By Poker, I mean its most popular variant: Texas Hold'em.

Below is the table enumerating the frequency of 5 card poker hands, sorted in the 9 hand types, assuming cards are randomly drawn from a 52 card deck (obviously without replacement).

The definition of the 9 hand types and the details of the relatively simple computations leading to the results in the table are very well described in Wikipedia.

Below is the table of the frequency of 7 card poker hands, sorted in the 9 hand types, each card being randomly drawn from a 52 card deck. These computations are significantly trickier than those in the previous table, as the length of some formulae suggest. In the four most complex cases, 'Full House', 'Flush', 'Straight', and 'Two Pairs' hand types, I put the formulae in subtables, for better readability.

Below is the table enumerating the frequency of 5 card poker hands, sorted in the 9 hand types, assuming cards are randomly drawn from a 52 card deck (obviously without replacement).

The definition of the 9 hand types and the details of the relatively simple computations leading to the results in the table are very well described in Wikipedia.

Below is the table of the frequency of 7 card poker hands, sorted in the 9 hand types, each card being randomly drawn from a 52 card deck. These computations are significantly trickier than those in the previous table, as the length of some formulae suggest. In the four most complex cases, 'Full House', 'Flush', 'Straight', and 'Two Pairs' hand types, I put the formulae in subtables, for better readability.