Chess is a game of complete and perfect information
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Multiple academic and reference sources confirm that chess is a game characterized by complete and perfect information, where all game states are fully visible to both players.
Imperfect information games are a category of games in which players have incomplete information about the current state of play. Unlike perfect information games such as chess, where all game states are fully visible to all players, imperfect information games introduce an additional layer of complexity by requiring decisions based on limited observations and beliefs. Classic examples include card games like poker, where players do not know the unseen cards in the deck or their opponents' hands. These games present unique challenges for developing artificial intelligence agents, as solutions must be designed to handle uncertainty and the lack of complete information effectively. This thesis focuses on developing an agent for gin rummy inspired primarily by a state-of-the-art counterfactual regret minimization (CFR) algorithm. Given the extremely large action state space and resulting game tree in gin rummy, vanilla CFR cannot be directly applied. Therefore, this work explores various simplification and abstraction methods to reduce the game tree's complexity without losing essential game aspects. Additionally, the thesis examines integrating neural networks to complement the CFR-based approach, potentially enhancing the agent's performance. Several simpler algorithms were implemented throughout the project and used as benchmarks for the main agent.
Amazons is a board game which combines elements of Chess and Go. It has become popular in recent years, and has served as a useful platform for both game-theoretic study and AI games research. Buro showed that simple Amazons endgames are NP-equivalent, leaving the complexity of the general case as an open problem. We settle this problem, by showing that deciding the outcome of an n x n Amazons position is PSPACE-hard. We give a reduction from one of the PSPACE-complete two-player formula games described by Schaefer. Since the number of moves in an Amazons game is polynomially bounded (unlike Chess and Go), Amazons is in PSPACE. It is thus on a par with other two-player, bounded-move, perfect-information games such as Hex, Othello, and Kayles. Our construction also provides an alternate proof that simple Amazons endgames are NP-equivalent. Our reduction uses a number of amazons polynomial in the input formula length; a remaining open problem is the complexity of Amazons when only a constant number of amazons is used.
Quoridor is an award-winning abstract strategy game designed by Mirko Marchesi and published in 1997. Similar games include Maze Attack, Blockade (also known as Cul-de-sac), and Pinko Pallino. In line with chess, checkers, Go, and other classic combinatorial games, Quoridor is a turn-based, deterministic, perfect-information game played on a square grid. We show that it is PSPACE-complete to determine whether a given player has a winning strategy in a given Quoridor position on a board with size $n \times n$. We prove this by reduction from Gpos(POS CNF), a Boolean formula game originally defined in 1978 by T. Schaefer.
In many application domains we have seen an explosive growth in the capabilities to both generate and collect data. Representative examples are business, medical, and scientific databases. In the game of chess (and similar games), we have a similar situation. Moreover, in chess we have gigantic databases with perfect information available. An endgame database is a very rare case of an information source with complete knowledge. However, this information, although complete, is not in a form which is particularly useful to human beings. Therefore, the raw data inside an endgame database have to be transformed into knowledge in understandable form. This task concerning chess endgame databases is, in principle, the same as in KDD in general.
For two-player games of perfect information such as Chess, we introduce "uniqueness" properties to describe game positions in which a winning strategy (should one exist) is forced to be unique. Depending on how uniqueness is forced, and whether it applies to both players, the uniqueness property is classified as (bi-) weak, (bi-) strong, or global. We prove that any reasonable two-player game G is extendable to a game G* with the bi-strong uniqueness property, so that e.g., QBF remains PSPACE-complete under this restriction. For global uniqueness, we introduce a simple game GUPQBF over Boolean formulas with this property, and prove that any reasonable two-player game with global uniqueness is reducible to this game. On the other hand, we also show that GUPQBF resides in "small" counting classes believed properly contained in PSPACE. Our results give a new characterization to some complexity classes such as PSPACE and EXPTIME.
Artificial intelligence (AI) in games has advanced significantly, notably in perfect information games such as Go and Chess. Imperfect information games, in which participants do not have complete information about the game state, create more difficulties. They incorporate both public and private observations, where strategies must be improved to achieve a Nash equilibrium. This study investigates artificial intelligence and reinforcement learning approaches, in which agents learn to maximize future rewards through interactions with their surroundings. The paper then focuses on card game research platforms such as RLCard and OpenAI Gym. It gives a comprehensive summary of research in No Limit Texas Hold'em, a difficult two-player poker game with a large decision space. DeepStack and Libratus are successful systems that have attained expert-level and superhuman play, respectively. Pluribus, a superhuman artificial intelligence for six-player poker, and DouZero, a pure reinforcement learning technique for the multiplayer card game, DouDiZhu, are both investigated. Overall, this paper provides background information on reinforcement learning and imperfect information games, analyzes commonly used research platforms, evaluates the effectiveness of AI algorithms in various card games, and offers future research areas and directions.
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