List of poker hands

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Five playing cards – the ace, king, queen, jack and ten of hearts – spread out in a fan.
An ace-high straight flush, commonly known as a royal flush, is the highest-ranking poker hand when not using wild cards.

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

Each poker hand falls into a category determined by the patterns formed by its cards.[5] Hands in a higher-ranking category always rank higher than hands in a lower-ranking category. Hands in the same category are ranked relative to each other by comparing the ranks of their respective cards.[6] Suits are not ranked in poker, so hands in the same category that differ by suit alone are of equal rank (e.g. J 8 5 3 2 has the same rank as J 8 5 3 2).[7]

Cards in poker are ranked, from highest to lowest: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2.[8] However, when forming part of an ace-to-five straight or straight flush, such as 5 4 3 2 A or 5 4 3 2 A, and in ace-to-five lowball, aces have the lowest rank.[9][10]

There are nine separate poker hand categories when using a standard 52-card deck with no wild cards. The fewer hands a category contains, the higher its rank.[1][8][11] There are 311,875,200 ways to deal five cards from the deck but only 2,598,960 distinct poker hands, because the order in which cards are dealt or arranged in a hand does not matter.[1][7][12] Moreover, since hands differing only by suit are of equal rank, there are only 7,462 distinct poker hand ranks.[13][14]

Basic poker hand categories
Rank Name Example Hands[a] Hand ranks[b] Probability[c]
1 Straight flush Jack of clubs10 of clubs9 of clubs8 of clubs7 of clubs 40 10 ~0.0015%
2 Four of a kind 6 of clubs6 of diamonds6 of hearts6 of spadesJack of diamonds 624 156 ~0.024%
3 Full house 5 of spades5 of clubs5 of diamondsKing of clubsKing of hearts 3,744 156 ~0.14%
4 Flush Jack of diamonds10 of diamonds8 of diamonds7 of diamonds2 of diamonds 5,108 1,277 ~0.20%
5 Straight King of diamondsQueen of clubsJack of spades10 of hearts9 of spades 10,200 10 ~0.39%
6 Three of a kind Ace of clubsAce of spadesAce of heartsQueen of diamonds2 of spades 54,912 858 ~2.1%
7 Two pair Queen of heartsQueen of spades8 of hearts8 of spades2 of clubs 123,552 858 ~4.8%
8 One pair 7 of spades7 of heartsKing of spades4 of clubs3 of spades 1,098,240 2,860 ~42%
9 High card Ace of diamonds10 of spades9 of hearts5 of diamonds4 of clubs 1,302,540 1,277 ~50%

Basic hand categories[edit]

Straight flush[edit]

"Straight flush" redirects here. For the World War II bomber, see Straight Flush (B-29). For the Soviet radar system, see 2K12 Kub.
Straight flush
Jack of clubs10 of clubs9 of clubs8 of clubs7 of clubs
A jack-high straight flush
Hands[a] 40
Hand ranks[b] 10
Probability[c] ~0.0015%

A straight flush is a poker hand containing five cards of sequential rank, all of the same suit, such as Q J 10 9 8 (a “queen-high straight flush”).[8] In ace-to-five lowball, straight flushes are not recognized.[10][15]

Each straight flush hand is ranked by the rank of its highest-ranking card, where aces have the lowest rank when forming part of a five-high straight flush, such as 5 4 3 2 A. For example, 10 9 8 7 6 ranks higher than 6 5 4 3 2, which ranks higher than 5 4 3 2 A. Straight flush hands that differ by suit alone, such as 7 6 5 4 3 and 7 6 5 4 3, are of equal rank. Aces may not have both a high and low rank in the same hand (e.g. 3 2 A K Q is an ace-high flush, not a straight flush).[9][16]

An ace-high straight flush, such as A K Q J 10, is commonly known as a royal flush and is the highest-ranking poker hand when not using wild cards.[8][17] A five-high straight flush, such as 5 4 3 2 A, is otherwise known as a steel wheel and is significant in ace-to-five high-low split games for being both the lowest-ranking hand and usually the highest-ranking hand of the showdown.[15]

