1098240 − 123552 − 54912 − 10200 − 5108 − 3744 − 624 − 40 = 1302540
different hands which are just a high card.
How good is a particular hand?
The useful thing to know is how likely I am to win if I have a
particular hand. For example, suppose I have a pair of
kings. How likely am I to win? This is actually a
relatively complicated problem to calculate exactly. For example,
it makes certain straights and flushes less likely. But these are
a small percentage of the total number of hands. Two kings beats
or ties all but one of the one pair hands and all of the high card
hands. This amounts to (12/13)(1098240) + 1302540 = 2316300, or
roughly 89% of hands. So I'm in good shape. A pair of twos
beats or ties only (1/13)(1098240) + 1302540 = 1387020, or roughly 53%
of hands. That is not a hand to be extremely confident about.
Variants of Poker.