List of poker hands
Encyclopedia
In poker
, players construct hands of five cards according to predetermined rules, which vary according to which variant of poker is being played. These hands are compared using a hand ranking system that is standard across all variants of poker, the player with the highest-ranking hand winning that particular deal in most variants of poker. In some variants, the lowest-ranking hand can win or tie.
Although used primarily in poker, these hand rankings are also used in some other card game
s, and in poker dice
.
The ranking of a particular hand is increased by including multiple cards of the same card rank, by all five cards being from the same suit
, or by all five cards being of consecutive rank. The relative ranking of the various hand categories is based on the probability
of being randomly dealt such a hand from a well-shuffle
d deck.
A hand always consists of five cards. In games where more than five cards are available to each player, the best five-card combination of those cards must be played. Any cards not included in the hand do not affect its ranking. For example, if player A holds and player B holds , and five cards are available to both players, the players hold equally ranking 3-4-5-6-7 straights despite the fact that the player B's ace ranks higher than the player A's queen.
Individual cards are ranked A (highest), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 (lowest). Aces can appear low (as if having a value of "1") when part of an A-2-3-4-5 straight or straight flush. In the poker variants ace-to-five and ace-to-six lowball, the ace only plays low, and only plays high in deuce-to-seven lowball. Individual card ranks are used to rank hands that are in the same rank category.
The suits
of the cards are used to determine whether a hand forms a flush or straight flush. In most variants, suits do not have an associated value, and play no part in determining the ranking of a hand. Sometimes a ranking called high card by suit is used for randomly selecting a player to deal. Low card by suit usually determines the bring-in better in stud games
.
Hands are ranked first by category, then by individual card ranks; even the lowest hand that qualifies in a certain category defeats all hands in all lower categories. For example, , the lowest-valued two pair hand, defeats all hands with just one pair or high card (such as ). Only between two hands in the same category are card ranks used to break ties.
A poker hand has the same hand ranking regardless of the order in which it is arranged by the deal, by a description, or by a picture. So a hand arranged as is ranked the same as even though in the first hand the three of a kind is not immediately obvious.
If there are multiple hands of the same rank at the showdown, the pot is divided equally between the winning players. If the divided number creates fractions (odd chip), the first hand clockwise from the button/dealer gets the chip.
There are 311 875 200 ways (5-permutation
s) of being dealt five cards from a 52-card deck,In general, the number of k-permutation
s taken from a set of n is
,
which in this case gives
but since the order of cards does not matter, there are 5! = 120 5-permutations giving any one hand, so there are only:
possible distinct hands.
, such as (a hand that meets the requirement of both a straight and a flush). Two such hands are compared by their card that is ranked highest. Aces can play low in straights and straight flushes: is a 5-high straight flush, also known as a "steel wheel". An ace-high straight flush such as is known as a royal flush, and is the highest ranking standard poker hand.
There are 40 possible straight flushes, including the four royal flushes. The probability of being dealt one in a five-card dealNote that the probabilities will vary slightly in games where the player can select from more than five cards (such as Texas Hold'em and Omaha), as the player is able to select the best possible hand from the cards available. is
.
) or games with wildcards it is possible for two or more players to obtain the same quad; in this instance, the unmatched card acts as a kicker, so defeats . If two hands have the same kicker, they tie and the pot is split.
There are 624 possible hands including four of a kind; the probability of being dealt one in a five-card deal is
and community card games
), the hand with the higher pair wins, so defeats . Full houses are described as "Three full of Pair" or occasionally "Three over Pair"; could be described as "Queens full of nines", "Queens over nines", or simply "Queens full".
There are 3,744 possible full houses; the probability of being dealt one in a five-card hand is
.
Flushes are described by their highest card, as in "queen-high flush" to describe . If the rank of the second card is important, it can also be included: is a "king-ten-high flush" or just a "king-ten flush", while is a "king-queen-high flush". In community card games the highest card in the flush may be a community card which is used by multiple players, in which case the flush may be described by the highest non-communal card; in a game with community cards , a player holding would have a "queen-high flush" while a player with holds a "king-high flush"; both players making use of the high ace.
