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In poker, players construct hands of playing 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 highestranking hand winning that particular deal in most variants of poker. In some variants, the lowestranking hand can win or tie.
These hand rankings are also used in some other card games, 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 the five cards forming a consecutive series. The relative ranking of the various hand categories is based on the probability of being randomly dealt such a hand from a wellshuffled deck.
The following rules apply to the ranking of all poker hands. Under typical rules there are nine distinct rankings.
A hand typically consists of five cards. In games where more than five cards are available to each player, the best fivecard 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 ace ranks higher than the player A's queen.
and player B holds , and five cards are available to both players, the players hold equally ranking 34567 straights despite the fact that the player B'sIndividual 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 A2345 straight or straight flush. In the poker variants acetofive and acetosix lowball, the ace only plays low, and only plays high in deucetoseven 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 bringin bettor 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, 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.
, the lowestvaluedA 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 three of a kind is not necessarily immediately obvious.
is ranked the same as even though in the first hand theIf there are multiple hands of the same rank at the showdown (therefore no kicker(s), or kickers have equal ranks), 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 (5permutations)^{[Note 1]} of being dealt five cards from a 52card deck, but since the order of cards does not matter, there are 5! = 120 5permutations given in any one hand, so there are only 2,598,960 () possible combinations in fivecard poker. Similarly, in sevencard poker there are 133,784,560 () combinations.^{[Note 2]}
If the game is played without the high card by suit rule, hands that have equivalent values are considered to be the same hand, there will be 7,462 distinct hands in fivecard poker, and 4,824 distinct hands when choosing the best five in sevencard poker, like Texas hold 'em; the number of sevencard poker is fewer than of fivecard poker because some hands are impossible with seven cards (e.g. 7high).^{[1]}
A straight flush is a hand that contains five cards in sequence, all of the same suit, such as (a hand that meets the requirements of both a straight, and a flush). Two such hands are compared by their card that is ranked highest. Aces can play high or low in straights and straight flushes: is a 5high straight flush, also known as a "steel wheel".^{[2]}^{[3]}
In fivecard poker, there are 40 possible straight flushes, including the four royal flushes. The probability of being dealt a straight flush is .
In sevencard poker such as Texas hold 'em, the frequency of straight flush is 41,584 (4,324 for royal flush and 37,260 for nonroyal straight flush); the probability of straight flush is approximately 0.0311% (0.0032% for royal flush and 0.0279% for nonroyal straight flush).^{[4]}^{[Note 3]}
An acehigh straight flush such as
is known as a royal flush, and is the highestranking standard poker hand. It is usually treated as a distinct hand in video poker. There are 4 different possibilities for a royal flush: one for each suit.Four of a kind, also known as quads, is a poker hand such as Texas Hold 'em) or games with wildcards or multiple decks 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. In some countries the term Carré is used.
, that contains all four cards of one rank and any other (unmatched) card. Quads with higherranking cards defeat lowerranking ones. In communitycard games (such asIn fivecard poker, there are 624 possible hands including four of a kind, the probability of being dealt one is .
In sevencard poker, the frequency of four of a kind is 224,848, the probability of being dealt one is approximately 0.168%.^{[4]}^{[Note 3]}
A full house, also known as a full boat, is a hand such as wild card 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".
, that contains three matching cards of one rank and two matching cards of another rank. Between two full houses, the one with the higherranking three cards wins, so defeats . If two hands have the same three cards (possible inIn fivecard poker, there are 3,744 possible full houses; the probability of being dealt one is .
An explanation of the formula: there are 13 ranks (ace through king), and four of each rank (one per suit), in the standard 52card deck. Denominator: we express choosing five cards out of the 52 cards in the deck. Numerator: first we multiply the number of ways to choose one rank out of the 13, then three cards out of four of that chosen rank. Second, we choose one out of 12 remaining ranks, and choose two cards out of four from that rank.
In sevencard poker, the frequency of full house is 3,473,184, the probability of being dealt one is approximately 2.60%.^{[4]}^{[Note 3]}
A flush is a poker hand such as high card hands; the highestranking card of each is compared to determine the winner. If both hands have the same highest card, then the second highestranking 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.
