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In poker, players form sets of five playing cards, called hands, according to the rules of the game.[1] Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot.[2] In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. In low games, like 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.[3][4]

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. Individual cards are ranked, from highest to lowest: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2.[5] However, aces have the highest rank under ace-to-five high or six-to-ace low rules, or under high rules as part of a five-high straight or straight flush.[6][7] Suits are not ranked, so hands that differ by suit alone are of equal rank.[8]

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 cards. The fewer hands a category contains, the higher its rank.[9] There are 52 ! ( 52 鈭?5 ) ! = 311,875,200 {\displaystyle {\begin{matrix}{\frac {52!}{(52-5)!}}=311{,}875{,}200\end{matrix}}} ways to deal five cards from the deck but only 52 ! ( 52 鈭?5 ) ! 5 ! = 2,598,960 {\displaystyle {\begin{matrix}{\frac {52!}{(52-5)!5!}}=2{,}598{,}960\end{matrix}}} distinct hands, because the order in which cards are dealt or arranged in a hand does not matter.[10] Moreover, since hands differing only by suit are of equal rank, there are only 7,462 distinct hand ranks.[11]

Hand-ranking categories [ edit ]

* Only possible when using one or more wild cards ** Category does not exist under ace-to-five low rules

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If a player can expect, given probability to make more money than he or she bets, the action is said to have a positive expectation (+EV). Conversely if a bet or a call will, according to probability, likely result in less money being returned the action is said to be negative (-EV).

Poker/Expected value - Wikibooks, open books for an open world

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