List of poker hands

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List of poker hands

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.

Although used primarily in poker, these hand rankings are also used in some other card games, and in poker dice.

The ranking of a particular hand is increased by its including multiple cards of the same card rank, by all five cards being from the same suit, or by all five cards being of consecutive rank. The relative ranking of the various hand categories is based on the probability of being randomly dealt such a hand from a well-shuffled deck.

General rules

The following rules apply to ranking all poker hands.

Individual cards are ranked A (highest), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 (lowest). Aces can appear low when part of an A-2-3-4-5 straight or 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.

The suits of the cards are used to determine whether a hand forms a flush or straight flush. In most variants, if two players have hands that are identical except for suit, then they are tied and split the pot (so 3♠ 4♠ 5♠ 6♠ 7♠ is tied with 3♦ 4♦ 5♦ 6♦ 7♦). 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 bettor in stud games.

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 plays.

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, 2♦ 2♠ 3♦ 3♣ 4♠, the lowest-valued two pair hand, defeats all hands with just one pair or high card (such as A♠ A♦ K♦ Q♥ J♣). Only between two hands in the same category are card ranks used to break ties.

A poker hand has the same hand ranking at showdown regardless of the order in which it is arranged by the deal, by a description, or by a picture. So a hand arranged as 10♠ 8♦ 10♦ 6♣ 10♣ is ranked the same as 10♣ 10♦ 10♠ 8♦ 6♣ even though in the first hand the three of a kind is not immediately obvious.

There are 311,875,200 ways (permutations) of being dealt five cards from a 52 card deck,^{[Note 1]} but since the order of cards does not matter there are only ${52 \choose 5} = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!} = 2,598,960$ possible distinct hands (combinations).

Hand categories

Straight flush

"Straight Flush" redirects here. For The World War II bomber, see Straight Flush (B-29).

Defeats

Ties with

Straight flush examples

A straight flush is a hand that contains five cards in sequence, all of the same suit, such as Q♣ J♣ 10♣ 9♣ 8♣. Two such hands are compared by their card that is ranked highest. Because suits have no relative value, two otherwise identical straight flushes tie (so 10♣ 9♣ 8♣ 7♣ 6♣ ties with 10♥ 9♥ 8♥ 7♥ 6♥). Aces can play low in straights and straight flushes: 5♦ 4♦ 3♦ 2♦ A♦ is a 5-high straight flush, also known as a "steel wheel".^[1]^[2] An ace-high straight flush such as A♠ K♠ Q♠ J♠ 10♠ is known as a royal flush, and is the highest ranking standard poker hand.

There are 40 possible straight flushes, including the four royal flushes. The probability of being dealt one in a five-card deal^{[Note 2]} is $\frac {40} {52 \times 51 \times 50 \times 49 \times 48 \div 5!} = \frac {40}{2,598,960} \approx 0.0015%$

Four of a kind

Defeats

Four of a kind examples

Four of a kind, also known as quads, is a poker hand such as 9♣ 9♠ 9♦ 9♥ J♥, which contains four cards of one rank, and an unmatched card of another rank. Quads with higher ranking cards defeat lower ranking ones. In community-card games (such as Texas Hold 'em) or games with wildcards it is possible for two or more players to obtain the same quad; in this instance, the unmatched card acts as a kicker, so 7♣ 7♠ 7♦ 7♥ J♥ defeats 7♣ 7♠ 7♦ 7♥ 10♣. If two hands have the same kicker, they tie and the pot is split.

There are 624 possible hands including four of a kind; the probability of being dealt one in a five-card deal is $\frac {13 \times 48} {2,598,960} \approx 0.024%$

Full house

Defeats

Full house examples

A full house, also known as a full boat, is a hand such as 3♣ 3♠ 3♦ 6♣ 6♥, which 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 7♠ 7♥ 7♦ 4♠ 4♣ defeats 6♠ 6♥ 6♦ A♠ A♣. If two hands have the same three cards (possible in wild card and community card games), the hand with the higher pair wins, so 5♥ 5♦ 5♠ Q♥ Q♣ defeats 5♣ 5♦ 5♠ J♠ J♦. Full houses are described as "Three full of Pair" or occasionally "Three over Pair"; Q♣ Q♦ Q♠ 9♥ 9♣ could be described as "Queens over nines", "Queens full of nines", or simply "Queens full". However, "Queens over nines" is more commonly used to describe the hand containing two pairs, one pair of queens and one pair of nines, as in Q♠ Q♥ 9♣ 9♠ J♦.

There are 3,744 possible full houses; the probability of being dealt one in a five-card hand is $\frac {(13 \times 4) \times (12 \times 6)} {2,598,960} \approx 0.14%$

Flush

Defeats

Flush examples

A flush is a poker hand such as Q♣ 10♣ 7♣ 6♣ 4♣, which contains five cards of the same suit, not in rank sequence. Two flushes are compared as if they were 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.

