Science Fair Project Encyclopedia
A hand in poker can mean any of the following:
- A synonym for "round", a unit of play consisting of a deal, betting, and possibly a showdown. The term "hand" is preferred because "round" is sometimes used in the context of a "round of betting", and there can be multiple rounds of betting in one hand.
- A set of five cards with a certain value. For example, the hand A♥ 10♥ 9♥ 5♥ 3♥ is a "flush", or hand that is valuable because each card is of the same suit.
- 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". On the other hand, his best 5-card hand is the K/A full house.
Ranking of hands
Only 5-card hands are compared in poker, "three pair" or "6-straight" hands are not included in the ranking system. Most commonly, the ranking of hands is according to the following hierarchy. Hands are classified in the highest category for which they qualify.
- Royal flush: A straight flush that is ace-high. Example: A♠ K♠ Q♠ J♠ 10♠
- Straight flush: 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♠
- Flush: Five cards of the same suit. Example: K♠ J♠ 8♠ 4♠ 3♠
- Straight: Five cards in sequence. 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♥
- No pair: Also known as a high card hand. The following example is considered "Ace high." Example: A♦ 10♦ 9♠ 5♣ 4♣
Without wild cards, the probability distribution for 5-card hands is as follows:
|Royal flush||4 in 2,598,960||0||.000154%|
|Straight flush (non-royal)||36 in 2,598,960||0||.00139%|
|Four of a kind||624 in 2,598,960||0||.0240%|
|Full house||3,744 in 2,598,960||0||.144%|
|Flush||5,108 in 2,598,960||0||.197%|
|Straight||10,200 in 2,598,960||0||.392%|
|Three of a kind||54,912 in 2,598,960||2||.11%|
|Two pair||123,552 in 2,598,960||4||.75%|
|One pair||1,098,240 in 2,598,960||42||.26%|
|No pair||1,302,540 in 2,598,960||50||.12%|
|TOTAL||2,598,960 in 2,598,960||100||.00%|
When ace-low straights and straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes become 9/10 as common as they otherwise would be.
There are 2,598,960 hand combinations that can be dealt in poker, excluding permutations of the same hand. It is calculated as , notated as .
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.
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 considered a mathematical combination, i.e., it is the same no matter what order the cards are received in.
- Wild Card paradox - curiouser.co.uk Discussion of a paradox that arises in the ranking of hands when wild cards are introduced.
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