There are 5,148 possible flushes, of which 40 are also straight flushes; the probability of being dealt a flush that is not also a straight flush, in a five-card hand is
.
Straights are described by their highest card, as in "ten-high straight" or "straight to the ten" for .
A hand such as is an ace-high straight (also known as Broadway or Royal straight), and ranks above a king-high straight such as . The ace may also be played as a low card (having a value of "1") in a five-high straight such as , which is colloquially known as a wheel. The ace may not "wrap around", or play both high and low; is not a straight.
There are 10,240 possible straights, of which 40 are also straight flushes; the probability of being dealt a straight that is not also a straight flush, in a five-card deal is
.
and other flop games, three of a kind is called a "set" usually when it is composed of a pocket pair and one card of matching rank on the board; It is called "trips" usually when it is made by one card that player has in the hole with two matching cards on the board.
Higher-valued three of a kind defeat lower-valued three of a kind, so defeats . If two hands contain three of a kind of the same value, which is possible in games with wild cards
or community cards, the kicker
s are compared to break the tie, so defeats .
There are 54,912 possible three of a kind hands that are not also full houses or four of a kind; the probability of being dealt one in a five-card deal is
.
determines the winner, so beats . Finally, if both hands have the same two pair and same kicker, the pot is split.
Two pair are described by the higher pair first, followed by the lower pair if necessary; is described as "Kings over nines", "Kings and nines", or simply "Kings up" if the nines are not important.
There are 123,552 possible two pair hands that are not also full houses; the probability of being dealt one in a five-card deal is
.
s) are compared in descending order to determine the winner.
There are 1,098,240 possible one pair hands; the probability of being dealt one in a five-card deal is
.
High card hands are described by the one or two highest cards in the hand, such as "king high", "ace-queen high", or by as many cards as are necessary to break a tie. They are also referred to as "nothing", "garbage", and other derogatory terms.
The lowest possible high card is seven-high (such as ), because a hand such as would be a straight, and in the ace would serve as the high card.
Of the 2,598,960 possible hands, 1,302,540 do not contain any pairs and are neither straights nor flushes. As such, the probability of being dealt "no pair" in a five-card deal is
.
as a bug
creates a variation to game play. When a joker is introduced, it most commonly functions as a fifth ace, unless it can be used to complete a flush or straight. Some casino
draw poker
variants use a joker, and thus the best possible hand is five of a kind aces, or J with the joker representing the fifth ace. In lowball, the joker plays as the lowest card not already in the hand. In non-casino settings the joker is sometimes a full wild card
.
The odds of being dealt a five of a kind (of any kind) in a five-card deal is ~0.0005%, three times less likely than a straight flush. The odds of being dealt five of a kind aces is ~0.0000348%—one in every 2,869,685 deals.
, in some draw poker
varieties, and in deuce-to-seven (known as Kansas City lowball).
poker is sometimes played with a stripped deck
. This variant is commonly known as "seven-to-ace" or "ace-to-seven" (abbreviated as A-7 or 7-A). It can be played by up to five players. When four or fewer players play, a normal 32-card deck without jokers, with ranks ranging from ace to seven, is used. With five players, the sixes are added to make a 36-card deck. The deck thus contains only eight or nine different card ranks, compared to 13 in a standard deck. This affects the probabilities of making specific hands, so a flush ranks above a full house and below four of a kind
in the seven-to-ace five-card draw.
Poker
Poker is a family of card games that share betting rules and usually hand rankings. Poker games differ in how the cards are dealt, how hands may be formed, whether the high or low hand wins the pot in a showdown , limits on bet sizes, and how many rounds of betting are allowed.In most modern poker...
, players construct hands of five cards according to predetermined rules, which vary according to which variant of poker is being played. These hands are compared using a hand ranking system that is standard across all variants of poker, the player with the highest-ranking hand winning that particular deal in most variants of poker. In some variants, the lowest-ranking hand can win or tie.
