A Game Theoretical Analysis: Texas Hold Em Poker
Poker: A Game Theoretical Analysis
Mathematics HL
Mahmoud Talaat
Introduction
I have been playing Texas Hold ‘em Poker since I was 14 years old, and since then, I had a pact with my friends that we would meet every Friday night and play some Poker. Poker is a group of card games that involve betting, strategy, and individual play. One of these card games is called Texas Hold ‘em. Texas Hold ‘em Poker consists of two “hole” cards dealt to each player and five “community” cards held face-up by the dealer on the deck. The player that wins is the player that has, in a way, the most similar cards to the cards on the deck. For instance, a pair consists of two cards that have the same number, like the 6 of hearts and the 6 of diamonds, regardless …show more content…
Game theory, which is the study of strategic decision-making, is particularly useful for poker as poker involves probability. In other words, it involves the probability of a specific hand being played. Poker also involves other strategic elements, such as bluffing, which is when a player tricks another player into thinking he/she will play a specific card, usually by the use of facial expressions. Poker is naturally a zero-sum game, a game in which the sum of all gains and losses will always equal to zero. I will limit the scope of my analysis to a two-person zero-sum game, as multiple player games are too complex and a two-person zero-sum game will allow me to analyze in greater depth. Also, I will limit the amount of cards in the game to three: the king, the queen, and the jack, as that also increases the depth of my analysis. In order to make the game less complex, I will consider the highest card to be the winning card. For instance, if player 1 is dealt the king and player 2 is dealt the queen, then player 1 wins the round. The highest card is the king, followed by the queen, and finally the jack. In this essay, using game theory, I will analyze
Mathematics HL
Mahmoud Talaat
Introduction
I have been playing Texas Hold ‘em Poker since I was 14 years old, and since then, I had a pact with my friends that we would meet every Friday night and play some Poker. Poker is a group of card games that involve betting, strategy, and individual play. One of these card games is called Texas Hold ‘em. Texas Hold ‘em Poker consists of two “hole” cards dealt to each player and five “community” cards held face-up by the dealer on the deck. The player that wins is the player that has, in a way, the most similar cards to the cards on the deck. For instance, a pair consists of two cards that have the same number, like the 6 of hearts and the 6 of diamonds, regardless …show more content…
Game theory, which is the study of strategic decision-making, is particularly useful for poker as poker involves probability. In other words, it involves the probability of a specific hand being played. Poker also involves other strategic elements, such as bluffing, which is when a player tricks another player into thinking he/she will play a specific card, usually by the use of facial expressions. Poker is naturally a zero-sum game, a game in which the sum of all gains and losses will always equal to zero. I will limit the scope of my analysis to a two-person zero-sum game, as multiple player games are too complex and a two-person zero-sum game will allow me to analyze in greater depth. Also, I will limit the amount of cards in the game to three: the king, the queen, and the jack, as that also increases the depth of my analysis. In order to make the game less complex, I will consider the highest card to be the winning card. For instance, if player 1 is dealt the king and player 2 is dealt the queen, then player 1 wins the round. The highest card is the king, followed by the queen, and finally the jack. In this essay, using game theory, I will analyze