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| {{For|nicknames of pocket cards in Texas hold 'em|List of playing-card nicknames}}
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| {{Imageframe|width=300|caption=Examples of poker hand categories in descending order|align=right|content=
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| <hr />
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| '''[[#Straight flush|Straight flush]]'''<br /><!--
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| -->{{card|club|J|60px}}{{card|club|10|60px}}{{card|club|9|60px}}{{card|club|8|60px}}{{card|club|7|60px}}
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| <hr />
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| '''[[#Four of a kind|Four of a kind]]'''<br /><!--
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| -->{{card|club|4|60px}}{{card|diamond|4|60px}}{{card|heart|4|60px}}{{card|spade|4|60px}}{{card|club|A|60px}}
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| <hr />
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| '''[[#Full house|Full house]]'''<br /><!--
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| -->{{card|spade|5|60px}}{{card|heart|5|60px}}{{card|diamond|5|60px}}{{card|spade|8|60px}}{{card|heart|8|60px}}
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| <hr />
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| '''[[#Flush|Flush]]'''<br /><!--
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| -->{{card|spade|A|60px}}{{card|spade|J|60px}}{{card|spade|10|60px}}{{card|spade|6|60px}}{{card|spade|3|60px}}
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| <hr />
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| '''[[#Straight|Straight]]'''<br /><!--
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| -->{{card|spade|9|60px}}{{card|diamond|8|60px}}{{card|spade|7|60px}}{{card|heart|6|60px}}{{card|club|5|60px}}
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| <hr />
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| '''[[#Three of a kind|Three of a kind]]'''<br /><!--
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| -->{{card|club|3|60px}}{{card|diamond|3|60px}}{{card|heart|3|60px}}{{card|spade|Q|60px}}{{card|spade|2|60px}}
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| <hr />
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| '''[[#Two pair|Two pair]]'''<br /><!--
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| -->{{card|club|K|60px}}{{card|spade|K|60px}}{{card|heart|9|60px}}{{card|diamond|9|60px}}{{card|heart|J|60px}}
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| <hr />
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| '''[[#One pair|One pair]]'''<br /><!--
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| -->{{card|diamond|2|60px}}{{card|heart|2|60px}}{{card|heart|Q|60px}}{{card|heart|7|60px}}{{card|club|6|60px}}
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| <hr />
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| '''[[#High card|High card]]'''<br /><!--
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| -->{{card|heart|A|60px}}{{card|heart|K|60px}}{{card|club|Q|60px}}{{card|heart|10|60px}}{{card|club|2|60px}}
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| <hr />
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| }}
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| 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.
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| These hand rankings are also used in some other [[card game]]s, and in [[poker dice]].
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| 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 (cards)|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 well-[[shuffle]]d [[deck (cards)|deck]].
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| ==General rules==
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| The following rules apply to the ranking of all poker hands. Under typical rules there are nine distinct rankings.
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| 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 {{cards|3s|qd}} and player B holds {{cards|3c|ac}}, and five cards {{cards|4c|5d|6d|7s|th}} 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.
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| '''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|straight]] or [[#Straight flush|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.
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| The '''[[Suit (cards)|suits]]''' of the cards are used to determine whether a hand forms a [[#Flush|flush]] or [[#Straight flush|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#Bring-in|bring-in]] bettor in [[stud poker|stud games]].
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| 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, {{cards|2d|2s|3d|3c|4s}}, the lowest-valued [[#Two pair|two pair]] hand, defeats all hands with just [[#One pair|one pair]] or [[#High card|high card]] (such as {{cards|as|ad|kd|qh|jc}}). Only between two hands in the same category are card ranks used to break ties.
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| 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 {{cards|ts|8d|td|6c|tc}} is ranked the same as {{cards|tc|td|ts|8d|6c}} even though in the first hand the [[#Three of a kind|three of a kind]] is not immediately obvious.
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| If 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.