Although used primarily in poker, these hand rankings are also used in some other card game
Card game
A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games...
s, and in poker dice
Poker dice
Poker dice are dice which, instead of having number pips, have representations of playing cards upon them. Poker dice have six sides, one each of an Ace, King, Queen, Jack, ten and nine, and are used to form a poker hand....
.
The ranking of a particular hand is increased by including multiple cards of the same card rank, by all five cards being from the same suit
Suit (cards)
In playing cards, a suit is one of several categories into which the cards of a deck are divided. Most often, each card bears one of several symbols showing to which suit it belongs; the suit may alternatively or in addition be indicated by the color printed on the card...
, or by all five cards being of consecutive rank. The relative ranking of the various hand categories is based on the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of being randomly dealt such a hand from a well-shuffle
Shuffle
Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome.-Shuffling techniques:...
d deck.
General rules
The following rules apply to the ranking of all poker hands. Under typical rules there are 7,462 distinct ranks.A hand always consists of five cards. In games where more than five cards are available to each player, the best five-card combination of those cards must be played. Any cards not included in the hand do not affect its ranking. For example, if player A holds and player B holds , and five cards are available to both players, the players hold equally ranking 3-4-5-6-7 straights despite the fact that the player B's ace ranks higher than the player A's queen.
Individual cards are ranked A (highest), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 (lowest). Aces can appear low (as if having a value of "1") when part of an A-2-3-4-5 straight or straight flush. In the poker variants ace-to-five and ace-to-six lowball, the ace only plays low, and only plays high in deuce-to-seven lowball. Individual card ranks are used to rank hands that are in the same rank category.
The suits
Suit (cards)
In playing cards, a suit is one of several categories into which the cards of a deck are divided. Most often, each card bears one of several symbols showing to which suit it belongs; the suit may alternatively or in addition be indicated by the color printed on the card...
of the cards are used to determine whether a hand forms a flush or straight flush. In most variants, suits do not have an associated value, and play no part in determining the ranking of a hand. Sometimes a ranking called high card by suit is used for randomly selecting a player to deal. Low card by suit usually determines the bring-in better in stud games
Stud poker
Stud poker is any of a number of poker variants in which each player receives a mix of face-down and face-up cards dealt in multiple betting rounds. Stud games are also typically non-positional games, meaning that the player who bets first on each round may change from round to round...
.
Hands are ranked first by category, then by individual card ranks; even the lowest hand that qualifies in a certain category defeats all hands in all lower categories. For example, , the lowest-valued two pair hand, defeats all hands with just one pair or high card (such as ). Only between two hands in the same category are card ranks used to break ties.
A poker hand has the same hand ranking regardless of the order in which it is arranged by the deal, by a description, or by a picture. So a hand arranged as is ranked the same as even though in the first hand the three of a kind is not immediately obvious.
If there are multiple hands of the same rank at the showdown, the pot is divided equally between the winning players. If the divided number creates fractions (odd chip), the first hand clockwise from the button/dealer gets the chip.
There are 311 875 200 ways (5-permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
s) of being dealt five cards from a 52-card deck,In general, the number of k-permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
s taken from a set of n is
,which in this case gives
but since the order of cards does not matter, there are 5! = 120 5-permutations giving any one hand, so there are only:
possible distinct hands.Straight flush
A straight flush is a hand that contains five cards in sequence, all of the same suitSuit (cards)
In playing cards, a suit is one of several categories into which the cards of a deck are divided. Most often, each card bears one of several symbols showing to which suit it belongs; the suit may alternatively or in addition be indicated by the color printed on the card...
, such as (a hand that meets the requirement of both a straight and a flush). Two such hands are compared by their card that is ranked highest. Aces can play low in straights and straight flushes: is a 5-high straight flush, also known as a "steel wheel". An ace-high straight flush such as is known as a royal flush, and is the highest ranking standard poker hand.
