[chaos]

The hardest part for me is not that calculations themselves but defining exactly what I want to calculate and then listing all the cases to calculate without omissions or duplications.

For example many people say they will play any four cards 9 or higher. At first glance this appears to be
C(24,4) = 10,626. But this number is too high because what you actually want to calculate is any four cards 9 or higher minus the obviously unplayable hands like quads and trips. So you would need to calculate the unplayable hands and subtract them from 10,626. Or you could try and enumerate all the hands you would play and calculate the number of combinations of each.