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| There are 311,875,200 ways (5-[[permutation]]s)<ref group=Note>In general, the number of ''k''-[[permutation]]s taken from a set of ''n'' is
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| :<math>n^{\underline k} = \frac {n!}{(n-k)!}</math>,
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| which in this case gives
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| <math>
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| \frac {52!}{(52-5)!} = \frac {52!}{47!} = 52\times51\times50\times49\times48 = 311,875,200
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| </math>
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| </ref> of being dealt five cards from a 52-card deck, but since the order of cards does not matter, there are 5! = 120 5-permutations given in any one hand, so there are only 2,598,960 (<math>\begin{matrix} {52 \choose 5} \end{matrix}</math>) possible combinations in five-card poker. Similarly, in seven-card poker there are 133,784,560 (<math>\begin{matrix} {52 \choose 7} \end{matrix}</math>) combinations.<ref group=Note><math>
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| {52 \choose 5} = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!} = \frac {52 \times 51 \times 50 \times 49 \times 48} { 5 \times 4 \times 3 \times 2 \times 1} = 2{,}598{,}960
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| </math>;<br />
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| <math>
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| {52 \choose 7} = \frac{52!}{7!(52-7)!} = \frac{52!}{7!45!} = \frac {52 \times 51 \times 50 \times 49 \times 48 \times 47 \times 46} { 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 133{,}784{,}560
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| </math></ref>
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| 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 five-card poker, and 4,824 distinct hands when choosing the best five in seven-card poker, like [[Texas hold 'em]]; the number of seven-card poker is fewer than of five-card poker because some hands are impossible with seven cards (e.g. 7-high).<ref>{{cite web|url=http://www.suffecool.net/poker/7462.html |title=Five-Card Poker Hands |publisher=Suffecool.net |date= |accessdate=2014-01-19}}</ref>
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| ==Hand categories==
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| ===Straight flush===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Straight flush]] and [[Royal flush (poker)]] -->
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| {{redirect|Straight flush|the World War II bomber|Straight Flush (B-29)|NATO designation of the Soviet radar|2K12 Kub}}
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| {{Imageframe|width=250|caption=Straight flush examples|align=left|content=
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| {{card|heart|8|50px}}{{card|heart|7|50px}}{{card|heart|6|50px}}{{card|heart|5|50px}}{{card|heart|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|spade|6|50px}}{{card|spade|5|50px}}{{card|spade|4|50px}}{{card|spade|3|50px}}{{card|spade|2|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|club|J|50px}}{{card|club|10|50px}}{{card|club|9|50px}}{{card|club|8|50px}}{{card|club|7|50px}}<br /><!--
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| -->'''Ties with'''<br /><!--
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| -->{{card|diamond|J|50px}}{{card|diamond|10|50px}}{{card|diamond|9|50px}}{{card|diamond|8|50px}}{{card|diamond|7|50px}}
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| }}
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| A '''straight flush''' is a hand that contains five cards in sequence, all of the same [[Suit (cards)|suit]], such as {{cards|qc|jc|tc|9c|8c}} (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 low in '''straights''' and '''straight flushes''': {{cards|5d|4d|3d|2d|ad}} is a '''5'''-high '''straight flush''', also known as a "steel wheel".<ref>{{cite web|url=http://www.pokertips.org/glossary/w/STEEL+WHEEL|accessdate=2007-12-20|title=Glossary|publisher=PokerTips.com}}</ref><ref>{{cite web|url=http://pokerworks.com/poker-dictionary/steel-wheel.html|accessdate=2007-12-20|title=Poker dictionary|publisher=PokerWorks.com |archiveurl = http://web.archive.org/web/20071227073226/http://pokerworks.com/poker-dictionary/steel-wheel.html <!-- Bot retrieved archive --> |archivedate = 2007-12-27}}</ref>
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| In five-card poker, there are 40 possible '''straight flushes''', including the 4 '''royal flushes'''. The probability of being dealt a '''straight flush''' is <math>\frac {4\cdot 10}{2{,}598{,}960} \approx 0.0015\%</math>.
