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The Princess of Poker

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On my quest to improve my heads-up play I inevitably stumbled across a little something called the "Nash Equilibrium." After going through my past hand history with Chillipops, I discovered some spots that I was  missing when short stacked and so the Nash Push/Fold charts were a good place to start. Using these charts has also given me a better understanding about adjusting ranges in different positions. So in this blog post I am going to explore the concept of Nash Equilibrium as well as  remembering such a beautiful mind, John Nash himself! 

 

Who Was John Nash?


John Nash (1928-2015) was an American mathematician who contributed significantly in game theory and economics. In the poker world he is best known for the Nash Equilibrium, whilst in the maths world he is known for various theorems and functions such as the Nash-Moser theorem. His amazing life story was captured in the film, "A Beautiful Mind." His contributions earned him the Nobel Memorial Prize in Economics (1994).

 

What is the Nash Equilibrium & How does it apply in Poker?


The Nash Equilibrium is a strategy in game theory involving the following principles:

1. Each player is making the best possible decision taking into account the opponent's decisions.

2. No player can gain an advantage by changing their strategy.

 

An example from Wikipedia can illustrate this further:

"Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged."

 

In poker this concept can be applied in the following situations:


1. Heads up
2. Push/Fold (with less than 20BBs)


Since I have been using the  Nash Equilibrium Push/Fold charts I have gained a better understanding about where I have been playing too tight with a short stack heads-up and therefore missing spots. I've found these useful also for helping me to think about ranges and position.
 

When finding out more about this concept, I've read that there are some limitations such as not every opponent will be playing optimally, and that it's use can be applied in specific situations. However, after using the charts to improve my game and understanding, overall I think it is a good place to start for anyone who may be missing spots when short stacked, heads up, and in push/fold mode! 

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