There are 40 possible straight flush hands and 10 distinct ranks of straight flush. The probability of being dealt a straight flush from a standard 52-card deck is 1 in 64,974 (or approximately 0.0015%).[13][14]

Four of a kind[edit]

Four of a kind
6 of clubs6 of diamonds6 of hearts6 of spadesJack of diamonds
Four of a kind, sixes
Hands[a] 624
Hand ranks[b] 156
Probability[c] ~0.024%

Four of a kind, also known as quads, is a poker hand containing four cards of the same rank and one card of another rank (the kicker), such as 9 9 9 9 J ("four of a kind, nines").[8]

Each four of a kind hand is ranked first by the rank of its quadruplet, and then by the rank of its kicker. For example, K K K K 3 ranks higher than 7 7 7 7 A, which ranks higher than 7 7 7 7 10. Four of a kind hands that differ by suit alone, such as 4 4 4 4 Q and 4 4 4 4 Q, are of equal rank.[8][9][16]

There are 624 possible four of a kind hands and 156 distinct ranks of four of a kind. The probability of being dealt four of a kind from a standard 52-card deck is 1 in 4,165 (or approximately 0.024%).[13][14]

Full house[edit]

Full house
5 of spades5 of clubs5 of diamondsKing of clubsKing of hearts
A full house, fives over kings
Hands[a] 3,744
Hand ranks[b] 156
Probability[c] ~0.14%

A full house, also known as a full boat, is a poker hand containing three cards of one rank and two cards of another rank, such as 3 3 3 6 6 (a “full house, threes over sixes” or “threes full of sixes” or “threes full”).[8][18]

Each full house hand is ranked first by the rank of its triplet, and then by the rank of its pair. For example, 8 8 8 7 7 ranks higher than 4 4 4 9 9, which ranks higher than 4 4 4 5 5. Full house hands that differ by suit alone, such as K K K J J and K K K J J, are of equal rank.[9][16]

There are 3,744 possible full house hands and 156 distinct ranks of full house. The probability of being dealt a full house from a standard 52-card deck is 6 in 4,165 (or approximately 1 in 694 or 0.14%).[13][14]

Flush[edit]

Flush
Jack of diamonds10 of diamonds8 of diamonds7 of diamonds2 of diamonds
A jack-high flush
Hands[a] 5,108
Hand ranks[b] 1,277
Probability[c] ~0.20%

A flush is a poker hand containing five cards all of the same suit, not all of sequential rank, such as K 10 7 6 4 (a “king-high flush” or “king-ten-high flush”).[8][19] In ace-to-five lowball, flushes are not recognized.[10]

Each flush hand is ranked first by the rank of its highest-ranking card, then by the rank of its second highest-ranking card, then by the rank of its third highest-ranking card, then by the rank of its fourth highest-ranking card, and finally by the rank of its lowest-ranking card. For example, A J 9 6 4 ranks higher than K Q 7 6 5, which ranks higher than K 10 9 4 2, which ranks higher than K 10 8 6 3, which ranks higher than K 10 8 4 3, which ranks higher than K 10 8 4 2. Flush hands that differ by suit alone, such as Q 10 9 8 7 and Q 10 9 8 7, are of equal rank.[9][16]

There are 5,108 possible flush hands and 1,277 distinct ranks of flush. The probability of being dealt a flush from a standard 52-card deck is 1,277 in 649,740 (or approximately 1 in 509 or 0.20%).[13][14]

Straight[edit]

Straight
King of diamondsQueen of clubsJack of spades10 of hearts9 of spades
A king-high straight
Hands[a] 10,200
Hand ranks[b] 10
Probability[c] ~0.39%

A straight is a poker hand containing five cards of sequential rank, not all of the same suit, such as 7 6 5 4 3 (a “seven-high straight”).[8] In ace-to-five lowball, straights are not recognized.[8][10]

