Toward Modeling Player-Specific Chess Behaviors

Chess engines have evolved from search-based systems optimized solely for strength to neural policies capable of modeling human decisions across much of the rating spectrum. Maia-3, the strongest human-like move policy for chess, models the typical moves of a given rating but does not model high Elo strength well (2500+ Lichess Elo) nor has an extensible architecture for modeling individual play style. On the other hand, search-based engines like Stockfish are far stronger than any known human but struggle to model human-like play. To solve these problems, we present Matilda, a permutation-invariant set transformer that re-ranks the full legal-move distribution produced by a frozen Maia-3 and improves it along both dimensions with one 1.7M-parameter model. Matilda uses Maia-3 to provide both global context and search candidates. Context is encoded from Maia-3's hidden representation, time control, and an optional 32-dimensional player-style vector, while the top-16 candidate moves are optionally rescored by Stockfish. A zero-initialized head scatters per-candidate adjustments back into the policy logits, so the untrained model is exactly Maia-3 and every gain is value-added under full-vocabulary NLL. On a 2500+ Elo benchmark from Lichess, Matilda improves on Maia-3 by +0.5-0.6% below 2800 but +4.3%, +11.9%, and +21.9% at 2800-2900, 2900-3000, and 3000+, respectively, and an additional +0.41% overall from player-style embeddings. Ablations show that the improvements are primarily driven by the engine-derived features, the mechanism is not engine-specific, and the gains survive memorization, sibling, and account audits while preserving Maia-3 at 1000-2500 Elo. Because search supervision is modular, Matilda naturally supports interchangeable search engines, demonstrated by replacing Stockfish with an AlphaZero-family engine.

Chess has long served as a canonical testbed for artificial intelligence, but modeling approaches for its central tasks have diverged. Maximizing playing strength, predicting human play, and enabling interpretability are typically solved with disparate architectures, and these designs are often misaligned with the geometry of the domain. This raises the natural question of whether these objectives require separate modeling paradigms, or if there exists a single architecture that supports them simultaneously. We introduce Chessformer, a unified architecture that advances the state of the art on all three central goals in chess modeling. Chessformer is an encoder-only transformer that represents board squares as tokens, augments self-attention with a novel dynamic positional encoding called Geometric Attention Bias (GAB) that adapts to domain-specific geometry, and predicts actions with an attention-based source-destination policy head. We evaluate Chessformer on each front. First, we develop \maiathree, a family of models for human move prediction that reaches 57.1% move-matching accuracy, significantly surpassing the previous state of the art with fewer than a quarter of the parameters. Second, we integrate Chessformer into Leela Chess Zero, a leading open-source engine, adding over 100 Elo of playing strength and resulting in tournament victories over Stockfish in major computer chess competitions. Third, we show that Chessformer's square-token design makes attention patterns and activations directly attributable to board squares, enabling granular interpretability analyses that prior architectures do not naturally support. More broadly, our results demonstrate that aligning a model's tokenization, positional encoding, and output design with the underlying structure of a domain can yield simultaneous gains in performance, human compatibility, and interpretability.

Otter is a 15.3M-parameter human chess AI that predicts human move selection by modeling play as a time-aware, sequential process rather than treating each position in isolation. It combines two conditioning signals: (1) a move history encoder that conditions predictions on the last 20 moves, capturing opening preferences, positional drift, and intra-game behavioral tendencies; and (2) a time control module that modulates predictions based on clock pressure. Otter is trained on 6.1 billion positions from 117 million Lichess rapid games over 30 days on a single T4 GPU. Otter achieves 55.23% top-1 and 90.95% top-5 move-prediction accuracy, surpassing the prior state-of-the-art human chess model, Maia 2, with far fewer parameters and less training data. Across 11 Elo brackets (<1100 to >=2000), accuracy peaks at 57.38% in the 1900-1999 bracket. These results show that modeling chess as a time-aware, sequential activity yields more human-accurate move prediction than position-only approaches, using a smaller model. Code, trained models, and complete training logs are publicly released.