There are 40 possible straight flushes, including the four royal flushes. The probability of being dealt one in a five-card dealNote that the probabilities will vary slightly in games where the player can select from more than five cards (such as Texas Hold'em and Omaha), as the player is able to select the best possible hand from the cards available. is
.Four of a kind
Four of a kind, also known as quads, is a poker hand such as , that contains all four cards of one rank and any other (unmatched) card. Quads with higher ranking cards defeat lower ranking ones. In community-card games (such as Texas Hold 'emTexas hold 'em
Texas Hold 'em is a variation of the standard card game of poker. The game consists of two cards being dealt face down to each player and then five community cards being placed face-up by the dealer—a series of three then two additional single cards , with...
) or games with wildcards it is possible for two or more players to obtain the same quad; in this instance, the unmatched card acts as a kicker, so defeats . If two hands have the same kicker, they tie and the pot is split.
There are 624 possible hands including four of a kind; the probability of being dealt one in a five-card deal is
Full house
A full house, also known as a full boat, is a hand such as , that contains three matching cards of one rank and two matching cards of another rank. Between two full houses, the one with the higher ranking three cards wins, so defeats . If two hands have the same three cards (possible in wild cardWild card (poker)
Card games, particularly poker games, may contain one or more cards designated as wild. These may be jokers, or they may be normal ranked and suited cards pressed into wild card duty . In most cases, the wild card or cards must be agreed upon by all players before the cards are dealt and play...
and community card games
Community card poker
Community card poker refers to any game of poker that uses community cards , which are cards dealt face up in the center of the table and shared by all players. In these games, each player is dealt privately an incomplete hand , which are then combined with the community cards to make a complete...
), the hand with the higher pair wins, so defeats . Full houses are described as "Three full of Pair" or occasionally "Three over Pair"; could be described as "Queens full of nines", "Queens over nines", or simply "Queens full".
There are 3,744 possible full houses; the probability of being dealt one in a five-card hand is
.Flush
A flush is a poker hand such as , where all five cards are of the same suit, but not in sequence. Two flushes are compared as if they were high card hands; the highest ranking card of each is compared to determine the winner. If both hands have the same highest card, then the second-highest ranking card is compared, and so on until a difference is found. If the two flushes contain the same five ranks of cards, they are tied and split the pot, that is, suits are not used to rank them.Flushes are described by their highest card, as in "queen-high flush" to describe . If the rank of the second card is important, it can also be included: is a "king-ten-high flush" or just a "king-ten flush", while is a "king-queen-high flush". In community card games the highest card in the flush may be a community card which is used by multiple players, in which case the flush may be described by the highest non-communal card; in a game with community cards , a player holding would have a "queen-high flush" while a player with holds a "king-high flush"; both players making use of the high ace.
There are 5,148 possible flushes, of which 40 are also straight flushes; the probability of being dealt a flush that is not also a straight flush, in a five-card hand is
.Straight
A straight is a poker hand such as , that contains five cards of sequential rank in at least two different suits. Two straights are ranked by comparing the highest card of each. Two straights with the same high card are of equal value, suits are not used to separate them.Straights are described by their highest card, as in "ten-high straight" or "straight to the ten" for .
A hand such as is an ace-high straight (also known as Broadway or Royal straight), and ranks above a king-high straight such as . The ace may also be played as a low card (having a value of "1") in a five-high straight such as , which is colloquially known as a wheel. The ace may not "wrap around", or play both high and low; is not a straight.
There are 10,240 possible straights, of which 40 are also straight flushes; the probability of being dealt a straight that is not also a straight flush, in a five-card deal is
.Three of a kind
Three of a kind, also called trips or a set, is a poker hand such as that contains three cards of the same rank, plus two cards which are not of this rank nor the same as each other. In Texas hold 'emTexas hold 'em
Texas Hold 'em is a variation of the standard card game of poker. The game consists of two cards being dealt face down to each player and then five community cards being placed face-up by the dealer—a series of three then two additional single cards , with...
and other flop games, three of a kind is called a "set" usually when it is composed of a pocket pair and one card of matching rank on the board; It is called "trips" usually when it is made by one card that player has in the hole with two matching cards on the board.
