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Nash equilibrium

Nash equilibrium is a part of the games theory; it was written by American mathematician John Nash. This theory demonstrates the optimal game "in a vacuum": when to go all-in or to call the opponents' push. It is important to understand that Nash's push/call strategy in modern poker realities is no longer the only truthful one. It is optimal only if your opponents know about this strategy and stick to it without deflections.

The optimum use of the push/fold strategy by Nash can be done only against strong and understanding players. With a minimum deflection the effectiveness of this strategy is being significantly reduced. The most profitable option of using Nash equilibrium is to adjust to the opponents and correct your own game on the basis of the opponents' ranges.

Where to use the Nash equilibrium?

The ranges of Nash equilibrium are suitable for playing in MTT, Sit & Go and Spin & Go tournaments. You should apply this strategy when your stack is being reduced to 15 big blinds or lower and your game is come down to only push/fold decisions. In order to master your game skills, you should use special software that simulates such situations as: SNGWizard and ICMIZER.

Suppose your opponent goes all-in and you have 14 big blinds left. According to Nash equilibrium, you can call with a wide range of hands, having 20 BB, including pocket triples, QJ, QT and even K2s.

But it is a range "in a vacuum", which doesn't take into account the type of tournament, the stage and the difference in payouts. This strategy is mathematically correct but only if the game consists of two pre-flop decisions: push or fold. In modern realities strong players can play a deep post-flop hand even with a stack of 15 big blinds.

Besides the use of Nash equilibrium you can always just wait for a good hand and call the opponent. But if you don't know exactly what hand is good in reference to the size of your stack, Nash charts can help you to orient.

Push range by Nash

Nash equilibrium

Call range by Nash

Nash's ranges

Green color - an effective stack from 15 to 20 big blinds.

Yellow and dark-yellow color - an effective stack from 6 to 14 big blinds

Red color - an effective stack from 1 to 5 big blinds.

Usage of Nash equilibrium in the game will suit the novice players as it will provide an initial understanding of the push or call ranges for standard tournament situations and will help players to start earning money with poker fast enough.