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A History of Texas No Limit Hold'em
Texas No Limit Hold'em is the most widely played poker variant in the world. No-Limit Texas Hold'em (NLHE) is played live in casinos or on the Internet via gaming platforms. A game is played with two or more players and up to ten at a single table. In a traditional game with a total of 52 cards, each player involved in a game is dealt two cards of which only he or she is aware. Once the compulsory bets have been placed, five face-up cards are gradually revealed, first three (the flop), then another (the turn) and a final one (the river). Before the flop, and then at each felling, each player can bet or speak to see the rest of the table. Then, in order to win the pot that has been made up, one must either pass his opponent or show a better hand than his opponent, i.e. the best five-card combination between his private and open cards, from a single high to a royal flush.
Although the exact date of birth of Texas Hold'em and its origin are unknown, it is estimated that it was in the town of Robstown, Texas, in the early 1900s that the game was first played. It gradually replaced closed poker (a draw game) and was popularised in the casinos of the gambling iconic city, Las Vegas, from the 1960s onwards. The World Series Of Poker Championships at Binion's Casino in 1970 finally established Texas Hold'em as a flagship game and its fame has only grown ever since. Numerous books were published to explain the rules and understand the strategy of poker, right up to the more technological content of today such as video tutorials and computer software. It was in the 2000s that the Texas NLHE reached its apogee, notably thanks to Chris Moneymaker's victory in the $10,000 Main Event of the World Series Of Poker in 2003. Qualified via an internet tournament for only $18, the amateur won the title for $2.5 million, living the dream of all lovers of this game. From 839 entrants, participation in the event skyrocketed to nearly 2,500 the following year. Before continuing to grow exponentially since.
Texas No Limit Hold'em is a strategy game with incomplete information. In order to establish an optimal strategy in Texas NLHE, several factors must be taken into account, including the position at the table, the value of the starting hand, the bets placed, but also the mathematical aspect. It is the latter that interests us with push or fold tables. While poker as a whole cannot be analysed mathematically solely through game theory and its applications, they can nevertheless prove very useful in certain specific situations
John Nash and game theory
In the 1920s, a mathematical concept emerged through various scientific articles published in Europe and then brought to light by the American mathematician John Nash Forbes: game theory. This is a field of mathematics dealing with the reasoned or unreasoned choices of individuals in interactions. This theory applies to the social sciences but also to economics, politics, international relations etc.
After the essays of the German Ernst Zermelo and the French Emile Borel, the book Theory Of Games and Economic Behavior by John von Neumann and Oskar Morgenstern in 1944 lays the foundations of game theory and details the method of solving zero-sum games. Poker is a zero-sum game because the interest of one player is strictly opposed to the interest of the other player, one winner and one loser.
It was in the 1950s that the American mathematician and economist John Forbes Nash brought to light the notion of equilibrium, now known as the "Nash equilibrium", which determines an optimal strategy, with each player having no interest in deviating from it. This is a very specific situation that requires each player to predict the opponent's choice and maximize his or her winnings accordingly. If we apply this theory to poker, an optimal strategy is applied according to the opponent's strategies and this despite the absence of crucial information, the value of the opponent's cards. All aspects of the decision are taken into account in order to establish the best possible choice simultaneously and stick to it
Jennifear's charts and their use
L'équilibre de Nash appliqué au poker permettrait donc au joueur de ne jamais être perdant et cela quelque soit la stratégie adverse. Ainsi, pas de regret en cas de défaite car l'on a joué de la meilleure manière possible, celle qui nous assure d'un profit sur le long terme. Certes, le poker, jeu à information incomplète, avec de nombreux facteurs de décision, ne relève pas d'une forme de résolution mathématique. Mais certaines hypothèses basées sur l'équilibre de Nash peuvent aider à simplifier le jeu et ainsi le rendre résoluble mathématiquement. L'application concrète de cette résolution mathématique, ce sont les tableaux de Jennifear utilisés dans notre outil de calculateur push or fold. Car si le poker se simplifie à faire tapis ou passer, alors les décisions deviennent calculables.
Fonctionnement de l'outil
Avant d'utiliser notre outil, il faut prendre connaissance de plusieurs éléments. Outre la valeur de nos cartes, et si elles sont ou non de la même couleur, notez soigneusement votre position (suis-je premier de parole, en milieu de position ou en bataille de blindes ?), le montant de l'ante par rapport à celui des blindes ou encore votre nombre total de grosses blindes. Évidemment, le calculateur ne prend en compte que les situations de push (faire tapis directement) ou de fold (passer tout de suite sa main) dans une situation de full ring avec 20 blindes ou moins, et non pas les simples relances, dans l'optique d'un jeu simplifié et automatique. Grâce à cette résolution mathématique, votre espérance de gain sur le long terme ne pourra être que positive.