Let me show and explain to you how I usually come up with my ranges. I will introduce the necessary theory and apply it in future articles.

The basis of almost all of my turbo tournament ranges are mostly the Poker Nash Equilibrium. I take that equilibrium and than decide how much tighter than the Poker Nash Equilibrium I want to play based on my opponents strategies. This article uses a lot of math-language and might not be the easiest to read – I challenge you to read it till the end and think about it!

### Nash Equilibrium

The Nash Equilibrium comes from game theory. The Nash Equilibrium strategy is the strategy that guarantees a certain result in your game regardless of what your opponents strategy is!

A lot of board and card games are zero sum games which means if both play optimally nobody wins in the long run. This optimal strategy is called the Nash Equilibrium. You could also look at the Nash Equilibrium strategy from a different light in zero sum games: You are guaranteed to at least break even regardless of what your opponents do.

### Nash Equilibrium and Tournament Poker – Poker Nash Equilibrium

Lets look at tournament poker. There is a Nash Equilibrium strategy for tournament poker. I will call it the Poker Nash Equilibrium strategy. If you play the Poker Nash Equilibrium strategy you are guaranteed to at least break even regardless of what your opponents do. This is assuming there was no rake. If you play the Poker Nash Equilibrium strategy in a tournament with rake, you are guaranteed to lose no more than the rake on average.

### Poker Nash Equilibrium – The crux

There is only one problem with all of this: It is close to impossible to find the exact Poker Nash Equilibrium strategy for games with many possible strategies. You are left with trying to find a near optimal solution. This alone is still really hard because the possibilities of a games as complex as poker are vast. What usually ends up happening is that you are left with looking at simplified game and try learn and apply your knowledge to the original game.

The second problem is that humans are humans after all. Its close to impossible to memorize a complex system. All you can do is try and memorize some rule of thumbs.

### Poker Nash Equilibrium – Applied to Turbo Tournaments

After all this bad news finally some good ones: As soon as you eliminate all options in a poker game except for push or fold, the game gets simplified a lot. This condition is very often true in a turbo tournament. There are near optimal solutions for turbo tournaments where people only push fold. A great resource can be found at HoldemResources.net. They have a great Poker Nash Equilibrium calculator. I will go into more detail in the near future of how to use it.

### Profit and Poker Nash Equilibrium

The natural question that arises at this point: Break even is all nice and good, but will I actually make profit? I am glad you asked – You will actually make profit playing a Poker Nash Equilibrium strategy in general, because in many cases your opponent plays a strategy that has certain parts that are dominated by the Poker Nash Equilibrium strategy.

A dominated strategy is a strategy that is acting irrational – that means there is a better strategy for the situation. Human opponents tend to play irrational and chose those dominated strategies in many situations, especially if the game is as complex as poker.

### Max Profit and Poker Nash Equilibrium

The next question you should ask yourself: But how do I maximize my profit? Great question, you are thinking along! If you look at what the Poker Nash Equilibrium does, it is minimizing your potential losses, but for the most part you are probably concerned with maximizing profit. Maximizing profits will vastly depend on your opponents strategy, there is no single general Max Profit strategy. We have to find it based on our opponents strategies.

### Finding the Max Profit Strategy

The way I go about finding the Max Profit strategy is that I start out with the Poker Nash Equilibrium strategy. I than change parts of that strategy based on my opponents tendencies to maximize my profit.

This approach will result in a strategy that is rather close to the Poker Nash Equilibrium strategy while exploiting my opponents strategy mistakes.

### Summary

- The Poker Nash Equilibrium strategy is a strategy that guarantees you to at least break even regardless of our opponents strategy.
- We deviate from the Poker Nash Equilibrium to exploit our opponents strategies and try to approach the Max Profit Strategy.

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