Poker Hand

1. The set of cards held by an individual player during play. Joe took another look at his hand when Virginia raised. The term holding can be used for less ambiguity. In Texas hold 'em, these are more commonly known as hole cards or pocket cards.
2. The value of a player's hand(1), as determined by the rules of the game being played (see below). Karen's hand was a flush, but lost to Steve's full house. The term hand value can be used for less ambiguity.
3. A single instance of poker game play, also called a deal. We played eight hands of draw poker, then eight hands of stud poker.

There are many poker variants, but unless otherwise specified in the rules of the variant being played, hands are evaluated using the traditional set of five-card hands. These are, from worst to best:

• No pair (for example, A-Q-10-5-2)
• One pair (for example, 10-10-K-7-4)
• Two pair (for example, K-K-9-9-J)
• Three of a kind (for example, 4-4-4-K-9)
• Straight (for example, 9-8-7-6-5)
• Flush (for example, K-J-8-7-4 of one suit)
• Full house (for example, 2-2-2-Q-Q)
• Four of a kind (for example, J-J-J-J-6)
• Straight flush (for example, Q-J-10-9-8 of one suit)
• Royal straight flush (only A-K-Q-J-10 of a single suit; not technically a separate hand, but sans wild cards the highest possible in poker [also called simply a royal flush])
• Five of a kind (for example, 6-6-6-6-(Wild), only possible in Wild card games)

These hands are called the traditional hands or high hands.

The probability distribution of the various hands for a 5-card game without wild cards and playing Ace high only is as follows:

If Ace is played low as well as high, then the probabilities of the following hands change:

The number 2,598,960 is the number of total hands that can be dealt in poker, excluding permutations of the same hand.

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.

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 (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 unconventional hands, or have special exceptions to the rules above. For example, in the game of Pai gow poker as played in Nevada, a Wheel (poker) (5-4-3-2-A) ranks above a king-high straight, but below an ace-high straight. This is not the case in California, where the nearly identical game is played under the name Double-hand poker using traditional hand values.

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.

• 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 order in which cards are dealt is unimportant.

For ease of explanation, hands are shown here neatly arranged, but a poker hand is the same no matter what order the cards are received in.