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The fundamental theorem of poker is a principle first articulated by David Sklansky [1] that he believes expresses the essential nature of poker as a game of decision-making in the face of incomplete information.
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
The fundamental theorem is stated in common language, but its formulation is based on mathematical reasoning. Each decision that is made in poker can be analyzed in terms of the expected value of the payoff of a decision. The correct decision to make in a given situation is the decision that has the largest expected value. If a player could see all of their opponents' cards, they would always be able to calculate the correct decision with mathematical certainty, and the less they deviate from these correct decisions, the better their expected long-term results. This is certainly true heads-up, but Morton's theorem, in which an opponent's correct decision can benefit a player, may apply in multi-way pots.
Suppose Bob is playing limit Texas hold 'em and is dealt 9♣ 9♠ under the gun before the flop. He calls, and everyone else folds to Carol in the big blind who checks. The flop comes A♣ K♦ 10♦, and Carol bets.
Bob now has a decision to make based upon incomplete information. In this particular circumstance, the correct decision is almost certainly to fold. There are too many turn and river cards that could kill his hand. Even if Carol does not have an A or a K, there are 3 cards to a straight and 2 cards to a flush on the flop, and she could easily be on a straight or flush draw. Bob is essentially drawing to 2 outs (another 9), and even if he catches one of these outs, his set may not hold up.
However, suppose Bob knew (with 100% certainty) that Carol held 8♦ 7♦. In this case, it would be correct to raise. Even though Carol would still be getting the correct pot odds to call, the best decision for Bob is to raise. Therefore, by folding (or even calling), Bob has played his hand differently from the way he would have played it if he could see his opponent's cards, and so by the fundamental theorem of poker, his opponent has gained. Bob has made a "mistake", in the sense that he has played differently from the way he would have played if he knew Carol held 8♦ 7♦, even though this "mistake" is almost certainly the best decision given the incomplete information available to him.
This example also illustrates that one of the most important goals in poker is to induce the opponents to make mistakes. In this particular hand, Carol has practiced deception by employing a semi-bluff — she has bet a hand, hoping Bob will fold, but she still has outs even if he calls or raises. Carol has induced Bob to make a mistake.
The Fundamental Theorem of Poker applies to all heads-up decisions, but it does not apply to all multi-way decisions. This is because each opponent of a player can make an incorrect decision, but the "collective decision" of all the opponents works against the player.
This type of situation occurs mostly in games with multi-way pots, when a player has a strong hand, but several opponents are chasing with draws or other weaker hands. Also, a good example is a player with a deep stack making a play that favors a short-stacked opponent because he can extract more expected value from the other deep-stacked opponents. Such a situation is sometimes referred to as implicit collusion.
The fundamental theorem of poker is simply expressed and appears axiomatic, yet its proper application to the countless varieties of circumstances that a poker player may face requires a great deal of knowledge, skill, and experience.
In poker, the strength of a hand is often called its value; however, in the context of poker strategy the term is more often used to describe a betting tactic, a bet for value. This bet is intended to increase the size of the pot, by inducing opponents to call. A bet for value is in contrast to a bluff or a protection bet.
In a poker game with more than one betting round, an out is any unseen card that, if drawn, will improve a player's hand to one that is likely to win. Knowing the number of outs a player has is an important part of poker strategy. For example, in draw poker, a hand with four diamonds has nine outs to make a flush: there are 13 diamonds in the deck, and four of them have been seen. If a player has two small pairs, and he believes that it will be necessary for him to make a full house to win, then he has four outs: the two remaining cards of each rank that he holds.
In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call. Pot odds are compared to the odds of winning a hand with a future card in order to estimate the call's expected value. The purpose of this is to statistically guide a player's decision between the options of call or fold. Raising is an alternative to place this decision on the opponent.
Position in poker refers to the order in which players are seated around the table and the related poker strategy implications. Players who act first are in "early position"; players who act later are in "late position"; players who act in between are in "middle position". A player "has position" on opponents acting before him and is "out of position" to opponents acting after him. Because players act in clockwise order, a player "has position" on opponents seated to his right, except when the opponent has the button and certain cases in the first betting round of games with blinds.
Omaha hold 'em is a community card poker game similar to Texas hold 'em, where each player is dealt four cards and must make their best hand using exactly two of them, plus exactly three of the five community cards. The exact origin of the game is unknown, but casino executive Robert Turner first brought Omaha into a casino setting when he introduced the game to Bill Boyd, who offered it as a game at the Las Vegas Golden Nugget Casino. Omaha uses a 52-card French deck. Omaha hold 'em 8-or-better is the "O" game featured in H.O.R.S.E.
