Poker is a card game played between two or more players and won by the player with the highest hand. It has become one of the world’s most popular card games and is played in casinos, private homes, club rooms, and over the Internet. It is sometimes referred to as the national card game of the United States and its play and jargon have influenced American culture.
The game requires at least two cards per player and may involve multiple betting rounds. After the final betting round, the cards are revealed and the winning hand takes the pot. Players may also choose to discard their cards and take new ones from the deck at any time during or after the betting round. Depending on the rules of the game, replacement cards can be either face up or face down.
The game was first described by the mathematician John von Neumann, who developed a strategy based on the fact that, given the size of the pot and the number of opponents, optimal betting frequencies for both bluffs and calls depend on the ratio between the strength of your own hand and the probability that your opponent has a better one. In later work, von Neumann used this information to determine the optimal bet sizes for both bluffs and call-and-raise strategies, and to prove that no player can win by simply calling every time (or raising every time) with their best hands.