List of poker hands: Difference between revisions

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For the article on the WWII B-29 of the same name, see Straight Flush.
This article is for standard poker hands only, otherwise refer to non-standard poker hand.

In poker, certain combinations of cards, or hands, outrank other hands, based on the frequency with which these combinations appear. The player with the best poker hand at the showdown wins the pot.

Although used in poker, these hand rankings are also used in a variety of other card games.

Note that with community cards, a player may refer to their set of non-communal cards as their "hand". In this article "hand" refers to the best five-card combination, consisting of both communal and non-communal cards, that a player can have according to the rules stated below. In general discussion, a "hand" may also refer to a single round of play, including a deal, one or more rounds of betting, and possibly a showdown.

General rules

The following general rules apply to evaluating poker hands, whatever set of hand values are used.

Individual cards are ranked A (high), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A. Aces only appear low when part of an A-2-3-4-5 straight or straight flush. Individual card ranks are used to compare hands that contain no pairs or other special combinations, or to compare the kickers of otherwise equal hands. The ace only plays low in ace-to-five and ace-to-six lowball games, and only plays high in deuce-to-seven lowball.
Suits have no value. The suits of the cards are mainly used in determining whether a hand fits a certain category (specifically the flush and straight flush hands). In most variants, if two players have hands that are identical except for suit, then they are tied and split the pot (so 3♠ 4♠ 5♠ 6♠ 7♠ does not beat 3♦ 4♦ 5♦ 6♦ 7♦). Sometimes a ranking called high card by suit is used for randomly selecting a player to deal.
A hand always consists of five cards. In games where more than five cards are available to each player, each player must choose some five-card subset according to the rules of the game, and comparing that five-card hand against the five-card hands of the other players. Whatever cards remain after choosing the five to be played are of no consequence in determining the winner.
Hands are ranked first by category, then by individual card ranks: even the lowest qualifying hand in a certain category defeats all hands in all lower categories. The smallest two pair hand (2♦ 2♠ 3♦ 3♣ 4♠), for example, defeats all hands with just one pair or high card. Only between two hands in the same category are card ranks used to break ties.

Standard ranking

Printable, one-page chart of poker hand rankings (associated file page)

Straight flush

Defeats

Ties with

A straight flush is a poker hand such as Q♣ J♣ 10♣ 9♣ 8♣, which contains five cards in sequence, all of the same suit. As such it is both a straight and a flush. Two such hands are compared by their highest card; since suits have no relative value, two otherwise identical straight flushes tie (so 10♣ 9♣ 8♣ 7♣ 6♣ ties with 10♥ 9♥ 8♥ 7♥ 6♥). Aces can play low in straights and straight flushes: 5♦ 4♦ 3♦ 2♦ A♦ is a 5–high straight flush, also known as a "steel wheel"^{[citation needed]}. An ace-high straight flush such as A♠ K♠ Q♠ J♠ 10♠ 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 a straight flush is ${\frac {40}{52\times 51\times 50\times 49\times 48\div 5!}}={\frac {40}{2,598,960}}\approx 0.0015\%$

Four of a kind

Defeats

Deffeats

Four of a kind, also known as quads, is a poker hand such as 9♣ 9♠ 9♦ 9♥ J♥, which contains four cards of one rank, and an unmatched card of another rank. It ranks above a full house and below a straight flush. Higher ranking quads defeat lower ranking ones. In community-card games (such as Texas Hold 'em 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 7♣ 7♠ 7♦ 7♥ J♥ defeats 7♣ 7♠ 7♦ 7♥ 10♣. There are 624 possible hands including four of a kind; the probability of being dealt one is ${\frac {624}{2,598,960}}\approx 0.024\%$ A four of a kind hand including four kings is occasionally known as a "Four Horsemen"^[1]

Full house

Defeats

A full house, also known as a full boat, is a hand such as 3♣ 3♠ 3♦ 6♣ 6♥, which contains three matching cards of one rank, and two matching cards of another rank. It ranks below a four of a kind and above a flush. Between two full houses, the one with the higher ranking set of three wins, so 7♠ 7♥ 7♦ 4♠ 4♣ defeats 4♠ 4♥ 4♦ 7♠ 7♣. If two hands have the same set of three (possible in wild card and community card games), the hand with the higher pair wins, so 5♣ 5♦ 5♠ J♠ J♦ loses to 5♥ 5♦ 5♠ Q♥ Q♣. Full houses are described as "Three full of Pair" or occasionally "Three over Pair"; Q♣ Q♦ Q♠ 9♥ 9♣ could be described as "Queens over nines", "Queens full of nines", or simply "Queens full". However, "Queens over nines" is more commonly used to describe the hand containing two pairs, one pair of queens and one pair of nines, as in Q♠ Q♥ 9♣ 9♠ J♦.