Each straight hand is ranked by the rank of its highest-ranking card, where aces have the lowest rank when forming part of a five-high straight, such as 5 4 3 2 A. For example, J 10 9 8 7 ranks higher than 10 9 8 7 6, which ranks higher than 5 4s 3 2 A. Straight hands that differ by suit alone, such as 9 8 7 6 5 and 9 8 7 6 5, are of equal rank. Aces may not have both a high and low rank in the same hand (e.g. 3 2 A K Q is an ace-king high card hand, not a straight).[9][16]

An ace-high straight, such as A K Q J 10, is otherwise known as a broadway straight,[20] while a five-high straight, such as 5 4 3 2 A, is otherwise known as a baby straight,[21] bicycle or wheel and is the best possible hand in ace-to-five lowball.[22][23]

There are 10,200 possible straight hands and 10 distinct ranks of straight. The probability of being dealt a straight from a standard 52-card deck is 5 in 1,274 (or approximately 1 in 255 or 0.39%).[13][14]

Three of a kind[edit]

"Three of a kind" redirects here. For other uses, see Three of a Kind (disambiguation).
Three of a kind
Ace of clubsAce of spadesAce of heartsQueen of diamonds2 of spades
Three of a kind, aces
Hands[a] 54,912
Hand ranks[b] 858
Probability[c] ~2.1%

Three of a kind, also known as trips or a set, is a poker hand containing three cards of the same rank and two cards of two other ranks (the kickers), such as 2 2 2 K 6 ("three of a kind, twos" or "trip twos" or a "set of twos").[8]

Each three of a kind hand is ranked first by the rank of its triplet, then by the rank of its highest-ranking kicker, and finally by the rank of its lowest-ranking kicker. For example, 6 6 6 K 4 ranks higher than 3 3 3 A 2, which ranks higher than 3 3 3 J 7, which ranks higher than 3 3 3 J 3. Three of a kind hands that differ by suit alone, such as 9 9 9 10 8 and 9 9 9 10 8, are of equal rank.[9][16]

In community card games, such as Texas hold ‘em, three of a kind is called a set only when it comprises a pocket pair and a third card on the board.[24]

There are 54,912 possible three of a kind hands and 858 distinct ranks of three of a kind. The probability of being dealt three of a kind from a standard 52-card deck is 88 in 4,165 (or approximately 1 in 47.3 or 2.1%).[13][14]

Two pair[edit]

Two pair
Queen of heartsQueen of spades8 of hearts8 of spades2 of clubs
Two pair, queens and eights
Hands[a] 123,552
Hand ranks[b] 858
Probability[c] ~4.8%

Two pair is a poker hand containing two cards of the same rank, two cards of another rank and one card of a third rank (the kicker), such as J J 4 4 9 (“two pair, jacks and fours” or “two pair, jacks over fours” or “jacks up”).[8][18][25]

Each two pair hand is ranked first by the rank of its highest-ranking pair, then by the rank of its lowest-ranking pair, and finally by the rank of its kicker. For example, 10 10 2 2 K ranks higher than 5 5 4 4 10, which ranks higher than 5 5 3 3 A, which ranks higher than 5 5 3 3 J. Two pair hands that differ by suit alone, such as K K 7 7 8 and K K 7 7 8, are of equal rank.[9][16]

There are 123,552 possible two pair hands and 858 distinct ranks of two pair. The probability of being dealt two pair from a standard 52-card deck is 198 in 4,165 (or approximately 1 in 21.0 or 4.8%).[13][14]

One pair[edit]

One pair
7 of spades7 of heartsKing of spades4 of clubs3 of spades
One pair, sevens
Hands[a] 1,098,240
Hand ranks[b] 2,860
Probability[c] ~42%

One pair, or simply a pair, is a poker hand containing two cards of the same rank and three cards of three other ranks (the kickers), such as 4 4 K 10 5 ("one pair, fours" or a “pair of fours”).[8]

Each one pair hand is ranked first by the rank of its pair, then by the rank of its highest-ranking kicker, then by the rank of its second highest-ranking kicker, and finally by the rank of its lowest-ranking kicker. For example, 9 9 K J 5 ranks higher than 6 6 A 7 4, which ranks higher than 6 6 K Q 2, which ranks higher than 6 6 K 8 7, which ranks higher than 6 6 K 8 3. One pair hands that differ by suit alone, such as 8 8 10 6 5 and 8 8 10 6 5, are of equal rank.[9][16]

