Generating all 5 card poker hands

Question

This problem sounds simple at first glance, but turns out to be a lot more complicated than it seems. It\'s got me stumped for the moment.

There are 52c5 = 2,598,960

Answer 1

Chances are you really want to generate the number of distinct hands, in the sense of non-equivalent. In that case, according to the wikipedia article there are 7462 possible hands. Here is a python snippet that will enumerate them all.

The logic is simple: there is one hand for each 5-set of ranks; in addition, if all the ranks are distinct, another, different kind of hand can be formed by making all the suits match.

count = 0 

for i in range(0,13):
    for j in range (i,13):
        for k in range(j,13):
            for l in range(k,13):
                for m in range(l,13):
                    d = len(set([i,j,k,l,m])) # number of distinct ranks
                    if d == 1: continue    # reject nonsensical 5-of-a-kind
                    count += 1
                    # if all the ranks are distinct then 
                    # count another hand with all suits equal
                    if d == 5: count += 1

print count   # 7462