# How many different kinds of hands can appear in a single Texas Hold 'em game?

Texas Hold 'em is a form of poker where each player has 2 "pocket" cards, which they combine with 3 (or more) community cards from a pool of 5 to form their hand, which are then scored under poker ranks.

Poker cards are scored on the following hands, from best to worst.

• Straight flush (5 consecutive cards of the same suit)
• Four-of-a-kind (4 cards of the same rank, and one other card)
• Full House (3 cards of the same rank, and 2 cards of another rank)
• Flush (5 cards of the same suit, not consecutive)
• Straight (5 consecutive cards, not suited)
• Three of a Kind (3 cards of the same rank, 2 cards of other different ranks)
• Two pair (2 cards of the same rank, 2 cards of another rank, and 1 card of yet another rank)
• One pair (2 cards of the same rank, 3 cards of different other ranks)
• High Card (5 cards of different ranks, neither suited nor consecutive)

For the purposes of this puzzle:

• Players are required to select the highest possible hand. If they have 2 spades as their pocket and there are 3 spades in the community cards, they cannot form any hand worse than a flush.
• All hands of the same type are equivalent. E.g. all straight flushes are treated as the same hand, even ace-high royal flushes.

Is it possible to form a set of community cards and 9 sets of pocket cards so that all 9 kinds of scoring hands are formed? If not, what is the maximum number of different kinds of hands that can be formed?