Is there an algorithm for poker?

en.wikipedia.org - Effective hand strength algorithm - Wikipedia

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Effective Hand Strength (EHS) is a poker algorithm conceived by computer scientists Darse Billings, Denis Papp, Jonathan Schaeffer and Duane Szafron that was published for the first time in the research paper (1998). "Opponent Modeling in Poker" (PDF). AAAI-98 Proceedings. It has since then been considered as a reference in the realm of poker artificial intelligence and has been the basis of further research such as:

Algorithm [ edit ]

The algorithm is a numerical approach to quantify the strength of a poker hand where its result expresses the strength of a particular hand in percentile (i.e. ranging from 0 to 1), compared to all other possible hands. The underlying assumption is that an Effective Hand Strength (EHS) is composed of the current Hand Strength (HS) and its potential to improve or deteriorate (PPOT and NPOT): E H S = H S × ( 1 − N P O T ) + ( 1 − H S ) × P P O T {\displaystyle EHS=HS\times (1-NPOT)+(1-HS)\times PPOT}

where:

E H S {\displaystyle EHS}

H S {\displaystyle HS}

N P O T {\displaystyle NPOT}

P P O T {\displaystyle PPOT}

Pseudocode [ edit ]

Hand Strength (HS) will enumerate all possible opponent hand cards and count the occurrences where our hand is strongest (+50% of the cases where we are tied): HandStrength(ourcards, boardcards) { ahead = tied = behind = 0 ourrank = Rank(ourcards, boardcards) for each case(oppcards) { opprank = Rank(oppcards, boardcards) if (ourrank > opprank) ahead += 1 else if (ourrank == opprank) tied += 1 else behind += 1 } handstrength = (ahead + tied / 2) / (ahead + tied + behind) return handstrength } In addition, EHS will consider the hand potential (i.e. its probabilities to improve or deteriorate): HandPotential(ourcards,boardcards) { // Hand potential array, each index represents ahead, tied, and behind integer array HP[3][3] // initialize to 0 integer array HPTotal[3] // initialize to 0 ourrank = Rank(ourcards, boardcards) // Consider all two card combinations of the remaining cards for the opponent for each case(oppcards) { opprank = Rank(oppcards, boardcards) if (ourrank > opprank) index = ahead else if (ourrank == opprank) index = tied else index = behind HPTotal[index] += 1 // All possible board cards to come for each case(turn, river) { // Final 5-card board board = [boardcards, turn, river] ourbest = Rank(ourcards, board) oppbest = Rank(oppcards, board) if (ourbest > oppbest) HP[index][ahead] += 1 else if (ourbest == oppbest) HP[index][tied] += 1 else HP[index][behind] += 1 } } // Ppot: were behind but moved ahead Ppot = (HP[behind][ahead] + HP[behind][tied] / 2 + HP[tied][ahead] / 2) / (HPTotal[behind] + HPTotal[tied]) // Npot: were ahead but fell behind Npot = (HP[ahead][behind] + HP[tied][behind] / 2 + HP[ahead][tied] / 2) / (HPTotal[ahead] + HPTotal[tied]) return [ Ppot, Npot ] }

Applicability [ edit ]

EHS is applicable to a wide variety of poker games such as Texas hold 'em poker, Omaha hold 'em poker, ... Given the complexity of the algorithm, it can not be computed manually and has to be used in an Artificial Intelligence context.

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