Flushes are described by their highest card, as in "queen-high flush" to describe Q♦ 9♦ 7♦ 4♦ 3♦. If the rank of the second card is important, it can also be included: K♠ 10♠ 5♠ 3♠ 2♠ is a "king-ten-high flush" or just a "king-ten flush", while K♥ Q♥ 9♥ 5♥ 4♥ is a "king-queen-high flush".

There are 5,148 possible flushes, of which 40 are also straight flushes; the probability of being dealt a flush in a five-card hand is $\frac {5108} {2,598,960} \approx 0.20%$

Straight

Defeats

Ties

Straight examples

A straight is a poker hand such as Q♣ J♠ 10♠ 9♥ 8♥, which contains five cards of sequential rank but in more than one suit. 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.

Straights are described by their highest card, as in "ten-high straight" or "straight to the ten" for 10♣ 9♦ 8♥ 7♣ 6♠.

A hand such as A♣ K♣ Q♦ J♠ 10♠ is an ace-high straight (also known as Broadway), and ranks above a king-high straight such as K♥ Q♠ J♥ 10♥ 9♣. The ace may also be played as a low card in a five-high straight such as 5♠ 4♦ 3♦ 2♠ A♥, which is colloquially known as a wheel. The ace may not "wrap around", or play both high and low: 3♣ 2♦ A♥ K♠ Q♣ is not a straight, just an ace-high high card.

There are 10,240 possible straights, of which 40 are also straight flushes; the probability of being dealt a straight in a five-card deal is $\frac {10,200} {2,598,960} \approx 0.39%$ .

It is impossible to have a straight hand without either a five card or a ten card.

Three of a kind

Defeats

Three of a kind examples

Three of a kind, also called trips or a set, is a poker hand such as 2♦ 2♠ 2♣ K♠ 6♥, which contains three cards of the same rank, plus two unmatched cards. In Texas hold 'em and other flop games, three of a kind is called a "set" only when it is composed of a pocket pair and one card of matching rank on the board (as opposed to two matching cards on the board and a third in the player's hand).^[3]

Higher-valued three of a kind defeat lower-valued three of a kind, so Q♠ Q♥ Q♦ 7♠ 4♣ defeats J♠ J♣ J♦ A♦ K♣. If two hands contain three of a kind of the same value, which is possible in games with wild cards or community cards, the kickers are compared to break the tie, so 4♦ 4♣ 4♠ 9♦ 2♣ defeats 4♦ 4♣ 4♠ 8♣ 7♦.

There are 54,912 possible three of a kind hands in a five-card deal which are not also full houses; the probability of being dealt one in a five-card hand is $\frac {54,912} {2,598,960} \approx 2.1%$

Two pair

Defeats

Two pairs examples

A poker hand such as J♥ J♣ 4♣ 4♠ 9♥, which contains two cards of the same rank, plus two cards of another rank (that match each other but not the first pair), plus one unmatched card, 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 10♠ 10♣ 8♥ 8♣ 4♠ defeats 8♥ 8♣ 4♠ 4♣ 10♠). If both hands have the same top pair, then the second pair of each is compared, such that 10♠ 10♣ 8♥ 8♣ 4♠ defeats 10♠ 10♣ 4♠ 4♥ 8♥. Finally, if both hands have the same two pairs, the kicker determines the winner, so 10♠ 10♣ 8♥ 8♣ 4♠ loses to 10♠ 10♣ 8♥ 8♣ A♦.

Two pair are described by the higher pair first, followed by the lower pair if necessary; K♣ K♦ 9♠ 9♥ 5♥ is described as "Kings over nines," "Kings and nines," or simply "Kings up" if the nines are not important.

There are 123,552 possible two pair hands that are not also full houses; the probability of being dealt one in a five-card deal is $\frac {123,552} {2,598,960} \approx 4.8%$

One pair

Defeats

One pair examples

One pair is a poker hand such as 4♥ 4♠ K♠ 10♦ 5♠, which contains two cards of the same rank, plus three other unmatched cards. Higher ranking pairs defeat lower ranking pairs; if two hands have the same pair, the non-paired cards (the kickers) are compared in descending order to determine the winner.

There are 1,098,240 possible one pair hands; the probability of being dealt one in a five-card deal is $\frac {1,098,240} {2,598,960} \approx 42%$

High card

Defeats

High card examples

A high-card or no-pair hand is a poker hand such as K♥ J♣ 8♣ 7♦ 3♠, in which no two cards have the same rank, the five cards are not in sequence, and the five cards are not all the same suit. 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.

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.

The lowest possible high card is seven-high (such as 7♠ 5♣ 4♦ 3♦ 2♣), because a hand such as 6♦ 5♣ 4♠ 3♦ 2♥ would be a straight.

Of the 2,598,960 possible hands, 1,302,540 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 $\frac {1,302,540} {2,598,960} \approx 50%$

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General rules

Hand categories

Straight flush

Four of a kind

Full house

Flush

Straight

Three of a kind

Two pair

One pair

High card

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