Poker Hand Ranking

In poker, certain combinations of cards (hands) outrank other hands, based on the frequency with which these combinations appear. The player with the best poker hand at the showdown wins the pot. A hand is defined as the best five-card combination, consisting of both communal and non-communal cards, that a player can have according to the rules stated below. The hands are ranked from the best (least frequent) to the worst (most frequent) hand.

 

Straight Flush

A straight flush contains five cards of the same suit in sequence. The best possible hand is an ace-high straight flush, also known as a "Royal Straight Flush".

Example:

Probability to make a Royal Flush: 1 out of 649,740 Five Card Hands 1 out of 108,290 Six Card Hands 1 out of 30,940 Seven Card Hands

Probability to make a Straight Flush: 1 out of 72,193 Five Card Hands 1 out of 12,294 Six Card Hands 1 out of 3,591 Seven Card Hands

 

Four of a Kind

Four of a kind, or "quads", is a poker hand which contains four cards of the same rank.

Example:

Probability to make a Four of a Kind: 1 out of 4,165 Five Card Hands 1 out of 1,388 Six Card Hands 1 out of 595 Seven Card Hands

 

Full House

A full house or a full boat contains three matching cards of one rank (three of a kind) and two matching cards of another rank (a pair).

Example:

Probability to make a Full House: 1 out of 694 Five Card Hands 1 out of 123 Six Card Hands 1 out of 39 Seven Card Hands

 

Flush

A flush contains five cards of the same suit.

Example:

Probability to make a Flush: 1 out of 509 Five Card Hands 1 out of 99 Six Card Hands 1 out of 33 Seven Card Hands

 

Straight

A straight contains five cards in sequence.

Example:

Probability to make a Straight: 1 out of 255 Five Card Hands 1 out of 56 Six Card Hands 1 out of 22 Seven Card Hands

 

Three of a Kind

A three of a kind, or "trips", contains three cards of the same rank.

Example:

Probability to make a Three of a Kind: 1 out of 47 Five Card Hands 1 out of 28 Six Card Hands 1 out of 21 Seven Card Hands

 

Two Pair

A poker hand with two cards of the same rank, and another two cards of the same rank is called two pair.

Example:

Probability to make Two Pair: 1 out of 21 Five Card Hands 1 out of 8 Six Card Hands 1 out of 4 Seven Card Hands

 

One Pair

Two cards of the same rank.

Example:

Probability to make One Pair: 1 out of 2 Five Card Hands (42.2%) 1 out of 2 Six Card Hands (47.7%) 1 out of 2 Seven Card Hands (43.8%)

 

High Card

A high card is a poker hand in which none of the cards have the same rank.

Example:

Probability to have a High Card: 1 out of 2 Five Card Hands (50.1%) 1 out of 3 Six Card Hands (32.4%) 1 out of 6 Seven Card Hands (17.4%)