There are 3,744 possible full houses; the probability of being dealt one in a five-card hand is ${\frac {3744}{2,598,960}}\approx 0.14\%$

Flush

Defeats

A flush is a poker hand such as Q♣ 10♣ 7♣ 6♣ 4♣, which contains five cards of the same suit, not in rank sequence. It ranks above a straight and below a full house. 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 – suits are not used to differentiate them. Flushes are described by their highest card, as in "queen-high flush" to describe Q♦ 9♦ 7♦ 4♦ 3♦. If the rank of the second card is important, it can also be included: K♠ 10♠ 5♠ 3♠ 2♠ is a "king-ten-high flush" or just a "king-ten flush", while K♥ Q♥ 9♥ 5♥ 4♥ is a "king-queen-high flush".

There are 5,148 possible flushes, of which 40 are also straight flushes; the probability of being dealt a flush in a five-card hand is ${\frac {5108}{2,598,960}}\approx 0.20\%$

Straight

Defeats

Ties

A straight is a poker hand such as Q♣ J♠ 10♠ 9♥ 8♥, which contains five cards of sequential rank but in more than one suit. It ranks above three of a kind and below a flush. 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 10♣ 9♦ 8♥ 7♣ 6♠.

A hand such as A♣ K♣ Q♦ J♠ 10♠ is an ace-high straight, and ranks above a king-high straight such as K♥ Q♠ J♥ 10♥ 9♣. The ace may also be played as a low card in a five-high straight such as 5♠ 4♦ 3♦ 2♠ A♥, which is colloquially known as a wheel.^[1] The ace may not "wrap around", or play both high and low in the same hand: 3♣ 2♦ A♥ K♠ Q♣ is not a straight, but just ace-high no pair.

There are 10,240 possible straights, of which 40 are also straight flushes; the probability of being dealt a straight in a five-card hand is ${\frac {10240}{2,598,960}}\approx 0.39\%$

Three of a kind

Defeats

Three of a kind, also called trips, set or a prile (the latter from its use in three card poker^[2]), is a poker hand such as 2♦ 2♠ 2♣ K♠ 6♥, which contains three cards of the same rank, plus two unmatched cards. It ranks above two pair and below a straight. In Texas Hold 'Em, a "set" refers specifically to a three of a kind comprised of a pocket pair and one card of matching rank on the board.^[3] Higher-valued three of a kind defeat lower-valued three of a kind, so Q♠ Q♥ Q♦ 7♠ 4♣ defeats J♠ J♣ J♦ A♦ K♣. If two hands three of a kinds of the same value, possible in games with wild cards or community cards, the kickers are compared to break the tie, so 4♦ 4♣ 4♠ 8♦ 6♣ defeats 4♦ 4♣ 4♠ 6♣ 5♦.

There are 54,912 possible three of a kind hands which are not also full houses; the probability of being dealt one in a five-card hand is ${\frac {54912}{2,598,960}}\approx 2.1\%$

Two pair

Defeats

A poker hand such as J♥ J♣ 4♣ 4♠ 9♥, which contains two cards of the same rank, plus two cards of another rank (that match each other but not the first pair), plus one unmatched card, is called two pair. It ranks above one pair and below three of a kind. To rank two hands both containing two pair, the higher ranking pair of each is first compared, and the higher pair wins (so 10♠ 10♣ 8♥ 8♣ 4♠ defeats 8♥ 8♣ 4♠ 4♣ 10♠). If both hands have the same "top pair", then the second pair of each is compared, such that 10♠ 10♣ 8♥ 8♣ 4♠ defeats 10♠ 10♣ 4♠ 4♥ 8♥). Finally, if both hands have the same two pairs, the kicker determines the winner: 10♠ 10♣ 8♥ 8♣ 4♠ loses to {{10♠ 10♣ 8♥ 8♣ A♦. Two pair are described by the higher pair first, followed by the lower pair if necessary; K♣ K♦ 9♠ 9♥ 5♥ could be 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 hand is ${\frac {123552}{2,598,960}}\approx 4.75\%$

One pair

Defeats

One pair is a poker hand such as 4♥ 4♠ K♠ 10♦ 5♠, which contains two cards of the same rank, plus three other unmatched cards. It ranks above any high card hand, but below all other poker hands. Higher ranking pairs defeat lower ranking pairs; if two hands have the same pair, the non-paired cards (the kickers) 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 hand is ${\frac {1098240}{2,598,960}}\approx 42.26\%$

High card

Defeats

A high-card or no-pair hand is a poker hand such as K♥ J♣ 8♣ 7♦ 3♠, in which no two cards have the same rank, the five cards are not in sequence, and the five cards are not all the same suit. It is also referred to as "no pair", as well as "nothing", "garbage," and various other derogatory terms. High card ranks below all other poker hands; two such 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.

