  Between the poker hands of straight, flush, and full house, which hand is
more common? In standard 5-card poker, the order from most common to least
common is straight, flush, full house. The same order is true for 7-card poker
such as Texas hold'em. However, is the same true for n-card poker for larger n?
We study the probability of obtaining these various hands for n-card poker for
various values of $n\geq 5$. In particular, we derive equations for the
probability of flush, straight and full house and show that the probability of
flush is less than a straight when $n\leq 11$, and is more than a straight when
n>11. Similarly, we show that the probability of full house is less than a
straight when $n\leq 19$, and is more than a straight when n>19. This means
that for games such as Big Two where the ordering of 13-card hands depends on
the ordering in 5-card poker, the ranking ordering does not follow the
occurrence probability ordering, contrary to what intuition suggests.