There are 1,098,240 possible one pair hands and 2,860 distinct ranks of one pair. The probability of being dealt one pair from a standard 52-card deck is 352 in 833 (or approximately 1 in 2.34 or 42%).[13][14]

High card[edit]

High card
Ace of diamonds10 of spades9 of hearts5 of diamonds4 of clubs
High card, ace
Hands[a] 1,302,540
Hand ranks[b] 1,277
Probability[c] ~50%

High card, also known as no pair or simply nothing, is a poker hand containing five cards not all of sequential rank or of the same suit, and none of which are of the same rank, such as K J 8 7 4 ("high card, king" or "king-jack-high" or “king-high”).[8][18][26]

Each high card hand is ranked first by the rank of its highest-ranking card, then by the rank of its second highest-ranking card, then by the rank of its third highest-ranking card, then by the rank of its fourth highest-ranking card, and finally by the rank of its lowest-ranking card. For example, K 6 5 3 2 ranks higher than Q J 6 5 3, which ranks higher than Q 10 8 7 4, which ranks higher than Q 10 7 6 4, which ranks higher than Q 10 7 5 4, which ranks higher than Q 10 7 5 2. High card hands that differ by suit alone, such as 10 8 7 6 4 and 10 8 7 6 4, are of equal rank.[9][16]

A seven-five-high card hand, such as 7 5 4 3 2, is usually the lowest-ranking poker hand, being the set of cards with the lowest cumulative rank that does not fall under any other category.[27] However, in ace-to-five lowball aces have the lowest rank and straights, flushes and straight flushes are not recognized; thus, the lowest-ranking hand becomes a five-high card hand, such as 5 4 3 2 A or 5 4 3 2 A.[10]

There are 1,302,540 possible high cards hands and 1,277 distinct ranks of high card. The probability of being dealt a high card from a standard 52-card deck is 1,277 in 2,548 (or approximately 1 in 2.00 or 50%).[13][14]

Additional hand categories[edit]

Five of a kind[edit]

Five of a kind
Ace of spadesAce of clubsAce of heartsAce of diamondsJoker
Five of a kind, aces

Five of a kind is a poker hand containing five cards of the same rank, such as 3 3 3 3 3 ("five of a kind, threes"). Five of a kind ranks above a straight flush and is only possible when using a wild card that can have the same rank as the other four cards.[9]

Most commonly, five of a kind becomes possible when a joker is added to the deck as a bug, a form of wild card that may either act as a fifth ace or be used to complete any straight, flush or straight flush. Under these rules, the only possible five of a kind is five aces, such as A A A A A, which becomes the highest-ranking poker hand.[8]

See also[edit]

Notes[edit]

  1. ^ a b c d e f g h i j The number of 5-card combinations that can be drawn from a standard 52-card deck.
  2. ^ a b c d e f g h i j The number of 5-card combinations that can be drawn from a standard 52-card deck, ignoring the specific suit of cards.
  3. ^ a b c d e f g h i j The probability of dealing a hand from a well-shuffled standard 52-card deck.

References[edit]

