For a set of 32 cards, there are N = 8 and straights from 7-8-9-10-V to 10-J-Q-K-A, and is obtained S = 4.Įach player receives five cards systematically.If the white straight is not allowed, one has only S = 9. For a deck of 52 cards, there are N = 13 and counting the straights of A-2-3-4-5 (white straight) to 10-J-Q-K-A (royal flush), is obtained S = 10.So the total number of cards is 4N.Īnd we note S the number of accepted straights. In what follows we note N the number of values. So in this case as there are also n possibilities. And choosing (n-1) means choosing the one that deviates. In fact the number of possible choices of an element of n is simply… equal to n. However, note that for all n integer ( n 1) = ( n n-1) = n.
Remember that we note ( n p) the number of combinations (without repetition) of p elements from a set of n elements. The calculation of the probabilities of the various possible hands is mainly through the calculations of combinations. We can calculate the probability of each type of hand of 5-card in poker.