Note that 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. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair. 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. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1. The royal flush is a case of the straight flush. Straight (excluding royal flush and straight flush) Mathematical expression of absolute frequencyįlush (excluding royal flush and straight flush) The nCr function on most scientific calculators can be used to calculate hand frequencies entering nCr with 52 and 5, for example, yields as above.

(The frequencies given are exact the probabilities and odds are approximate.) Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement.

In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Calculate probability of poker hand