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| In seven-card poker such as Texas hold 'em, the [[frequency]] of straight flush is 41,584 (4,324 for royal flush and 37,260 for non-royal straight flush), the probability of straight flush is approximately 0.0311% (0.0032% for royal flush and 0.0279% for non-royal straight flush).<ref name="7cardprobref">{{cite web|url=http://people.math.sfu.ca/~alspach/comp20/|title=7-Card Poker Hands|date=18 January 2000|work=Brian Alspach|accessdate=24 May 2012}}</ref><ref group="Note" name="7cardprob">See also [[Poker probability#Derivation of frequencies of 7-card poker hands]] for the derivation. This can apply to [[Texas hold 'em]] and [[seven-card stud]]. Note that the probabilities vary in [[Omaha hold 'em|Omaha]], the derivation of frequencies of Omaha hands is different than of 7-card or 9-card poker hands.</ref>
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| {{clear}}
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| ====Royal flush====
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| {{Imageframe|width=250|caption=Royal flush example|align=left|content=
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| {{card|spade|A|50px}}{{card|spade|K|50px}}{{card|spade|Q|50px}}{{card|spade|J|50px}}{{card|spade|10|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|spade|8|50px}}{{card|spade|7|50px}}{{card|spade|6|50px}}{{card|spade|5|50px}}{{card|spade|4|50px}}
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| }}
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| An ace-high '''straight flush''' such as {{cards|ad|kd|qd|jd|td}} is known as a '''royal flush''', and is the highest-ranking 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.
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| {{clear}}
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| ===Four of a kind===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Four of a kind (poker)]] -->
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| {{Imageframe|width=250|caption=Four of a kind examples|align=right|content=
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| {{card|club|10|50px}}{{card|diamond|10|50px}}{{card|heart|10|50px}}{{card|spade|10|50px}}{{card|diamond|5|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|diamond|6|50px}}{{card|heart|6|50px}}{{card|spade|6|50px}}{{card|club|6|50px}}{{card|spade|K|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|club|10|50px}}{{card|diamond|10|50px}}{{card|heart|10|50px}}{{card|spade|10|50px}}{{card|club|Q|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|club|10|50px}}{{card|diamond|10|50px}}{{card|heart|10|50px}}{{card|spade|10|50px}}{{card|diamond|5|50px}}
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| }}
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| '''Four of a kind''', also known as '''quads''', is a poker hand such as {{cards|9c|9s|9d|9h|jh}}, 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 '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 {{cards|7c|7s|7d|7h|jh}} defeats {{cards|7c|7s|7d|7h|tc}}. If two hands have the same kicker, they tie and the pot is split. In some countries the term '''Carré''' is used.
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| In five-card poker, there are 624 possible hands including four of a kind, the probability of being dealt one is <math>\frac {C_{13}^1 C_{4}^4 \cdot C_{12}^1 C_{4}^1} {C_{52}^5} = \frac {13 \cdot 1 \cdot 12 \cdot 4} {2{,}598{,}960} \approx 0.024\%</math>.
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| In seven-card poker, the frequency of four of a kind is 224,848, the probability of being dealt one is approximately 0.168%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===Full house===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Full house]] -->
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| {{Redirect|Full house}}
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| {{Imageframe|width=250|caption=Full house examples|align=left|content=
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| {{card|spade|10|50px}}{{card|heart|10|50px}}{{card|diamond|10|50px}}{{card|spade|4|50px}}{{card|diamond|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|heart|9|50px}}{{card|club|9|50px}}{{card|spade|9|50px}}{{card|heart|A|50px}}{{card|club|A|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|spade|A|50px}}{{card|club|A|50px}}{{card|heart|A|50px}}{{card|diamond|4|50px}}{{card|club|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|spade|A|50px}}{{card|heart|A|50px}}{{card|diamond|A|50px}}{{card|spade|3|50px}}{{card|diamond|3|50px}}
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| }}
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| A '''full house''', also known as a '''full boat''', is a hand such as {{cards|3c|3s|3d|6c|6h|}}, 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 {{cards|7s|7h|7d|4s|4c}} defeats {{cards|6s|6h|6d|As|Ac}}. If two hands have the same three cards (possible in [[Wild card (poker)|wild card]] and [[Community card poker|community card games]]), the hand with the higher pair wins, so {{cards|5h|5d|5s|qh|qc}} defeats {{cards|5c|5d|5s|Js|jd}}. Full houses are described as "''Three'' full of ''Pair''" or occasionally "''Three'' over ''Pair''"; {{cards|qc|qd|qs|9h|9c}} could be described as "Queens full of nines", "Queens over nines", or simply "Queens full".
