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Language Models that Play Chess and Explain Their Moves

Adithya Bhaskar, Jeffrey Cheng, Danqi Chen

arXiv:2610.03695v1cs.CL

TL;DR

Chess engines play strongly but do not explain their moves, while language models can generate explanations but often struggle to choose strong moves. QUEEN combines an expert chess encoder and language model with iterative explanation distillation; it reaches a 2697 rating and produces explanations that are fluent and approach GPT-5.6-Sol in coherence.

  • Problem

    Chess engines provide strong play without natural-language reasoning, while language models often struggle to select strong moves, limiting the utility of their explanations.

    Source: §1 · p. 2, §3 · p. 4

  • Method

    QUEEN connects a silent expert chess encoder to a language model and iteratively distills explanations built from analyses of candidate-move positions.

    Source: §1 · p. 2, §3.1 · p. 4

  • Results

    2697 estimated rating, versus GPT-5.6-Sol (2071) and Gemini-3.1-Pro (2201); QUEEN also has a higher tactical-puzzle no-mistake rate than all baselines and explanations approaching GPT-5.6-Sol in coherence.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The framework is presented as a recipe for coupling language models with silent experts in domains including games, robotics, and computer use.

    Source: §1 · p. 2, §6 · p. 9

    Tactical-puzzle mistakes are defined as moves causing a 10% or greater drop in expected win rate relative to the Stockfish oracle.

    Source: §3.3 · p. 6

Abstract

from arXiv · show

Modern chess engines are silent experts: they play at a superhuman level, but do not offer explanations for their play. On the other hand, language models (LMs) can generate plausible-sounding explanations, but their weak playing strength limits the utility of their explanations. We introduce Queen, a 4B-parameter chess-language model that can explain its moves and plans while playing at the level of a typical Grandmaster. Our novel framework enables domain-specific reasoning through complementary components: an encoder-decoder architecture and an iterative distillation algorithm. This architecture integrates a silent expert chess encoder with an instruction-tuned LM through cross-attention, which we train via a question-answering curriculum to extract chess concepts from the encoder's representations. Building on this domain-adapted model, we iteratively improve its explanations with a natural-language analog of the Bellman update: the model analyzes the positions after its top candidate moves and consolidates them into an explanation of the current position, which is then distilled back into the model. Over seven iterations, our model gains over 900 Elo points (1782 to 2697), substantially surpassing all frontier models on both playing strength and puzzle accuracy, despite containing three orders of magnitude fewer parameters. Furthermore, LM-based evaluations show that our explanations are fluent and approach GPT-5.6-Sol (high) in coherence. The generality of our architecture and training procedure suggests a recipe for applying language models to domains where silent expert encoders are available, like games, robotics, and computer use.

1 INTRODUCTION

Chess engines play strongly but do not explain their reasoning, while language models can explain positions but often struggle to select strong moves. QUEEN combines an expert chess encoder with a language model and iterative explanation distillation, achieving strong play and explanations evaluated for accuracy, substantiation, and coherence.

1 INTRODUCTION

  • Existing chess engines do not communicate their reasoning, while language models often struggle to choose strong moves and frontier models carry substantial computational cost.Prior language-model approaches have largely focused on isolated puzzles rather than full games.Source: §1 · p. 2
  • The proposed architecture connects a silent chess encoder to a language-model decoder through cross-attention, trained with a curriculum from static board understanding to future move transitions.Figure 2 depicts Lc0 embeddings flowing into Flamingo blocks; previously trained parameters are frozen during domain adaptation.Source: §1 · p. 2, Figure 2 · p. 2
  • Iterative distillation combines child-position explanations and verdicts into a root-position explanation, then distills it back into the model to improve implicit search and look-ahead.The procedure is inspired by the Bellman value update and addresses why the chosen move is best and alternatives are inferior.Source: §1 · p. 2
  • QUEEN reaches an estimated rating of 2697, surpassing GPT-5.6-Sol (2071) and Gemini-3.1-Pro (2201), while its explanations are fluent and approach GPT-5.6-Sol in coherence.Its no-mistake rate on tactical puzzles is higher than all baselines.Source: §1 · p. 2
  • The architecture and iterative search-distillation procedure are presented as a recipe potentially extendable beyond chess to games, robotics, and computer use.The paper also evaluates explanations along accuracy, substantiation, and coherence.Source: §1 · p. 2

2 RELATED WORKS

Prior work includes strong chess engines, language models trained or adapted for chess, and systems that make chess expertise accessible through commentary or explanations. QUEEN is positioned as combining strong move selection with natural-language reasoning behind its choices.

