Today we introduce newbies with a tricky concept to understand but when you do, it is the basis of so much further study in poker.

The Nash Equilibrium is a game theory concept created by John Nash which can be applied to poker.

A Nash Equilbrium is achieved when two players have a strategy and neither player can increase their own expected payoff by changing their strategy.

The example below shows a toy game version of poker between two players where the only option is to push/call or fold. The numbers are the maximum number of big blinds for a push or call to be profitable. For example all pocket pairs can be pushed profitably for as much as 20 big blinds and most pocket pairs can be called for the same amount. 7-2 offsuit can only be pushed profitably when you are down to 1.6 big blinds or less and can only be called when you are down to 2.6.

In the example above the pusher could go all-in for 12 big blinds with Q8o and the caller could call with JTs and even if they knew what the other player’s range it would be the right move. If the caller started to only call with KQs or better then they could be exploited because they would be folding too much, and the pusher would pick up more than their fair share of chips. If the pusher started pushing as wide as Q5o then the caller would be able to exploit them by calling with their stronger overall range.

The point here is that when one of the two players deviates from the equilibrium strategy they are making the mistake. If you know your opponent understands Nash Equilibrium your only strategy would be to play it too. That would essentially force you both into a stalemate.

If your opponent does not understand Nash Equilibrium than you can deviate from that strategy. If they fold too much you can exploit this by pushing wider than Nash advocates, for example.

## The foundations for GTO

This is a very useful concept to know for two reasons. First of all, while it is a ‘toy game’ situation it is one that is close to replicated in Blind vs Blind battles. In fact some people say you can use this to determine your Button shoving ranges too by dividing the numbers above by 2 (for example a Button could shove 9 big blinds with K8o from the Button but shove as many as 18 big blinds from the Small Blind).

The broader reason for understanding this is because it is an important building block for understanding Game Theory Optimal (GTO) play vs exploitative play. A GTO approach is one which is hard to exploit and would be correct to adopt against another GTO player. When a weaker player deviates from a GTO strategy you automatically make a profit. An exploitative approach is one where you change your strategy to exploit an error in your opponent’s strategy, you potentially can win more money that way but you also leave yourself open to exploitation.

### Related Resources

#### Odds & Outs

Our regular Twitch coach LemOn36 makes this basic lesson fun and easy to follow

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