.

People who are familiar with it what are your thoughts on it? Just from a quick read over the article it seems too simplistic to work, and the theory only truly works if opponent is familiar with it also. In practice has anyone any experience if using it and what have you found when using it?

• Bronze
Joined: 11.05.2008
The Nash Equilibrium is really a huge topic, not only in tournament poker, but in cash game poker as well. Exploring the Nash Equilibria of situations exposes you to the game theory and mathematics behind scenes. I absolutely recommend you look into this because it opens up your eyes to an exceptional method of analysis at the very least.

A related topic is the Best Response, which is also part of the game theory of heads up short stack play, and that teaches you how to exploit your opponent, given that they make some set of mistakes (or no mistakes).

The game theoretical definition of the Nash Equilibria is that both players are playing their Best Response, and neither gains by deviating from this strategy.

I hope my game theory teaser has inspired to to lose this mentality:
Just from a quick read over the article it seems too simplistic to work, and the theory only truly works if opponent is familiar with it also.

As for the Heads-Up Nash Equilibrium Strategy, it certainly will benefit you if you know it. As you stated it greatly benefits you when you play someone else who knows it, because then you are playing the optimal counter-strategy. Even if you strictly played Nash, you guarantee yourself at least 50% equity in the tournament - strictly by definition of Nash Equilibrium. That's a pretty sweet promise.

However, if they don't know it, or you haven't established how they are playing, then you have a set of default plays, especially if your goal is to play your maximally exploitative pushing/calling range. Additionally you have a basis to deviate if your opponent is making exploitable mistakes.

Suppose you have established that your opponent is pushing tighter than Nash, then you can eliminate the weakest hands in your Nash calling range, and make what's called an exploitative fold. People who are able to do this most accurately are the best poker players. This type of analysis translates even to cash games. For example, game theory dictates that a player can bluff a certain amount on the river, and there is a Nash Equilibrium in this situation also, if you estimate that your opponent is bluffing too often in this spot than game theory suggests they should, then you can make an exploitative call and call wider than Nash suggests.

Of course, the Nash Equilibrium Strategy has it's failures too. Most importantly it does not take future game, meta-game, or skill edge into account.