  1. ^ a b c Bourne, Murray. "Probability and Poker". www.intmath.com. Retrieved 2016-07-12. 
  2. ^ Krieger, Lou (2006). "What is Poker?". The Poker Player's Bible. South Africa: Struik Publishers. pp. 12–14. ISBN 978-177007-469-9. 
  3. ^ Harrock, Richard (2011). "The Basics of Play". Poker for Dummies, Mini Edition. United States of America: Wiley Publishing, Inc. ISBN 978-0-470-05565-6. 
  4. ^ Sklansky, David (2005). The Theory of Poker. United States of America: Two Plus Two Publishing LLC. p. 2. ISBN 1-880685-00-0. 
  5. ^ "Poker Hands | Official Poker Hand Rankings | partypoker". www.partypoker.com. Retrieved 2016-07-12. 
  6. ^ "Poker Hands Order - Poker Hand Rankings at PokerStars". www.pokerstars.com. Retrieved 2016-07-12. 
  7. ^ a b "Poker Hand Ranking | Official World Series of Poker Online". www.wsop.com. Retrieved 2016-07-12. 
  8. ^ a b c d e f g h i j k l m n o Krieger, Lou (2006). The Poker Player's Bible. South Africa: Struik Publishers. pp. 30–34. ISBN 978-177007-469-9. 
  9. ^ a b c d e f g h i j k Greiner, Ron (2005). The Everyday Guide to Recreational Poker. Everyday Endeavors, LLC. pp. 46–60. ISBN 0976970309. 
  10. ^ a b c d e Scott, Alex (2010). "How to Play Lowball Draw". What I Know about Poker: Lessons in Texas Hold'em, Omaha and Other Poker Games. p. 24. ISBN 978-0-9567151-3-5. 
  11. ^ "PROBABILITY: 5-CARD POKER HANDS". www.math.hawaii.edu. Retrieved 2016-07-12. 
  12. ^ "How many poker hands are there?". Retrieved 2016-07-13. 
  13. ^ a b c d e f g h i j Berg, Henry (2013-05-13). "FiveCardSingleDeckHands.txt". Code Throwdown. Retrieved 2016-07-13. 
  14. ^ a b c d e f g h i j "Poker". Wolfram MathWorld. Wolfram. Retrieved 2016-07-13. 
  15. ^ a b Braids, Sam (2003). The Intelligent Guide to Texas Hold'em. Towson, Maryland: Intelligent Games Publishing. p. 166. ISBN 0967755123. 
  16. ^ a b c d e f g h i Kreiger, Lou; Bykofsky, Sheree (2006). The Rules of Poker. Lyle Stuart. pp. 99–102. ISBN 0818406607. 
  17. ^ Miller, Ed; Sklansky, David; Malmuth, Mason (2005). Small Stakes Hold 'em. United States of America: Two Plus Two Publishing LLC. pp. 343–358. ISBN 1-880685-32-9. 
  18. ^ a b c Wenzel, John (2004). The Everything Poker Strategy Book. United States of America: F+W Publications, Inc. pp. 6–10. ISBN 1-59337-140-3. 
  19. ^ Sklansky, David (2007). The Theory of Poker. Two Plus Two Publishing LLC. p. 124. ISBN 1-880685-00-0. 
  20. ^ Erickson, David (2015). "3.2.5.3 Broadway straight". Superior Texas Hold'em: Evolved Poker Strategy. United States of America: Evergent Teknologies. ISBN 978-0-9938197-0-4. 
  21. ^ Zee, Ray (2007). High-Low-Split Poker, Seven-Card Stud and Omaha Eight-or-better for Advanced Players. United States of America: Two Plus Two Publishing LLC. p. 323. ISBN 978-1880685105. 
  22. ^ Sklansky, David (2005). "Glossary of Poker Terms". The Theory of Poker. United States of America: Two Plus Two Publishing LLC. pp. 277–293. ISBN 1-880685-00-0. 
  23. ^ Malmuth, Mason (1998). "Ace-to-Five Lowball". Winning Concepts in Draw and Lowball (2nd ed.). United States of America: Two Plus Two Publishing. p. 45. ISBN 1-880685-07-8. 
  24. ^ Sklansky, David (2004). Small Stakes Hold 'Em (1 ed.). Two Plus Two Publishing. p. 127. ISBN 978-1880685327. 
  25. ^ Cardoza, Avery (2012). Poker Talk. Cardoza Publishing. ISBN 978-1-58042-502-5. 
  26. ^ Gelling, Jonathan (2009). Poker Tips that Pay. Play to Pay Publishing. p. 333. ISBN 978-0-9840822-9-2. 
  27. ^ Kimberg, Daniel (2002). Serious Poker. ConJelCo LLC. pp. 229–277. ISBN 1-886070-16-4. 

External links[edit]