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| In five-card poker, there are 3,744 possible full houses; the probability of being dealt one is <math>\frac {C_{13}^1 C_4^3 \cdot C_{12}^1 C_4^2} {C_{52}^5} = \frac{13 \cdot 4 \times 12 \cdot 6}{2{,}598{,}960} \approx 0.1441 \% </math>.
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| An explanation of the formula: there are 13 [[Playing card|ranks]] (ace through king), and four of each rank (one per [[Suit (cards)|suit]]), in the standard 52-card deck. Denominator: we express choosing 5 cards out of the 52 cards in the deck. Numerator: first we multiply the number of ways to choose 1 rank out of the 13 ranks, then 3 cards out of 4 of that chosen rank. Second, we choose 1 out of 12 remaining ranks, and choose 2 cards out of 4 from that rank.
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| In seven-card poker, the frequency of full house is 3,473,184, the probability of being dealt one is approximately 2.60%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===Flush===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Flush (poker)]] -->
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| {{Imageframe|width=250|caption=Flush examples|align=right|content=
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| {{card|heart|A|50px}}{{card|heart|Q|50px}}{{card|heart|10|50px}}{{card|heart|5|50px}}{{card|heart|3|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|spade|K|50px}}{{card|spade|Q|50px}}{{card|spade|J|50px}}{{card|spade|9|50px}}{{card|spade|6|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|diamond|A|50px}}{{card|diamond|K|50px}}{{card|diamond|7|50px}}{{card|diamond|6|50px}}{{card|diamond|2|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|heart|A|50px}}{{card|heart|Q|50px}}{{card|heart|10|50px}}{{card|heart|5|50px}}{{card|heart|3|50px}}
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| }}
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| A '''flush''' is a poker hand such as {{cards|qc|tc|7c|6c|4c}}, where all five cards are of the same suit, but not in sequence. Two flushes are compared as if they were [[#High card|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.
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| Flushes are described by their highest card, as in "queen-high flush" to describe {{cards|qd|9d|7d|4d|3d}}. If the rank of the second card is important, it can also be included: {{cards|ks|ts|5s|3s|2s}} is a "king-ten-high flush" or just a "king-ten flush", while {{cards|kh|qh|9h|5h|4h}} 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 {{cards|ac|10c|6c|2c}}, a player holding {{cards|qc|jd}} would have a "queen-high flush" while a player with {{cards|kc|10s}} holds a "king-high flush"; both players making use of the high ace.
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| In five-card 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 <math>\frac {4 \cdot C_{13}^5 - 40} {C_{52}^5} = \frac {4 \cdot 1{,}287 - 40} {2{,}598{,}960} = \frac {5{,}108} {2{,}598{,}960} \approx 0.196\% </math>.
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| In seven-card poker, the frequency of flush is 4,047,644, the probability of being dealt one is approximately 3.03%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===Straight===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Straight (poker)]] -->
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| {{Imageframe|width=250|caption=Straight examples|align=left|content=
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| {{card|spade|8|50px}}{{card|spade|7|50px}}{{card|heart|6|50px}}{{card|heart|5|50px}}{{card|spade|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|diamond|6|50px}}{{card|spade|5|50px}}{{card|diamond|4|50px}}{{card|heart|3|50px}}{{card|club|2|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|spade|8|50px}}{{card|spade|7|50px}}{{card|heart|6|50px}}{{card|heart|5|50px}}{{card|spade|4|50px}}<br /><!--
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| -->'''Ties with'''<br /><!--
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| -->{{card|heart|8|50px}}{{card|diamond|7|50px}}{{card|club|6|50px}}{{card|club|5|50px}}{{card|heart|4|50px}}
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| }}
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| A '''straight''' is a poker hand such as {{cards|Qc|Js|Ts|9h|8h}}, 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.
