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In [[poker]], players form sets of five [[playing card]]s, called ''hands'', according to the [[List of poker variants|rules of the game]].<ref name=":10">{{Cite book|title=The Poker Player's Bible|last=Krieger|first=Lou|publisher=Struik Publishers|year=2006|isbn=978-1-77007-469-9|location=South Africa|pages=12–14|chapter=What is Poker?}}</ref> Each hand has a [[Ranking|rank]], which is compared against the ranks of other hands participating in the [[Showdown (poker)|showdown]] to decide who wins the [[Pot (poker)|pot]].<ref>{{Cite book|title=Poker for Dummies, Mini Edition|last=Harrock|first=Richard|publisher=Wiley Publishing, Inc.|year=2011|isbn=978-0-470-05565-6|location=United States of America|chapter=The Basics of Play}}</ref> In high games, like [[Texas hold 'em]] and [[seven-card stud]], the highest-ranking hands win. In [[Lowball (poker)|low]] games, like [[Razz (poker)|razz]], the lowest-ranking hands win. In [[high-low split]] games, both the highest-ranking ''and'' lowest-ranking hands win, though different rules are used to rank the high and low hands.<ref>{{Cite book|title=The Theory of Poker|last=Sklansky|first=David|publisher=Two Plus Two Publishing LLC|year=2005|isbn=1-880685-00-0|location=United States of America|pages=[https://archive.org/details/theoryofpoker00skla/page/2 2]|url=https://archive.org/details/theoryofpoker00skla/page/2}}</ref><ref name=":9" />
Each hand belongs to a category determined by the patterns formed by its cards. A hand in a higher-ranking category always ranks higher than a hand in a lower-ranking category. A hand is ranked within its category using the ranks of its cards.<ref name=":1">{{Cite web|url=https://www.pokerstars.com/poker/games/rules/hand-rankings/|title=Poker Hands Order – Poker Hand Rankings at PokerStars|website=www.pokerstars.com|access-date=12 July 2016}}</ref> Individual cards are ranked, from highest to lowest: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2.<ref name=":12">{{Cite book|title=The Poker Player's Bible|last=Krieger|first=Lou|publisher=Struik Publishers|year=2006|isbn=978-1-77007-469-9|location=South Africa|pages=30–34}}</ref> However, aces have the lowest rank under [[ace-to-five low]] or [[ace-to-six low]] rules, or under high rules as part of a five-high straight or straight flush.<ref name=":4">{{Cite book|title=The Everyday Guide to Recreational Poker|last=Greiner|first=Ron|publisher=Everyday Endeavors, LLC|year=2005|isbn=0-9769703-0-9|pages=46–60}}</ref><ref name=":8">{{Cite book|title=What I Know about Poker: Lessons in Texas Hold'em, Omaha and Other Poker Games|last=Scott|first=Alex|year=2010|isbn=978-0-9567151-3-5|pages=24|chapter=How to Play Lowball Draw}}</ref> [[Suit (cards)|Suits]] are not ranked, so hands that differ by suit alone are of equal rank.<ref name=":2">{{Cite web|url=http://www.wsop.com/poker-hands/|title=Poker Hand Ranking {{!}} Official World Series of Poker Online|website=www.wsop.com|access-date=12 July 2016}}</ref>
There are nine categories of hand when using a [[standard 52-card deck]], except under ace-to-five low rules where straights, flushes and straight flushes are not recognized. An additional category, five of a kind, exists when using one or more [[Wild card (card games)|wild cards]]. The fewer hands a category contains, the higher its rank.<ref>{{Cite web|url=http://www.math.hawaii.edu/~ramsey/Probability/PokerHands.html|title=Probability: 5-Card Poker Hands|website=www.math.hawaii.edu|access-date=12 July 2016}}</ref> There are <math>\begin{matrix}\frac{52!}{(52-5)!} = 311,875,200\end{matrix}</math> ways to deal five cards from the deck but only <math>\begin{matrix}\frac{52!}{(52-5)!5!} = 2,598,960 \end{matrix}</math> distinct hands, because the order in which cards are [[Poker dealer|dealt]] or arranged in a hand does not matter.<ref name=":3">{{Cite web|url=http://www.intmath.com/counting-probability/poker.php|title=Probability and Poker|last=Bourne|first=Murray|website=www.intmath.com|access-date=12 July 2016}}</ref> Moreover, since hands differing only by suit are of equal rank, there are only 7,462 distinct hand ''ranks''.<ref name=":7">{{Cite web|url=http://www.codethrowdown.com/5CardSingleDeckHands.txt|title=FiveCardSingleDeckHands.txt|last=Berg|first=Henry|date=13 May 2013|website=Code Throwdown|access-date=13 July 2016}}</ref><ref>{{Cite web|url=https://lee-crocker.squarespace.com/blog/2013/2/27/how-many-poker-hands-are-there|title=How many poker hands are there?|access-date=13 July 2016}}</ref>
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