Chess engines

  • Chess engines use search and position evaluation to select continuations; Transformer-based Lc0 and Google DeepMind engines achieve near-superhuman play.Maia and Allie instead predict moves human players of a given skill level would make.Source: §2 · p. 3

Language models and chess

  • Chess language-model research spans next-token training, capability-specific benchmarks, commentary, latent concept extraction, and recent move-explanation approaches.Kim et al. (2025) generate commentary conditioned on a given move, while I et al. (2026) also integrate silent-expert representations into a language model.Source: §2 · p. 3
  • Because explanation quality depends on move quality, QUEEN distinguishes itself from prior explanation methods through substantially greater chess-playing strength.The related-work discussion identifies playing ability as a prerequisite for useful explanations.Source: §2 · p. 3

3 QUEEN: OUR APPROACH

QUEEN pairs a chess encoder with a language-model decoder to generate move recommendations, principal variations, and explanatory prose. It trains the bridge to interpret chess representations, then iteratively distills search-consolidated explanations into the model.

3 QUEEN: OUR APPROACH

  • Explanations combine a best-move recommendation, predicted principal variation, and prose that explains the line and reasoning about alternatives.The paper presents these as the three components of a high-quality explanation.Source: §3 · p. 3

3.1 ARCHITECTURE

  • A Leela chess encoder supplies board representations to a pretrained LM decoder through gated cross-attention, including representations from earlier encoder layers.The model receives a FEN and text; the decoder can condition on the chess position throughout autoregressive text generation.Source: §3.1 · p. 4

3.2 DOMAIN ADAPTATION: INTERPRETING ENCODER HIDDEN STATES

  • A sequential QA curriculum trains the bridge to extract current-board features, reason about moves, reconstruct future positions, and reason about those positions.The encoder and decoder are frozen during adaptation; only bridge parameters and new token embeddings are trained, with earlier question types replayed to limit forgetting.Source: §3.2 · p. 5

3.3 ITERATIVE SEARCH DISTILLATION: IMPROVING EXPLANATION QUALITY

  • Iterative search distillation generates candidate explanations, examines child positions, consolidates their explanations, and fine-tunes the model on explanations that pass Stockfish checks.The procedure samples roughly 400K root positions and runs seven training iterations, promoting PAWN-8 to QUEEN.Source: §3.3 · p. 6

4 EVALUATIONS

The evaluations test move accuracy in full games, variation substantiation on held-out positions, and explanation coherence. QUEEN leads the evaluated models in playing strength and substantiation, while its prose is fluent but weaker in conceptual coherence.

4 EVALUATIONS

  • The evaluation defines accuracy through full-game Elo, substantiation through principal-variation metrics, and coherence through a frontier-LM judge.The coherence assessment distinguishes structural coherence, conceptual coherence, and fluency; baselines include three frontier LMs and C1-4B.Source: §4 · p. 7

4.1 ACCURACY ON FULL GAME SIMULATIONS

  • QUEEN reaches 2697 Elo, the highest rating among evaluated models, beating SOL by over 600 points and GEMINI by over 450 after a 915-point gain across seven iterations.The rating is estimated from full-game simulations against fixed opponents.Source: Table 1 · p. 7, §4.1 · p. 7

4.2 SUBSTANTIATION ON HELD OUT POSITIONS

  • QUEEN performs best across all substantiation metrics on tactical and general positions, beating GEMINI by 2 points on NMR and 9 points on FNMR.NMR measures mistake-free predicted principal variations; FNMR measures positions where the first predicted move is not a mistake.Source: Table 2 · p. 8, §4.2 · p. 8

4.3 COHERENCE UNDER FRONTIER LM JUDGING

  • All models are fluent; QUEEN scores 3.51 on structural coherence, tied with SOL, and 2.76 on conceptual coherence.The authors suggest that hallucinated motifs may propagate during consolidation and identify this as a method limitation.Source: Table 3 · p. 8, §4.3 · p. 8

5 ANALYSIS

The analyses test the contributions of QUEEN’s encoder and domain-adaptation curriculum, whether it merely reproduces Leela’s policy, and whether frontier-model seeding is necessary.

Ablations

  • Removing either the Leela encoder or domain-adaptation curriculum substantially degrades performance, indicating both are important for initialization before iterative search-distillation.The ablations are evaluated after GPT-5.6-Sol seeding, using Elo and first-move no-mistake rate.Source: §5 · p. 9, Table 4 · p. 9

(Dis)agreement with Leela

  • QUEEN chooses a move different from Leela on 538 of 1,000 positions with at least five near-optimal options, suggesting it does not simply reproduce Leela’s policy.The positions were selected for having at least five moves within 3% of the Stockfish-optimal move’s expected win rate.Source: §5 · p. 9, Table 5 · p. 9

Moving away from frontier LM annotation

  • The HCE variant shows a similar Elo-improvement trajectory to QUEEN, suggesting frontier-model distillation is not strictly necessary for learning to generate high-quality explanations.The alternative training data uses features from Stockfish’s hand-crafted evaluation to generate templatic explanations.Source: §5 · p. 9

6 CONCLUSION

The conclusion presents QUEEN as a framework for pairing language models with expert encoders and iterative improvement, with potential use beyond chess. The appendix also outlines the domain-adaptation materials and ablations.