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| Straights are described by their highest card, as in "ten-high straight" or "straight to the ten" for {{cards|tc|9d|8h|7c|6s}}.
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| A hand such as {{cards|Ac|Kc|Qd|Js|Ts}} is an ace-high straight (also known as "[[Broadway (poker)|broadway]]" or "royal straight"), and ranks above a king-high straight such as {{cards|kh|qs|jh|th|9c}}. The ace may also be played as a low card (having a value of "1") in a five-high straight such as {{cards|5s|4d|3d|2s|Ah}}, which is colloquially known as a "[[Wheel (poker)|wheel]]". The ace may not "wrap around", or play both high and low; {{cards|3s|2d|ah|ks|qc}} is not a straight.
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| In five-card 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 <math>\frac {10 \cdot 4^5 - 40} {2{,}598{,}960} = \frac {10{,}200} {2{,}598{,}960} \approx 0.39\% </math>.
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| In seven-card poker, the frequency of straight is 6,180,020, the probability of being dealt one is approximately 4.62%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===Three of a kind===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Three of a kind (poker)]] -->
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| {{redirect|Three of a kind|other uses|Three of a Kind (disambiguation)}}{{Imageframe|width=250|caption=Three of a kind examples|align=right|content=
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| {{card|spade|Q|50px}}{{card|club|Q|50px}}{{card|diamond|Q|50px}}{{card|spade|5|50px}}{{card|club|3|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|club|5|50px}}{{card|heart|5|50px}}{{card|diamond|5|50px}}{{card|diamond|Q|50px}}{{card|club|10|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|club|8|50px}}{{card|heart|8|50px}}{{card|diamond|8|50px}}{{card|club|A|50px}}{{card|diamond|2|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|spade|8|50px}}{{card|heart|8|50px}}{{card|diamond|8|50px}}{{card|spade|5|50px}}{{card|club|3|50px}}
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| }}
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| '''Three of a kind''', also called '''trips''' or a '''set''', is a poker hand such as {{cards|2d|2s|2c|ks|6h}} 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 'em]] and other flop games, three of a kind is called a "set" usually when it is composed of a [[Glossary of poker terms#pocket pair|pocket pair]] and one card of matching rank on the [[Glossary of poker terms#board|board]];<ref>{{cite book|first=David|last=Sklansky|title=Small Stakes Hold 'Em|edition=1|page=127}}</ref> It is called "trips" usually when it is made by one card that player has in the [[List of poker terms#hole cards|hole]] with two matching cards on the board.<ref>{{cite web|url=http://poker.about.com/od/pokerglossary/g/Trips.htm|title=Trips Poker Term -- Definition of the Poker Term Trips|publisher=About.com|accessdate=13 September 2011}}</ref>
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| A higher-valued three-of-a-kind defeats a lower-valued three-of-kind, so {{cards|qs|qh|qd|7s|4c}} defeats {{cards|js|jc|jd|ad|kc}}. If two hands contain three of a kind of the same value, which is possible in games with [[Wild card (poker)|wild cards]] or [[community card]]s, the [[Kicker (poker)|kicker]]s are compared to break the tie, so {{cards|4d|4c|4s|9d|2c}} defeats {{cards|4d|4c|4s|8c|7d}}.
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| In five-card 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 <math>\frac {C_{13}^1 C_4^3 \cdot C_{12}^2 C_4^1 C_4^1} {C_{52}^5} = \frac {13 \cdot 4 \cdot 66 \cdot 4 \cdot 4} {2{,}598{,}960} = \frac {54{,}912} {2{,}598{,}960} \approx 2.11\% </math>.