The lowest possible high card is seven-high (such as 7♠ 5♣ 4♦ 3♦ 2♣), because a hand such as 6♦ 5♣ 4♠ 3♦ 2♥ would be a straight.

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 hand is ${\frac {1302540}{2,598,960}}\approx 50.12\%$

Decks using a bug

The use of joker as a bug creates a slight variation of game play. When a joker is introduced in standard poker games it functions as a fifth ace, or can be used as a flush or straight card (though it can be used as a wild card too). Normally casino draw poker variants use a joker, and thus the best possible hand is five of a kind Aces, or A♥ A♦ A♣ A♠ Joker.

Probabilities of drawing hands

The hands are ranked in the order they are because of the relative probabilities of their being dealt, with rarer hands ranking above more common hands. All five-card poker hands can be collapsed down to 7,462 distinct equivalence classes. For example, there are 24 different ways to create an aces over kings full house hand, but since they all hold the same poker ranking value, they can be collapsed into the same equivalence class. In this way, all 2,598,960 unique five card poker hands can be shrunk down to just 7,462 distinct classes of hands.

Notes

^ ^a ^b "Poker hand names". PokerWords.com. Retrieved 2007-12-20.
^ "Method and apparatus for playing card games".
^ Sklansky, David. Small Stakes Hold 'Em (1 ed.). p. p127. {{cite book}}: |page= has extra text (help)

External links

Poker hand rankings (printable chart)

[pokerwords-1] "Poker hand names". PokerWords.com. Retrieved 2007-12-20.

[2] "Method and apparatus for playing card games".

[3] Sklansky, David. Small Stakes Hold 'Em (1 ed.). p. p127. {{cite book}}: |page= has extra text (help)