, where all five cards are of the same suit, but not in sequence. Two flushes are compared as if they wereFlushes are described by their highest card, as in "queenhigh flush" to describe
. If the rank of the second card is important, it can also be included: is a "kingtenhigh flush" or just a "kingten flush", while is a "kingqueenhigh 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 noncommunal card; in a game with community cards , a player holding would have a "queenhigh flush" while a player with holds a "kinghigh flush"; both players making use of the high ace.In fivecard poker, 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 is .
In sevencard poker, the frequency of flush is 4,047,644, the probability of being dealt one is approximately 3.03%.^{[4]}^{[Note 3]}
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 "tenhigh straight" or "straight to the ten" for
.A hand such as broadway" or "royal straight"), and ranks above a kinghigh straight such as . The ace may also be played as a low card (having a value of "1") in a fivehigh 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.
is an acehigh straight (also known as "In fivecard poker, 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 is .
In sevencard poker, the frequency of straight is 6,180,020, the probability of being dealt one is approximately 4.62%.^{[4]}^{[Note 3]}
Three of a kind, also called trips or a set, is a poker hand such as Texas hold 'em 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;^{[5]} 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.^{[6]}
that contains three cards of the same rank, plus two cards which are not of this rank nor the same as each other. InA highervalued threeofakind defeats a lowervalued threeofkind, so wild cards or community cards, the kickers are compared to break the tie, so defeats .
defeats . If two hands contain three of a kind of the same value, which is possible in games withIn fivecard poker, 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 is .
In sevencard poker, the frequency of three of a kind is 6,461,620, the probability of being dealt one is approximately 4.83%.^{[4]}^{[Note 3]}
A poker hand such as kicker determines the winner, so beats .
, 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 higherranking 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, theTwo 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.In fivecard poker, there are 123,552 possible two pair hands that are not also three of a kind hands or higher hands; the probability of being dealt one is .
In sevencard poker, the frequency of two pair is 31,433,400, the probability of being dealt one is approximately 23.5%.^{[4]}^{[Note 3]}
One pair is a poker hand such as kickers) are compared in descending order to determine the winner.
, that contains two cards of one rank, plus three cards which are not of this rank nor the same as each other. Higherranking pairs defeat lowerranking pairs; if two hands have the same pair, the nonpaired cards (theIn fivecard poker, there are 1,098,240 possible one pair hands; the probability of being dealt one is .
In sevencard poker, the frequency of one pair is 58,627,800, the probability of being dealt one is approximately 43.8%. Unlike that in 5card poker, one pair hands are more frequent than "no pair" hands in 7card poker.^{[4]}^{[Note 3]}
A highcard or nopair 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 hand is the highest card. Nevertheless, they sometimes win a pot if the other players fold or even at a showdown. Two highcard hands are ranked by comparing the highestranking card. If those are equal, then the next highestranking 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", "acequeen 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 sevenhigh (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 fivecard combinations, do not contain any pairs and are neither straights nor flushes. As such, the probability of being dealt "no pair" in a fivecard deal is .
In sevencard poker, the frequency of such "no pair" is 23,294,460; the probability of being dealt one is approximately 17.4%.^{[4]}^{[Note 3]}
The use of a joker 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 with the joker representing the fifth ace. In lowball, the joker plays as the lowest card not already in the hand. In noncasino settings the joker is sometimes a full wild card.
The odds of being dealt a five of a kind (of any kind) in a fivecard 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.
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 acetofive low, deucetoseven low, acetosix low and deucetosix low. The acetofive (known as California lowball) is used in razz, in some draw poker varieties, and in deucetoseven (known as Kansas City lowball).
Fivecard draw poker is sometimes played with a stripped deck. This variant is commonly known as "seventoace" or "acetoseven" (abbreviated as A7 or 7A). It can be played by up to five players. When four or fewer players play, a normal 32card deck without jokers, with ranks ranging from seven to ace, is used. With five players, the sixes are added to make a 36card 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 seventoace fivecard draw.
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