Computer science. Heads-up limit hold'em poker is solved

Area of Science:

• Artificial Intelligence
• Game Theory
• Computer Science

Background:

• Many perfect-information games have been solved computationally.
• No nontrivial imperfect-information game played competitively by humans has been solved.
• Poker games exhibit imperfect information, posing significant computational challenges.

Purpose of the Study:

• To determine if heads-up limit Texas hold'em, a complex poker variant, could be computationally solved.
• To develop new algorithms capable of solving large-scale imperfect-information games.
• To formally verify strategic advantages in imperfect-information games.

Main Methods:

• The study utilized a novel algorithm, Counterfactual Regret Minimization plus (CFR(+)).
• CFR(+) enabled solving extensive-form games of unprecedented size and complexity.
• The algorithm was applied to the specific game of heads-up limit Texas hold'em.

Main Results:

• Heads-up limit Texas hold'em has been essentially weakly solved.
• The computation formally demonstrates the dealer's substantial advantage in the game.
• The CFR(+) algorithm significantly advanced the capability for solving large extensive-form games.

Conclusions:

• The computational solution of heads-up limit Texas hold'em marks a milestone in game theory and AI.
• The findings provide formal validation for long-held beliefs about game strategy and player advantage.
• The developed CFR(+) algorithm opens new possibilities for solving other complex imperfect-information games.