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 The hands are ranked in the order they are because of the relative probabilities of their being dealt, with rarer hands ranking above more common hands. All five-card poker hands can be collapsed down to 7,462 distinct [[equivalence classes]]. For example, there are 24 different ways to create an aces over kings full house hand, but since they all hold the same poker ranking value, they can be collapsed into the same equivalence class. In this way, all 2,598,960 unique five card poker hands can be shrunk down to just 7,462 distinct classes of hands.
-==Low-poker ranking==
-Some games called [[Lowball (poker)|lowball]] or '''low poker''' are played where players strive not for the highest ranking of the above combinations but for the lowest ranking hand. There are three methods of ranking low hands, called [[#Ace-to-five low|ace-to-five low]], [[#Deuce-to-seven low|deuce-to-seven low]], and [[#Ace-to-six low|ace-to-six low]].  The '''ace-to-five''' method is most common. A sub-variant within this category is '''high-low poker''', in which the highest and lowest hands split the pot (with the highest hand taking any odd chips if the pot does not divide equally).  Sometimes straights and/or flushes count in determining which hand is highest but not in determining which hand is lowest (being reckoned as a no-pair hand in the latter instance), so that a player with such a holding can win both ways and thus take the entire pot.
-===Ace-to-five===
-'''Ace-to-five low''' is the most common method for evaluating [[Low hand (poker)|low hand]]s in [[poker]], nearly universal in U.S. casinos, especially in [[high-low split]] games.
-As in all [[low hand (poker)|low hand]] games, pairs count against the player. That is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or three of a kind, etc. No-pair hands are compared starting with the highest ranking card, just as in high poker, except that the [[High hand (poker)|high hand]] loses. In ace-to-five low, [[#Straight|straights]] and [[#Flush|flushes]] are ignored, and aces play as the lowest card.
-For example, the hand '''8-5-4-3-2''' defeats '''9-7-6-4-3''', because eight-high is lower than nine-high.  The hand '''7-6-5-4-3''' defeats both, because seven-high is lower still, even though it would be a straight if played for high.  Aces are low, so '''8-5-4-3-A''' defeats '''8-5-4-3-2'''.  Also, '''A-A-9-5-3''' (a pair of aces) defeats '''2-2-5-4-3''' (a pair of deuces), but both of those would lose to any no-pair hand such as '''K-J-8-6-4'''.  In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): '''3-3-6-4-2''' defeats '''3-3-6-5-A'''.
-This is called ace-to-five low because the lowest (and therefore best) possible hand is '''5-4-3-2-A''', called a [[#Wheel|wheel]].  The next best possible hand is '''6-4-3-2-A''', followed by '''6-5-3-2-A''', '''6-5-4-2-A''', '''6-5-4-3-A''', '''6-5-4-3-2''', '''7-4-3-2-A''', '''7-5-3-2-A''', etc.
-When speaking, low hands are referred to by their highest ranking card or cards.  Any nine-high hand can be called "a nine", and is defeated by any "eight".  Two cards are frequently used: the hand '''8-6-5-4-2''' can be called "an eight-six" and will defeat "an eight-seven" such as '''8-7-5-4-A'''.
-Another common notation is calling a particular low hand "smooth" or "rough."  A smooth low hand is one where the remaining cards after the highest card are themselves very low; a rough low hand is one where the remaining cards are high.  For instance, '''8-7-6-3-A''' would be referred to as a "rough eight," but '''8-4-3-2-A''' would be referred to as a "smooth eight."
-[[High-low split]] games with ace-to-five low are usually played [[cards speak]], that is, without a [[Declaration (poker)|declaration]]. Frequently a qualifer is required for low (typically 8-high or 9-high).  Some hands (particularly small straights and flushes) may be both the low hand and the high hand, and are particularly powerful (or particularly dangerous if they are mediocre both ways).  Winning both halves of the pot in a split-pot game is called "scooping" or "hogging" the pot. The perfect hand in such a game is called a "steel wheel", '''5-4-3-2-A''' of one suit, which plays both as perfect low and a [[straight flush]] high. Note that it is possible--though unlikely--to have this hand and still lose money.  If the pot has three players, and one other player has a mixed-suit wheel, and a third has better straight flush, the higher straight flush wins the high half of the pot, and the two wheels split the low half, hence the steel wheel wins only a quarter of a three-way pot.
-Ace-to-five lowball, a five-card draw variant, is often played with a joker added to the deck.  The joker plays as the lowest card not already present in the hand (in other words, it is a [[Wild card (poker)|wild card]]): '''7-5-4-Joker-A''', for example, the joker plays as a '''2'''.  This can cause some interesting effects for high-low split games.  Let's say that Alice has '''6-5-4-3-2''' (called a "straight six")--a reasonably good hand for both high and low.  Burt has '''Joker-6-5-4-3'''.  By applying the rule for wild cards in straights, Burt's joker plays as a '''7''' for high, giving him a seven-high straight to defeat Alice's six-high straight.  For low, the joker plays as an ace--the lowest card not in Burt's hand--and his hand also defeats Alice for low, because his low hand is '''6-5-4-3-A''', lower than her straight six by one notch.  Jokers are very powerful in high-low split games.
-====Wheel====
