The Application of Nash Equilibrium to Poker
Poker is a game of calculated risk and reward, which in part comes from luck of the draw and part comes from skill in reading the situation of play and responding accordingly using some reactionary strategy. Poker is a game of applied mathematics and probability though, and using game theory a theoretical ideal version of the game can be assumed and the optimal strategy for each player can be calculated using a strategy matrix and discovering a Nash Equilibrium. The concept of a Nash Equilibrium in a complex game like poker might appear far fetch, but it is possible, under the correct assumptions and idealized conditions, to determine a Nash Equilibrium for any game with a finite number of players who have a finite number of strategies. A Nash Equilibrium can only occur though when players are all playing at their optimal ability and are not making any errors, which would compromise the structure. It is possible to calculate a matrix, which exposes a Nash Equilibrium that optimizes game play for all players involved and if the strategies under Nash Equilibrium are deviated from it would result in a worsened outcome for all players.
In reading the above, a lot of conditionals may be noticed as using a Nash Equilibrium in poker can only be done in highly idealized cases and the actual application of such a form of game play, though beneficial to those involved and would seem like cheating the system, is impossible in the real world where nothing is ever truly up to ideal standards. Still this application of a Nash Equilibrium exposes interesting concepts about the game of poker as less of a risky gamble and more of a controllable and readable game, which shows much more importance for the use of a solid strategy when playing. This does not mean that this theory of game play for poker goes without its benefits. ICMIZER, the second link listed below, offers a generator, which given the appropriate desired inputs, calculates a strategy matrix based of a game of poker and shows the better strategies to be used by a player, based of what their opponent is doing. This software offers the ability for beginners to poker to analyze what their best move would be based of their players and they can start to form a better understanding of what strategy should be used when, until they are able to fully understand these decisions on their own. This software obviously comes with its limitations as it is based of certain assumptions it chooses to make and can have variable outcomes based of different factors in each game played.
Sources:
https://www.pokerstars.com/en/blog/team_pokerstars_blogs/ivan_demidov/2014/poker-and-the-nash-equilibrium-151970.shtml?no_redirect=1
http://www.icmpoker.com/en/blog/nash-calculator-and-nash-equilibrium-strategy-in-poker/