The Nash Calculator, and the Nash Equilibrium strategy for poker

 The Nash Calculator, and the Nash Equilibrium strategy for poker

Definition of the Nash Equilibrium

In poker, Nash Equilibrium is when players' ranges are in equilibrium. This means that opponents play an optimal game against each other and they cannot both gain anything from straying from the equilibrium strategy. This can lead to a stalemate (long-term break-even proposition), and it is not logical for one opponent to depart from Nash if the opposing player follows Nash. If they do, this will mean that they are deviating form "optimal" strategy. The other player may gain. The other player may be able to do better if one of their ranges is off Nash. As we will see, following Nash in many situations is far from optimal.

Calculator Nash Equilibrium

How it works

The Nash calculator in ICMIZER takes the pay-out, stack size and blinds of the tournament into consideration to create optimal ranges. This allows you to see which ranges are best in each spot and what the players will do if they adopt this strategy. This program can generate the optimal ranges for every player at the table, not just the player who is active. All you need to do to calculate the Nash equilibrium is to hit the Calculate Nash Equilibrium buttons. The stacks' Nash ranges will then be assigned.

This is what makes it a great feature.

Simple results - ranges can be generated immediately by clicking a button. The feature is easy to use and very intuitive.

You would want to play with the best players and follow the Nash equilibrium push/fold strategy. Although you may not be playing the highest stakes 500$ hyper-turbo structure, it is still an advantage to have knowledge of Nash strategy. Technically, you can click a button to get the best strategy. This is what pro poker players use. This is fantastic! You won't find the postflop strategy of top SNGs regulars if you want it. They don't like sharing that information.

The suggested open Push and Overcall ranges that you'll get from the Nash calculator will work well in almost any stakes or structure. You can start using the Nash equilibrium ranges to open pushing and overcalling if you're new to ICM. Your end game will improve instantly. Calling ranges against one open push, as suggested by Nash equilibrium strategy, are unlikely to be very efficient because your opponents won't be pushing according to Nash.

Because Nash considers stack sizes relative to pay out structure (essentially ICM), it provides a solid baseline for inexperienced or new players who have difficulty putting opponents on ranges. The Nash range to push as the big stack onto the middle-stack on a bubble will typically be quite wide. This will help novice players realize that they can push far here. A tighter range is recommended to push the clear middle stack into the big stack on bubble. This will help players start to understand ICM dynamics. How to Use Your Poker Calculator as a Personal Coach