-A '''wheel''' or '''bicycle''' is the poker hand '''5-4-3-2-A''', regardless of suit, which is a five-high [[#Straight|straight]], the lowest-ranking of the straights.
-In [[#Ace-to-five low|ace-to-five low]] poker, where aces are allowed to play as low and straights and [[#Flush|flushes]] do not count against a hand's "low" status, this is the best possible hand. In high/low split games, it is both the best possible low hand and a competitive high hand.
-The origin of the name "Wheel" probably derives from the Bicycle playing cards issued by the [[United States Playing Card Company]].
-===Ace-to-six===
-'''Ace-to-six low''' is a method for evaluating [[Low hand (poker)|low hand]]s in poker.  It is not as commonly used as the [[ace-to-five low]] method, but it is common among home games in the eastern region of the [[United States]], and also common in the [[United Kingdom]] (it is the traditional ranking of [[Razz (poker)|London lowball]], a [[stud poker]] variant).
-As in all [[Lowball (poker)|lowball]] games, pairs and trips are bad: that is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or trips, etc.  No-pair hands are compared starting with the highest ranking card, just as in high poker, except that the [[Poker jargon#high hand|high hand]] loses.  In ace-to-six low, [[Rank of hands (poker)#Straight|straight]]s and [[Rank of hands (poker)#Flush|flushes]] count for high (and are therefore bad), and aces play as the lowest card.
-For example, the hand '''8-5-4-3-2''' defeats '''9-7-6-4-3''', because eight-high is lower than nine-high.  The hand '''7-6-5-4-2''' defeats both, because seven-high is lower still.  The hand '''7-6-5-4-3''' would lose, because it is a straight.  Aces are low, so '''8-5-4-3-A''' defeats '''8-5-4-3-2'''.  Also, '''A-A-9-5-3''' (a pair of aces) defeats '''2-2-5-4-3''' (a pair of deuces), but both of those would lose to any no-pair hand such as '''K-J-8-6-4'''.  In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): '''3-3-6-4-2''' defeats '''3-3-6-5-A'''.
-It is called ace-to-six low because the best possible hand is '''6-4-3-2-A''', followed by '''6-5-3-2-A''', '''6-5-4-2-A''', '''6-5-4-3-A''', '''7-4-3-2-A''', '''7-5-3-2-A''', etc.
-When speaking, low hands are referred to by their highest ranking card or cards.  Any nine-high hand can be called "a nine", and is defeated by any "eight".  Two cards are frequently used: the hand '''8-6-5-4-2''' can be called "an eight-six" and will defeat "an eight-seven" such as '''8-7-5-4-A'''.
-A [[Wild card (poker)|wild card]] plays as whatever rank would make the lowest hand.  Thus, in '''6-5-Joker-2-A''', the joker plays as a '''3''', while in '''Joker-5-4-3-2''' it would play as a '''7''' (an ace or six would make a straight).
-[[High-low split]] games with ace-to-six low are usually played with a [[Declaration (poker)|declaration]].
-===Deuce-to-seven===
-'''Deuce-to-seven low''' is a method for evaluating [[Low hand (poker)|low hands]] in [[poker]].  It is often called "Kansas City" low or just "low poker".  It is almost the direct opposite of standard poker: [[Poker jargon#high hand|high hand]] loses.  It is not as commonly used as the [[ace-to-five low]] method.
-As in all [[Lowball (poker)|lowball]] games, pairs and trips are bad: that is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or trips, etc.  No-pair hands are compared starting with the highest ranking card, just as in high poker, except that the high hand loses.  In deuce-to-seven low, [[Rank of hands (poker)#Straight|straight]]s and [[Rank of hands (poker)#Flush|flushes]] count for high (and are therefore bad).  Aces are always high (and therefore bad).
-For example, the hand '''8-5-4-3-2''' defeats '''9-7-6-4-3''', because eight-high is lower than nine-high.  The hand '''7-6-5-4-2''' defeats both, because seven-high is lower still.  The hand '''7-6-5-4-3''' would lose, because it is a straight.  Aces are high, so '''Q-8-5-4-3''' defeats '''A-8-5-4-3'''.  In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): '''3-3-6-4-2''' defeats '''3-3-6-5-2'''.
-Since the ace always plays high, '''A-5-4-3-2''' is not considered a straight; is simply ace-high no pair (it would therefore lose to any king-high, but would defeat '''A-6-4-3-2''').
-The best possible hand is '''7-5-4-3-2''' (hence the name deuce-to-seven low), followed by '''7-6-4-3-2''', '''7-6-5-3-2''', '''7-6-5-4-2''', '''8-5-4-3-2''', '''8-6-4-3-2''', etc.
-When speaking, low hands are referred to by their highest ranking card or cards.  Any nine-high hand can be called "a nine", and is defeated by any "eight".  Two cards are frequently used: the hand '''8-6-5-4-2''' can be called "an eight-six" and will defeat "an eight-seven" such as '''8-7-5-4-2'''.
-Another common notation is calling a particular low hand "smooth" or "rough."  A smooth low hand is one where the remaining cards after the highest card are themselves very low; a rough low hand is one where the remaining cards are high.  For instance, '''8-7-6-4-2''' would be referred to as a "rough eight," but '''8-5-4-3-2''' would be referred to as a "smooth eight."
-[[Wild card (poker)|Wild card]]s are rarely used in deuce-to-seven games, but if used they play as whatever rank would make the lowest hand.  Thus, in '''7-6-Joker-3-2''', the joker plays as a '''4''', while in '''Joker-5-4-3-2''' it would play as a '''7''' (a six would make a straight, and an ace would make ace-five high).
-[[High-low split]] games with deuce-to-seven low are usually played with a [[Declaration (poker)|declaration]].
 == Notes ==

List of poker hands: Difference between revisions

Revision as of 13:31, 20 December 2007

Contents

General rules