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In poker, a standard deck of 52 cards is used. Each card has one of 13 ranks, ranging from Ace to Deuce, and one of 4 suits: Spades, Hearts, Diamonds, or Clubs.

The rank of a card is crucial. For instance, holding an Ace and a Jack is significantly different from holding a King and a Jack, or an Ace and a Seven.

However, the suit of a card doesn’t hold individual importance. What matters is whether the cards share the same suit or not. For example, holding the King of Clubs and the Jack of Diamonds is equivalent to holding the King of Hearts and the Jack of Spades.

Poker players often talk about whether their cards are suited (sharing the same suit) or offsuit (having different suits). They describe the cards on the board as monotone, two-tone, or rainbow, and talk about holding a flush draw or backdoor flush draw. These terms don’t refer to the suit of an individual card, but rather to the pattern of suits among all the cards.

So, when encoding cards for a game of poker, it’s important to reflect these aspects. Instead of encoding the suit of each card, we should encode the relationships between the suits of all the cards. This approach captures the essence of how suits function in poker.

So, how can we create an encoding scheme that captures these relationships between the suits of cards in poker?

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  • $\begingroup$ ojs.aaai.org/index.php/AAAI/article/view/20394/20153 $\endgroup$
    – Alberto
    Nov 6, 2023 at 11:13
  • $\begingroup$ @Alberto, can you add your thought about the article? I think that this article does not answer this question because it do not use any encoding for suits. See Effective Game State Representation: "1) there is no abstraction of the card information thus reserves all the game information" $\endgroup$
    – Cohensius
    Nov 9, 2023 at 14:25

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This is normally handled by considering hand isomorphisms. So in pre-flop Texas holdem there are 169 isomorphisms, consisting of 13 pairs of the same rank, 78 suited pairs of different rank and 78 unsuited pairs of different rank. You can take a similar approach to post-flop boards. Iirc there are 1755 isomorphic flops, 16432 turns, and about 127000 rivers, quite a few of which are nut rivers. Google "A fast and optimal hand isomorphism algorithm"

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