Higher-valued three of a kind defeat lower-valued three of a kind, so defeats . If two hands contain three of a kind of the same value, which is possible in games with wild cards
Wild card (poker)
Card games, particularly poker games, may contain one or more cards designated as wild. These may be jokers, or they may be normal ranked and suited cards pressed into wild card duty . In most cases, the wild card or cards must be agreed upon by all players before the cards are dealt and play...
or community cards, the kicker
Kicker (poker)
A kicker, also called a side card, is a card in a poker hand that does not itself take part in determining the rank of the hand, but that may be used to break ties between hands of the same rank. For example, the hand Q-Q-10-5-2 is ranked as a pair of queens. The 10, 5, and 2 are kickers...
s are compared to break the tie, so defeats .
There are 54,912 possible three of a kind hands that are not also full houses or four of a kind; the probability of being dealt one in a five-card deal is
. Two pair
A poker hand such as , that contains two cards of the same rank, plus two cards of another rank (that match each other but not the first pair), plus any card not of either rank, is called two pair. To rank two hands both containing two pair, the higher ranking pair of each is first compared, and the higher pair wins (so defeats ). If both hands have the same top pair, then the second pair of each is compared, such that defeats . If both hands have the same two pairs, the kickerKicker (poker)
A kicker, also called a side card, is a card in a poker hand that does not itself take part in determining the rank of the hand, but that may be used to break ties between hands of the same rank. For example, the hand Q-Q-10-5-2 is ranked as a pair of queens. The 10, 5, and 2 are kickers...
determines the winner, so beats . Finally, if both hands have the same two pair and same kicker, the pot is split.
Two pair are described by the higher pair first, followed by the lower pair if necessary; is described as "Kings over nines", "Kings and nines", or simply "Kings up" if the nines are not important.
There are 123,552 possible two pair hands that are not also full houses; the probability of being dealt one in a five-card deal is
.One pair
One pair is a poker hand such as , that contains two cards of one rank, plus three cards which are not of this rank nor the same as each other. Higher ranking pairs defeat lower ranking pairs; if two hands have the same pair, the non-paired cards (the kickerKicker (poker)
A kicker, also called a side card, is a card in a poker hand that does not itself take part in determining the rank of the hand, but that may be used to break ties between hands of the same rank. For example, the hand Q-Q-10-5-2 is ranked as a pair of queens. The 10, 5, and 2 are kickers...
s) are compared in descending order to determine the winner.
There are 1,098,240 possible one pair hands; the probability of being dealt one in a five-card deal is
.High card
A high-card or no-pair hand is a poker hand such as , made of any five cards not meeting any of the above requirements. Essentially, no hand is made, and the only thing of any potential meaning in the player's hand is their highest card. Nevertheless, they sometimes win a pot if the other players fold or even at a showdown. Two high-card hands are ranked by comparing the highest ranking card. If those are equal, then the next highest ranking card from each hand is compared, and so on until a difference is found.High card hands are described by the one or two highest cards in the hand, such as "king high", "ace-queen high", or by as many cards as are necessary to break a tie. They are also referred to as "nothing", "garbage", and other derogatory terms.
The lowest possible high card is seven-high (such as ), because a hand such as would be a straight, and in the ace would serve as the high card.