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| In seven-card poker, the frequency of three of a kind is 6,461,620, the probability of being dealt one is approximately 4.83%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===Two pair===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[Two pair]] -->
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| {{Imageframe|width=250|caption=Two pairs examples|align=left|content=
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| {{card|heart|K|50px}}{{card|diamond|K|50px}}{{card|club|2|50px}}{{card|diamond|2|50px}}{{card|heart|J|50px}}<br /><!--
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| -->'''Defeats'''<br/>{{card|diamond|J|50px}}{{card|spade|J|50px}}{{card|spade|10|50px}}{{card|club|10|50px}}{{card|spade|9|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|club|9|50px}}{{card|diamond|9|50px}}{{card|diamond|7|50px}}{{card|spade|7|50px}}{{card|heart|6|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|heart|9|50px}}{{card|spade|9|50px}}{{card|heart|5|50px}}{{card|diamond|5|50px}}{{card|club|K|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|spade|4|50px}}{{card|club|4|50px}}{{card|spade|3|50px}}{{card|heart|3|50px}}{{card|diamond|K|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|heart|4|50px}}{{card|diamond|4|50px}}{{card|diamond|3|50px}}{{card|club|3|50px}}{{card|spade|10|50px}}
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| }}
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| A poker hand such as {{cards|jh|jc|4c|4s|9h}}, 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 {{cards|ts|tc|8h|8c|4s}} defeats {{cards|8h|8c|4s|4c|10s}}). If both hands have the same top pair, then the second pair of each is compared, such that {{cards|ts|tc|8h|8c|4s}} defeats {{cards|ts|tc|4s|4h|8h}}. If both hands have the same two pairs, the [[Kicker (poker)|kicker]] determines the winner, so {{cards|ts|tc|8h|8c|ad}} beats {{cards|ts|tc|8h|8c|4s}}.
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| Two pair are described by the higher pair first, followed by the lower pair if necessary; {{cards|kc|kd|9s|9h|5h}} is described as "Kings over nines", "Kings and nines", or simply "Kings up" if the nines are not important.
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| In five-card 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 <math>\frac {C_{13}^2 C_4^2 C_4^2 \cdot C_{11}^1 C_{4}^1} {C_{52}^5} = \frac {78 \cdot 6 \cdot 6 \cdot 11 \cdot 4} {2{,}598{,}960} = \frac {123{,}552} {2{,}598{,}960} \approx 4.75\% </math>.
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| In seven-card poker, the frequency of two pair is 31,433,400, the probability of being dealt one is approximately 23.5%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===One pair===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[One pair]] -->
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| {{Imageframe|width=250|caption=One pair examples|align=right|content=
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| {{card|club|10|50px}}{{card|spade|10|50px}}{{card|spade|6|50px}}{{card|heart|4|50px}}{{card|heart|2|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|heart|9|50px}}{{card|club|9|50px}}{{card|heart|A|50px}}{{card|diamond|Q|50px}}{{card|diamond|10|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|diamond|2|50px}}{{card|heart|2|50px}}{{card|spade|8|50px}}{{card|club|5|50px}}{{card|club|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|club|2|50px}}{{card|spade|2|50px}}{{card|club|8|50px}}{{card|heart|5|50px}}{{card|heart|3|50px}}
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| }}
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| '''One pair''' is a poker hand such as {{cards|4h|4s|ks|td|5s}}, 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 [[kicker (poker)|kicker]]s) are compared in descending order to determine the winner.
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| In five-card poker, there are 1,098,240 possible one pair hands; the probability of being dealt one is <math>\frac {C_{13}^1 C_4^2 \cdot (C_{12}^3 \cdot 4^3)} {C_{52}^5} = \frac {13 \cdot 6 \cdot (220 \cdot 64)} {2{,}598{,}960} = \frac {1{,}098{,}240} {2{,}598{,}960} \approx 42.26\% </math>.
