Poker Hands

A poker deck has 52 cards, divided into 4 suits (hearts, spades, diamonds, clubs) of 13 ranks each. The suits themselves are all valued equally – no one suit counts more or less than any other suit. Listed below are all of the possible poker hands, in order from least to greatest.

HIGHCARD

Probability: 0.501177
No two cards have the same rank, the five cards are not in sequence, and the five cards are not all the same suit. Your hand is valued by the highest ranking card you hold, and two high-card hands are ranked by comparing the highest ranking card.

ONE PAIR

Probability: 0.422569
Two cards have the same rank, the other three are unmatched. Higher ranking pairs defeat lower ranking pairs – if two hands have the same pair, the non-paired cards are compared in descending order to determine the winner.

TWO PAIR

Probability: 0.047539
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. To rank two hands both containing two pair, the higher ranking pair of each is first compared, and the higher pair wins. If both hands have the same top pair, then the second pair of each is compared, and if both hands have the same two pairs, the unmatched card determines the winner.

THREE OF A KIND

Probability: 0.0211285
Three cards of the same rank, plus two unmatched cards. Higher-valued three of a kind defeat lower-valued three of a kind.

STRAIGHT

Probability: 0.00392465
Five cards of sequential rank. If the cards were also all of the same suit, the hand would be a straight flush. 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. Aces can play low in straights and straight flushes.

FLUSH

Probability: 0.0019654
All five cards are of the same suit. 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.

FULL HOUSE

Probability: 0.00144058
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.

FOUR OF A KIND

Probability: 0.000240096
Four cards of one rank and an unmatched card of another rank. Four of a kinds with higher ranking cards defeat Four of a kinds with lower ranking ones.

STRAIGHT FLUSH

Probability: 0.0000138517
Five cards in sequence, all of the same suit. Two such hands are compared by their card that is ranked highest. Aces can play low in straights and straight flushes.

ROYAL FLUSH

Probability: 0.00000153908
An ace-high straight flush – this is the highest ranking poker hand in games where only one deck is used.

FIVE OF A KIND

Probability: 0.0000003484
Five cards all of the same rank. This hand is only possible when using more than 1 deck. Five of a kinds with higher ranking cards defeat Five of a kinds with lower ranking ones.