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Poker hands

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A hand in poker can mean any of the following:

1. A unit of play consisting of a deal, one or more rounds of betting, and possibly a showdown.
2. A set of five cards with a certain value. For example, the hand A♥ 10♥ 9♥ 5♥ 3♥ is a “flush”, a hand that is valuable because each card is of the same suit.
3. A player’s set of non-communal cards.

The second and third definitions are often used interchangeably. For example, in Texas hold ’em, a player holding A♣ K♠, with a board of A♥ K♣ K♦ 7♠ 3♦, might say, “my hand is ace-king”. However, his best 5-card hand (the portion of the hand which determines value) is the kings-over-aces full house.

General rules

The following general rules apply to evaluating poker hands, whatever set of hand values are used.

• Individual cards are ranked A (high), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 (low).
Individual card ranks are often used to evaluate hands that contain no pairs or other special combinations, or to rank the kickers of otherwise equal hands. The Ace is ranked low in ace-to-five and ace-to-six lowball games.
• Suits have no value.
The suits of the cards are mainly used in determining whether a hand fits a certain category (specifically the Flush and Straight flush hands). In most variants, if two players have hands that are identical except for suit, then they are tied and split the pot. Sometimes a ranking called high card by suit is used for randomly selecting a player to deal.
• A hand always consists of five cards.
In games where more than five cards are available to each player, hands are ranked by choosing some five-card subset according to the rules of the game, and comparing that five-card hand against the five-card hands of the other players. Whatever cards remain after choosing the five to be played are of no consequence in determining the winner. (For example, when comparing identical full houses, there are no “kickers”.)
• Hands are ranked first by category, then by individual card ranks.
That is, even the minimum qualifying hand in a certain category defeats all hands in all lower categories. The smallest Two pair hand, for example, defeats all hands with just One pair or No pair. Only between two hands in the same category are card ranks used to break ties. The highest single card in each flush or straight is used to break ties (the Ace-through-five straight is the lowest straight, the Ace being a low card in this context). Within two Two pair hands, the higher pairs are first compared. If they tie, then the secondary pairs are compared, and then finally the kicker.
• For ease of explanation, hands are shown here neatly arranged, but a poker hand has the same value no matter what order the cards are received in.

Ranking of hands

The standard ranking of poker hands are:

• Royal flush: Five cards in sequence and of the same suit, starting from the Ace down to the 10. Example: A♠ K♠ Q♠ J♠ 10♠ (Note: A Royal Flush is not a category of hand in and of itself, it is simply the highest-valued straight flush, and thus also the highest-valued hand. Since it is mentioned often in the context of hand rankings, it is worth noting in this list.)
• Straight flush: Any five cards in sequence and of the same suit. Example: Q♦ J♦ 10♦ 9♦ 8♦
• Four of a kind: A hand with four cards of the same rank. Example: 4♣ 4♦ 4♥ 4♠ 9♥
• Full house: A hand with three cards of one rank and two of another. Example: 8♣ 8♦ 8♠ K♥ K♠ (Often described as the three-of-a-kind rank full of the pair rank. The example is eights full of kings)
• Flush: Five cards of the same suit. Example: K♠ J♠ 8♠ 4♠ 3♠
• Straight: Five cards in sequence. (The ace can be considered higher than the king or lower than the two.) Example: 5♦ 4♥ 3♠ 2♦ A♦
• Three of a kind: Three cards of the same rank. Example: 7♣ 7♥ 7♠ K♦ 2♠
• Two pair: Two cards of one rank, two of another. Example: A♣ A♦ 8♥ 8♠ Q♠
• One pair: Two cards of the same rank. Example: 9♥ 9♠ A♣ J♠ 4♥
• High card: Also known as a “no pair” hand. The following example is considered “Ace high.” Example: A♦ 10♦ 9♠ 5♣ 4♣

The hands are ranked in this order because of their relative probabilities, with rarer hands ranking above more common hands. In addition, all 5 card poker hands can be collapsed down to 7,462 distinct equivalence classes. For example, there are 24 different ways to create an Aces over Kings Full House hand, but since they all hold the same poker ranking value, they can be collapsed into the same equivalence class. In this way, all 2,598,960 unique five card poker hands can be shrunk down to just 7,462 distinct classes of hands.

Variations

Some games called lowball or low poker are played where players strive not for the highest ranking of the above combinations but for the lowest ranking hand. There are three methods of ranking low hands, called Ace-to-five low, Deuce-to-seven low, and Ace-to-six low. The ace-to-five method is most common. A sub-variant within this category is high-low poker, in which the highest and lowest hands split the pot (with the highest hand taking any odd chips if the pot does not divide equally). Sometimes straights and/or flushes count in determining which hand is highest but not in determining which hand is lowest (being reckoned as a no-pair hand in the latter instance), so that a player with such a holding can win both ways and thus take the entire pot.

Certain variants use hands of only three cards, either high or low. Three-card low hands can be ranked by any of the three methods above, although with three cards they become ace-to-three (rather than ace-to-five), deuce-to-five, and ace-to-four. The ace-to-three method is the most common, just as the ace-to-five method is most common method for five cards. Three-card high hands are ranked in one of two ways: either with or without straights and flushes. Without them (which is the most common, and used such games as Chinese poker), the hands are simply no pair, one pair, and three of a kind. If you add straights and flushes, the order of hands should be changed to reflect the correct probabilities: no pair, one pair, flush, straight, three of a kind, straight flush. This order is used, for example, in Mambo stud.

Some poker games are played with a deck that has been stripped of certain cards, usually low-ranking ones. For example, the Australian game of Manila uses a 32-card deck in which all cards below the rank of 7 are removed, and Mexican stud removes the 8s, 9s, and 10s. In both of these games, a flush ranks above a full house, because having fewer cards of each suit available makes flushes rarer.

Some games add one or more non-standard poker hands, bugs, wild cards, or have other exceptions to the standard rules above. For example, in the game of Pai gow poker as played in Nevada, a wheel (5-4-3-2-A) ranks above a king-high straight, but below an ace-high straight.