Poker Straight Flush Probability
- Poker Straight Flush Probability Chart
- Poker Straight Flush Probability Formula
- Poker Straight Flush Probability Calculator
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.
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.
Poker Straight Flush Probability Chart
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.
Poker Straight Flush Probability Formula
Here is the Perl program that produced the tables. Mark Brader has placed both the program and the tables in the public domain.
Poker Straight Flush Probability Calculator
The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960. The full poker odds probability playlist: Poker cards created by Brgfx. The Probability of a Straight Flush (fraction) constant defines the probability of being dealt a Straight Flush and represent the probability as a fraction. The Straight Flush is a five card hand having five successive value cards all in the same suit exactly. The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739: 1. When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. There are 40 straight flushes (ten in each suit, from the “wheel” A-2–3–4–5 to the “royal” 10-J-Q-K-A.) The total number of five card hands is 52C5 = 52! 5!) = 2,598,960. So the probability of getting dealt a straight flush in five cards is 40 / 2,598,960 = 1 / 64,974 = 1.5391E-05.