List of poker hands

From Wikipedia, the free encyclopedia
  (Redirected from Hand (poker))
Jump to: navigation, search
A royal flush of hearts
A royal flush, the highest-ranking basic poker hand

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 ird 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]