# Poker probability

Royal, but it'll at least show you what happens in Stud at least on Stars PokerStars Game The use of wild cards also increases your chances of getting a royal flush, as the wild card can substitute for any of the natural cards in the royal flush. Did you try these steps? Please help improve it or discuss these issues on the talk page. Any hand consisting of three unpaired cards of different suits, but a fourth paired or suited card.

## How Often Do You Flop a Flush?

There are nine hand-ranking categories when using a standard card deck , except under ace-to-five low rules where straights, flushes and straight flushes are not recognized. An additional category, five of a kind, is introduced when using one or more wild cards. The fewer hands a category contains, the higher its rank. It ranks above a straight flush but is only possible when using one or more wild cards, as there are only four cards of each rank in a standard card deck.

Each five of a kind is ranked by the rank of its quintuplet. Under high rules, an ace can rank either high e. There are 40 possible straight flush hands and 10 distinct ranks of straight flush under high rules when using a standard card deck. It ranks below a straight flush and above a full house. There are possible four of a kind hands and distinct ranks of four of a kind when using a standard card deck.

There are 3, possible full house hands and distinct ranks of full house when using a standard card deck. There are 5, possible flush hands and 1, distinct ranks of flush under high rules when using a standard card deck. It ranks below a flush and above three of a kind.

There are 10, possible straight hands and 10 distinct ranks of straight under high rules when using a standard card deck. It ranks below a straight and above two pair. There are 54, possible three of a kind hands and distinct ranks of three of a kind when using a standard card deck.

In community card games, such as Texas hold 'em, three of a kind is called a set only when it comprises a pocket pair and a third card on the board. There are , possible two pair hands and distinct ranks of two pair when using a standard card deck. It ranks below two pair and above high card. There are 1,, possible one pair hands and 2, distinct ranks of one pair when using a standard card deck.

There are 1,, possible high cards hands and 1, distinct ranks of high card hand under high rules when using a standard card deck. From Wikipedia, the free encyclopedia. For other uses, see Straight flush disambiguation. The Poker Player's Bible. Poker for Dummies, Mini Edition. United States of America: The Theory of Poker. The Intelligent Guide to Texas Hold'em. Retrieved 12 July The Everyday Guide to Recreational Poker. What I Know about Poker: However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q high card hand.

There are 7, distinct poker hands. In some popular variations of poker such as Texas Hold 'Em , a player uses the best five-card poker hand out of seven cards. The frequencies are calculated in a manner similar to that shown for 5-card hands, except additional complications arise due to the extra two cards in the 7-card poker hand. It is notable that the probability of a no-pair hand is less than the probability of a one-pair or two-pair hand.

The Ace-high straight flush or royal flush is slightly more frequent than the lower straight flushes each because the remaining two cards can have any value; a King-high straight flush, for example, cannot have the Ace of its suit in the hand as that would make it ace-high instead. Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits.

Eliminating identical hands that ignore relative suit values leaves 6,, distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7 cards is 4, Perhaps surprisingly, this is fewer than the number of 5-card poker hands from 5 cards because some 5-card hands are impossible with 7 cards e. Some variants of poker, called lowball , use a low hand to determine the winning hand. In most variants of lowball, the ace is counted as the lowest card and straights and flushes don't count against a low hand, so the lowest hand is the five-high hand A , also called a wheel.

The frequencies given are exact; the probabilities and odds are approximate. As can be seen from the table, just over half the time a player gets a hand that has no pairs, three- or four-of-a-kinds. If aces are not low, simply rotate the hand descriptions so that 6-high replaces 5-high for the best hand and ace-high replaces king-high as the worst hand.

In some variants of poker a player uses the best five-card low hand selected from seven cards. The table does not extend to include five-card hands with at least one pair. Its "Total" represents Bluffing frequency can affect the probability of an opponent calling a bet or folding.