In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the phrase "calling somebody's bluff" is often used outside the context of poker to describe situations where one person demands that another proves a claim, or proves that they are not being deceptive.
Five-card stud is the earliest form of the card game stud poker, originating during the American Civil War, but is less commonly played today than many other more popular poker games. It is still a popular game in parts of the world, especially in Finland where a specific variant of five-card stud called Sökö is played. The word sökö is also used for checking in Finland.
Seven-card stud, also known as Seven-Toed Pete or Down-The-River, is a variant of stud poker. Before the 2000s surge of popularity of Texas hold 'em, seven-card stud was one of the most widely played poker variants in home games across the United States and in casinos in the eastern part of the country. Although seven-card stud is not as common in casinos today, it is still played online. The game is commonly played with two to eight players, however, eight may require special rules for the last cards dealt if no players fold. Playing with nine players is possible.
Texas hold 'em is one of the most popular variants of the card game of poker. Two cards, known as hole cards, are dealt face down to each player, and then five community cards are dealt face up in three stages. The stages consist of a series of three cards, later an additional single card, and a final card. Each player seeks the best five-card poker hand from any combination of the seven cards: the five community cards and their two hole cards. Players have betting options to check, call, raise, or fold. Rounds of betting take place before the flop is dealt and after each subsequent deal. The player who has the best hand and has not folded by the end of all betting rounds wins all of the money bet for the hand, known as the pot. In certain situations, a "split pot" or "tie" can occur when two players have hands of equivalent value. This is also called "chop the pot". Texas hold 'em is also the H game featured in HORSE and HOSE.
Slow playing is a deceptive play in poker where a player bets weakly or passively with a strong holding. It is the opposite of fast playing. A flat call can be a form of slow playing. The objective of slow playing is to lure opponents into a pot who might fold to a raise, or to cause them to bet more strongly than they would if the player had played aggressively. Slow playing sacrifices protection against hands that may improve and risks losing the pot-building value of a bet if the opponent also checks.
Morton's theorem is a poker principle articulated by Andy Morton in a Usenet poker newsgroup. It states that in multi-way pots, a player's expectation may be maximized by an opponent making a correct decision.
In community card poker, a player or hand is said to be counterfeited when a community card does not change the value of their hand, but makes it more likely that an opponent will beat it. This occurs primarily in Omaha hold 'em Hi-Lo split and sometimes in Texas hold 'em. Counterfeiting also occurs in the Badugi variant of draw poker.
Badugi is a draw poker variant similar to triple draw, with hand-values similar to lowball. The betting structure and overall play of the game is identical to a standard poker game using blinds, but, unlike traditional poker which involves a minimum of five cards, players' hands contain only four cards at any one time. During each of three drawing rounds, players can trade zero to four cards from their hands for new ones from the deck, in an attempt to form the best badugi hand and win the pot. Badugi is often a gambling game, with the object being to win money in the form of pots. The winner of the pot is the person with the best badugi hand at the conclusion of play. Badugi is played in cardrooms around the world, as well as online, in rooms such as PokerStars. Although it hasn’t had its own tournament per se at the WSOP, it is featured in the Dealers Choice events as well as in the Triple Draw Mix. The 2023 WSOP event does have a Badugi tournament scheduled.
Danny Nguyen is a poker dealer and poker player from San Jose, California.
Fold equity is a concept in poker strategy that is especially important when a player becomes short-stacked in a no limit tournament. It is the equity a player can expect to gain due to the opponent folding to his or her bets. It equates to:
Dario Minieri is an Italian professional poker player from Rome, Italy who won a bracelet at the 2008 World Series of Poker at the age of 23, is a member of team PokerStars, is an online poker player who was the first person to collect enough Frequent Player Points to buy an automobile with them, and is a three-time European Poker Tour final tablist.
The following is a glossary of poker terms used in the card game of poker. It supplements the glossary of card game terms. Besides the terms listed here, there are thousands of common and uncommon poker slang terms. This is not intended to be a formal dictionary; precise usage details and multiple closely related senses are omitted here in favor of concise treatment of the basics.
Poker is a popular card game that combines elements of chance and strategy. There are various styles of poker, all of which share an objective of presenting the least probable or highest-scoring hand. A poker hand is usually a configuration of five cards depending on the variant, either held entirely by a player or drawn partly from a number of shared, community cards. Players bet on their hands in a number of rounds as cards are drawn, employing various mathematical and intuitive strategies in an attempt to better opponents.
Gleek is an English card game for three people. It is played with a 44-card pack and was popular from the 16th century through the 18th century.