N-card hands

hand size N:

One of C(52,N)= possible hands.

as text:

Number of 5-card hands: 2,598,960

Poker
     hand              #   probability
straight_flush         40  0.00154%
four_of_a_kind        624  0.02401%
full_house           3744  0.14406%
flush                5108  0.19654%
straight            10200  0.39246%
three_of_a_kind     54912  2.11285%
two_pair           123552  4.75390%
one_pair          1098240 42.25690%
high card         1302540 50.1177%





P(a 5-card hand with no particular pip card) = (12/13)^5 = .670
P(a 5-card hand with no particular suit) = (3/4)^5 = .2373

Drawing to. chance of success:
outside straight:  17.02127 %
2-pair to full house:  8.51064 %
3-of-a-kind to full house:  6.66050 %
3-of-a-kind to 4-of-a-kind:  2.12766 %
4 same suit to flush:  19.14894 %