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| In seven-card poker, the frequency of one pair is 58,627,800, the probability of being dealt one is approximately 43.8%. Unlike that in 5-card poker, one pair hands are more frequent than "no pair" hands in 7-card poker.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ===High card===<!-- This section is linked from lots of articles, don't change the name. Shortcut: [[High card]] -->
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| {{Imageframe|width=250|caption=High card examples|align=left|content=
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| {{card|diamond|A|50px}}{{card|diamond|10|50px}}{{card|spade|9|50px}}{{card|club|5|50px}}{{card|club|4|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|club|K|50px}}{{card|diamond|Q|50px}}{{card|club|J|50px}}{{card|heart|8|50px}}{{card|heart|7|50px}}
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| <hr style="margin-top:0.7em;" /><hr style="margin-bottom:0.7em;" />
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| {{card|club|A|50px}}{{card|club|Q|50px}}{{card|diamond|7|50px}}{{card|heart|5|50px}}{{card|club|2|50px}}<br /><!--
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| -->'''Defeats'''<br /><!--
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| -->{{card|diamond|A|50px}}{{card|diamond|10|50px}}{{card|spade|9|50px}}{{card|club|5|50px}}{{card|club|4|50px}}
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| }}
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| A '''high-card''' or '''no-pair''' hand is a poker hand such as {{cards|kh|jh|8c|7d|4s}}, 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 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.
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| 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.
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| The lowest possible high card is seven-high (such as {{cards|7s|5c|4d|3d|2c}}), because a hand such as {{cards|6d|5c|4s|3d|2h}} would be a straight, and in {{cards|6d|4s|3d|2c|ah}} the ace would serve as the high card.
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| Of the 2,598,960 possible five-card combinations, <math>(C^5_{13} - 10)(4^5 - 4)=1{,}302{,}540</math> 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 <math>\frac {1{,}302{,}540} {2{,}598{,}960} \approx 50.11\%</math>.
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| In seven-card poker, the frequency of such "no pair" is 23,294,460; the probability of being dealt one is approximately 17.4%.<ref name="7cardprobref" /><ref group="Note" name="7cardprob" />
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| {{clear}}
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| ==Variations==
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| ===Decks using a wild card or bug===
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| The use of a [[Joker (playing card)|joker]] as a [[bug (poker)|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 {{cards|ah|ad|ac|as|jkr}} 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 (poker)|wild card]].
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| 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.
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| ===Lowball===
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| {{main|Lowball (poker)}}
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| 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 [[razz (poker)|razz]], in some [[draw poker]] varieties, and in deuce-to-seven (known as Kansas City lowball).
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| ===Stripped deck variant===
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| [[Five-card draw]] 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 seven to ace, 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.
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| ==See also==
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| {{Portal|Sports and games}}
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| *[[Glossary of poker terms]]
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| *[[List of poker hand nicknames]]
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| *[[Non-standard poker hand]]
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| *[[Poker probability]] – various probability calculations on poker hands
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| == Notes ==
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| {{reflist|group=Note}}
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| == References ==
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| {{reflist}}
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| {{refbegin}}
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| * {{cite book |title=The Poker Encyclopedia
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| |first1=Elkan |last1=Allan |first2=Hannah |last2=Mackay
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| |publisher=Anova |year=2007 <!-- 18 October -->|isbn=1-906032-09-2 }}
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| * {{cite book
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| | title = The Poker Player's Bible
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| | first = Lou
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| | last = Krieger
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| | publisher = Struik
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| | year = 2006
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| | isbn = 978-1-77007-469-9
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| | page = 249
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| }}
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| * {{cite book
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| | title = The Rules of Neighborhood Poker According to Hoyle
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| | first = Stewart
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| | last = Wolpin
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| | publisher = New Chapter Press
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| | year = 1990
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| | isbn = 978-0-942257-19-9
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| | page = 335
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| }}
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| {{refend}}
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| ==External links==
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| {{commonscat|Poker hands}}
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| *[[commons:Image:PokerHandRankings.pdf|Printable chart of poker hand rankings]] ([[.pdf]] format)
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| {{Featured list}}
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| {{Poker}}
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| [[Category:Poker hands|*]]
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