Effective Hand Strength (EHS) is a poker algorithm conceived by computer scientists Darse Billings,

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Jonathan Schaeffer Jonathan Herbert Schaeffer (born 1957) is a Canadian researcher and professor at the University of Alberta and the former Canada Research Chair in Artificial Intelligence. He led the team that wrote Chinook, the world's strongest American c ...

and

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that was published for the first time in the 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

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): :

EHS = HS \times (1 - NPOT) + (1-HS) \times PPOT

where: *

EHS

is the Effective Hand Strength *

HS

is the current Hand Strength (i.e. not taking into account potential to improve or deteriorate, depending on upcoming table cards *

NPOT

is the Negative POTential (i.e. the probability that our current hand, if the strongest, deteriorates and becomes a losing hand) *

PPOT

is the Positive POTential (i.e. the probability that our current hand, if losing, improves and becomes the winning hand)

Pseudocode

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)

In addition, EHS will consider the hand potential (i.e. its probabilities to improve or deteriorate):

HandPotential(ourcards, boardcards)

Applicability

EHS is applicable to a wide variety of poker games such as

Texas hold 'em poker Texas hold 'em (also known as Texas holdem, hold 'em, and holdem) is one of the most popular variants of the card game of poker. Two cards, known as hole cards, are dealt face down to each player, and then five community cards are dealt fac ...

Omaha hold 'em poker Omaha hold 'em (also known as Omaha holdem or simply Omaha) is a community card poker game similar to Texas hold 'em, where each player is dealt four cards and must make their best hand using exactly two of them, plus exactly three of the five ...

, ... Given the complexity of the algorithm, it can not be computed manually and has to be used in an Artificial Intelligence context.

References

{{Reflist Poker probability