Chess, one of the oldest and most universally played board games, presents an ideal testbed due to the wealth of both policy data and language data. In terms of policy data, it is reported that over ten million games are played daily on Chess.com, the most frequented online chess platform.

It isn't always easy to detect cheating in chess Just three judiciously deployed cheats can turn an otherwise equal chess game into a near-certain victory, a new analysis shows - and systems designed to crack down on cheating might not notice the foul play. Daniel Keren at the University of Haifa in Israel simulated 100,000 matches using the powerful Stockfish chess engine - a computer system that, at its maximum power, is better at playing chess than any human world champion. The matches were played between two computer engines competing at the level of an average chess player - 1500 on the Elo rating scale typically used to calculate skill level in chess. Half the games were logged without any further intervention, while the other half allowed occasional intervention by a stronger computer chess "player" with an Elo score of 3190 - a higher rating than any human player has ever achieved. Competitors usually have a slim advantage when playing white, with a 51 per cent chance of winning, on average, tied to the fact that they make the game's first move.

The advent of machine learning models that surpass human decision-making ability in complex domains has initiated a movement towards building AI systems that interact with humans. Many building blocks are essential for this activity, with a central one being the algorithmic characterization of human behavior. While much of the existing work focuses on aggregate human behavior, an important long-range goal is to develop behavioral models that specialize to individual people and can differentiate among them.To formalize this process, we study the problem of behavioral stylometry, in which the task is to identify a decision-maker from their decisions alone. We present a transformer-based approach to behavioral stylometry in the context of chess, where one attempts to identify the player who played a set of games. Our method operates in a few-shot classification framework, and can correctly identify a player from among thousands of candidate players with 98% accuracy given only 100 labeled games. Even when trained on amateur play, our method generalises to out-of-distribution samples of Grandmaster players, despite the dramatic differences between amateur and world-class players. Finally, we consider more broadly what our resulting embeddings reveal about human style in chess, as well as the potential ethical implications of powerful methods for identifying individuals from behavioral data.

Mastering games is a hard task, as games can be extremely complex, and still fundamentally different in structure from one another. While the AlphaZero algorithm has demonstrated an impressive ability to learn the rules and strategy of a large variety of games, ranging from Go and Chess, to Atari games, its reliance on extensive computational resources and rigid Convolutional Neural Network (CNN) architecture limits its adaptability and scalability. A model trained to play on a $19\times 19$ Go board cannot be used to play on a smaller $13\times 13$ board, despite the similarity between the two Go variants.In this paper, we focus on Chess, and explore using a more generic Graph-based Representation of a game state, rather than a grid-based one, to introduce a more general architecture based on Graph Neural Networks (GNN). We also expand the classical Graph Attention Network (GAT) layer to incorporate edge-features, to naturally provide a generic policy output format.Our experiments, performed on smaller networks than the initial AlphaZero paper, show that this new architecture outperforms previous architectures with a similar number of parameters, being able to increase playing strength an order of magnitude faster.

We introduce LLM CHESS, an evaluation framework designed to probe the generalization of reasoning and instruction-following abilities in large language models (LLMs) through extended agentic interaction in the domain of chess. We rank over 50 open and closed source models by playing against a random opponent using a range of behavioral metrics, including win and loss rates, move quality, move legality, hallucinated actions, and game duration. For a subset of top reasoning models, we derive an Elo estimate by playing against a chess engine with variably configured skill, which allows for comparisons between models in an easily understandable way. Despite the simplicity of the instruction-following task and the weakness of the opponent, many state-of-the-art models struggle to complete games or achieve consistent wins. Similar to other benchmarks on complex reasoning tasks, our experiments reveal a clear separation between reasoning and non-reasoning models. However, unlike existing static benchmarks, the stochastic and dynamic nature of LLM CHESS uniquely reduces overfitting and memorization while preventing benchmark saturation, proving difficult even for top reasoning models. To support future work on evaluating reasoning and instruction-following in LLMs, we release our experimental framework, a public leaderboard, and a dataset of associated games.

Pgx is available at https://github.com/sotetsuk/pgx. Figure 1: Example games included in Pgx.

We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes into skill leverage K and luck leverage L. Applying this to 30 games reveals a continuum from pure chance (coin toss, S = -1) through mixed domains such as backgammon (S = 0, Sigma = 1.20) to pure skill (chess, S = +1, Sigma = 0). Poker exhibits moderate skill dominance (S = 0.33) with K = 0.40 +/- 0.03 and Sigma = 0.80. We further introduce volatility Sigma to quantify outcome uncertainty over successive turns. The framework extends to general stochastic decision systems, enabling principled comparisons of player influence, game balance, and predictive stability, with applications to game design, AI evaluation, and risk assessment.

The advent of machine learning models that surpass human decision-making ability in complex domains raises the prospect of building AI systems that can collaborate and interact productively with humans.

The advent of machine learning models that surpass human decision-making ability in complex domains raises the prospect of building AI systems that can collaborate and interact productively with humans.

Do the main claims made in the abstract and introduction accurately reflect the paper's Did you describe the limitations of your work? Did you discuss any potential negative societal impacts of your work? Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? Did you include the total amount of compute and the type of resources used (e.g., type Did you include any new assets either in the supplemental material or as a URL? [N/A] Did you discuss whether and how consent was obtained from people whose data you're We start with a lemma that we will repeatedly use in the proofs. If has only one infoset, then Lemma 11 applies.