Probability Poker Hand Full House
There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. Three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise. Full house: 1 to 694. And the strongest poker combination. The probability of collecting royal flush in poker is 1 to 649 740. Time out of 220 hands. The tables below show the probabilities of being dealt various poker hands with different wild card specifications. Of Hands Probability. Full House 3,744 0.
Mark Brader has provided the following tables of probabilities of the various five-card poker hands when five cards are dealt from a single 52-card deck, and also when using multiple decks.
Probability Poker Hand Full House Or Flush Who Wins
. Drawing 5 cards from a standard deck of 52 poker cards (Four suits: clubs, spades, diamonds, hearts. Each suit has thirteen cards: A, 2, 3, 10, J, Q, K). What is the probability of the five cards being a Full House? A full house is a poker hand containing three cards of one rank and two cards of another rank, such as 3 3 3 6 6. Since a full house has the form of one pair plus a three-of-a-kind then there are 13. 12 = 78 choices for the ranks of the pair and the 3OAK (note that I don’t need to remove permutations from the choices because there is a difference in which of the pair or 3OAK gets which rank.
The traditional hand types are described on the poker hand ranking page. These include one hand that belongs to two types at once - a straight flush is both a straight and a flush. With two or more decks, it is possible for other combinations to occur, such as a hand that has both a flush and a pair (such as 4-6-6-8-9 all of one suit). The left-hand tables include these composite hand types for multiple decks; in these tables 'plain' means a hand that is not a flush.
The hands are listed in descending order of probability, which could be used as the basis for their ranking order in multi-deck poker variations. It can be seen that as the number of decks increases, flushes become easier to make than straights, and sets of equal cards become more common.
Probability Poker Hand Full House Rankings
Here is the Perl program that produced the tables. Mark Brader has placed both the program and the tables in the public domain.