Of the 2,598,960 possible hands, 1,302,540 do not contain any pairs and are neither straights nor flushes. As such, the probability of being dealt "no pair" in a five-card deal is
.Decks using a wild card or bug
The use of a jokerJoker (playing card)
Joker is a special type of playing card found in most modern decks, or else a type of tile in some Mahjong game sets.-Name:It is believed that the term "Joker" comes from a mispronunciation of Jucker, the German/Alsatian name for the game Euchre. The card was originally introduced in about 1860 for...
as a bug
Bug (poker)
A bug in poker is a limited form of wild card. One or both jokers are often added to the deck and played as bugs.In draw poker played for high and pai gow poker, the bug is considered to be an ace, unless it can be used as a missing card to complete a straight or a flush, in which case it becomes...
creates a variation to game play. When a joker is introduced, it most commonly functions as a fifth ace, unless it can be used to complete a flush or straight. Some casino
Casino
In modern English, a casino is a facility which houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships or other tourist attractions...
draw poker
Draw poker
Draw poker is any poker variant in which each player is dealt a complete hand before the first betting round, and then develops the hand for later rounds by replacing, or "drawing", cards....
variants use a joker, and thus the best possible hand is five of a kind aces, or J with the joker representing the fifth ace. In lowball, the joker plays as the lowest card not already in the hand. In non-casino settings the joker is sometimes a full wild card
Wild card (poker)
Card games, particularly poker games, may contain one or more cards designated as wild. These may be jokers, or they may be normal ranked and suited cards pressed into wild card duty . In most cases, the wild card or cards must be agreed upon by all players before the cards are dealt and play...
.
The odds of being dealt a five of a kind (of any kind) in a five-card deal is ~0.0005%, three times less likely than a straight flush. The odds of being dealt five of a kind aces is ~0.0000348%—one in every 2,869,685 deals.
Lowball
Some variants of poker called lowball or low poker are played with the standard hand rankings described here, but with the objective reversed: players strive not for the highest ranking of the above hands but for the lowest ranking hand. There are several methods of ranking low hands, including ace-to-five low, deuce-to-seven low, ace-to-six low and deuce-to-six low. The ace-to-five (known as California lowball) is used in razzRazz (poker)
Razz is a form of stud poker that is normally played for ace-to-five low . The object of Razz is to make the lowest possible five-card hand from the seven cards you are dealt. In Razz, straights and flushes do not count against the player for low, and the ace usually plays low...
, in some draw poker
Draw poker
Draw poker is any poker variant in which each player is dealt a complete hand before the first betting round, and then develops the hand for later rounds by replacing, or "drawing", cards....
varieties, and in deuce-to-seven (known as Kansas City lowball).
Stripped deck variant
Five-card drawFive-card draw
Five-card draw is a poker variant that is the simplest and often the first variant learned by most players. It is common in home games but rare in casino and tournament play...
poker is sometimes played with a stripped deck
Stripped deck
A stripped deck is a set of playing cards from which some cards have been removed. The removed cards are usually in the range from 2 to 9. The standard Anglo-French suited deck of 52 cards itself can be regarded as a stripped tarot deck from which the 21 numbered trumps, the fool and the 4 mounted...
. This variant is commonly known as "seven-to-ace" or "ace-to-seven" (abbreviated as A-7 or 7-A). It can be played by up to five players. When four or fewer players play, a normal 32-card deck without jokers, with ranks ranging from ace to seven, is used. With five players, the sixes are added to make a 36-card deck. The deck thus contains only eight or nine different card ranks, compared to 13 in a standard deck. This affects the probabilities of making specific hands, so a flush ranks above a full house and below four of a kind
Four of a Kind
Four of a Kind is the debut feature film for director Fiona Cochrane. It was completed in 2008 and released in 2009.It is based on the stage play Disclosure by Helen Collins as presented at La Mama Theatre during the 2006 Melbourne Fringe Festival. It was shot on location in Melbourne,...
in the seven-to-ace five-card draw.
See also
- Glossary of poker termsGlossary of poker termsThe following is a glossary of poker terms used in the card game of poker. It supplements the Glossary of card terms. Besides the terms listed here, there are thousands of common and uncommon poker slang terms...
- List of poker hand nicknames
- Non standard poker hands
- Poker probabilityPoker probabilityIn poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.-Frequency of 5-card poker hands:...
– various probability calculations on poker hands
External links
- Printable chart of poker hand rankings (.pdf format)