6 CONCLUSION

  • Table 6 compares QUEEN performance with and without frontier-model distillation; the HCE variant uses data derived from Stockfish’s hand-crafted evaluation.Source: Table 6 · p. 9
  • The framework couples a language model with a pretrained expert encoder and provides iterative improvement for stateful environments, with potential applications in games, robotics, and computer use.The authors describe expert models as providing domain-specific representations and evaluations that language models can turn into accessible explanations useful for further reasoning.Source: §6 · p. 9

A DOMAIN ADAPTATION PHASE DETAILS

A.1 DATA PROCESSING

The appendix details the question types and data composition used in four-stage domain adaptation.

A.1 DATA PROCESSING

  • The four domain-adaptation phases are STATIC-CURRENT, DYNAMIC-CURRENT, STATIC-FUTURE, and DYNAMIC-FUTURE, with questions using newly introduced tokens and answers carrying machine-parsable correctness sequences.The table lists each task alongside a sample response; it omits the checking sequence.Source: §A.1 · p. 13, Table 7 · p. 13
  • The final-stage data mixture combines the described sources, while a small proportion of earlier-stage data is replayed to prevent forgetting.Source: Table 8 · p. 13

A.2 TRAINING AND EVALUATION

This section points to the four-stage curriculum’s training hyperparameters and reports held-out test-set accuracies.

A.2 TRAINING AND EVALUATION

  • Table 9 lists the four-stage curriculum’s training hyperparameters, with settings shared across stages listed once.The supplied passages do not give individual hyperparameter values.Source: Table 9 · p. 14, §A.2 · p. 14
  • Table 10 presents the model’s held-out test-set accuracies.The supplied passage identifies the table but does not include its accuracy values.Source: Table 10 · p. 14, §A.2 · p. 14

A.3 ABLATIONS

The ablations compare bridge architectures and decoder families, and report Flamingo outperforming LLaVA. They select SmolLM3-3B as the decoder based on its size and accuracy across the evaluated tasks.

A.3 ABLATIONS

  • Flamingo inserts 16 gated cross-attention blocks that pair encoder and decoder states, accumulating multi-scale board features into the decoder’s residual stream.The gate starts at zero, making cross-attention initially a no-op; the bridge has about 470M parameters.Source: §A.3 · p. 14
  • LLaVA projects the 16 encoder states per square into 64 prefix soft tokens, using learned file-and-rank embeddings to encode board geometry.The decoder is adapted with rank-16 LoRA; the bridge has about 83M trainable parameters.Source: §A.3 · pp. 14–15
  • The KV Projection bridge trailed Flamingo and LLaVA by roughly 5–10 percentage points across STATIC-question configurations and was dropped from later experiments.It had approximately 612M trainable parameters.Source: §A.3 · p. 15
  • The decoder ablation holds data, optimizer, and scheduler constant across SmolLM3-3B, Qwen3-4B, and Gemma3-4B.Family-specific tokenizer and stop-token handling use adapters.Source: §A.3 · p. 15
  • Flamingo outperforms LLaVA on held-out STATIC and DYNAMIC accuracy, and SmolLM3-3B is smaller and more accurate on three of four evaluated tasks.With Flamingo fixed, Gemma3 is weakest; its dynamic-future accuracy is 79.8%.Source: §A.3 · p. 15, Table 11 · p. 15

B.1 DATA PROCESSING

The data-processing procedure builds on a pool of seed positions, recursively examines candidate continuations, and consolidates selected child explanations into training examples. The appendix also describes the seeding and self-distillation training data and hyperparameter tables.

B.1 DATA PROCESSING

  • The seed pool combines 210K human-play positions, 115K Lichess puzzles, and 50–100K positions from model–Stockfish games, with benchmark positions deduplicated.At most six positions are selected per human game; skewed game positions are downsampled fivefold.Source: §B.1 · pp. 15–16
  • For each root, the model analyzes three candidate moves and their child positions; if all root moves are mistakes, the worst is replaced with Stockfish’s best move.Sampling recurses into a child when its analysis recommends a mistake or illegal move, or its evaluation differs from Stockfish by more than 10% win rate; recursion stops after five attempts.Source: §B.1 · pp. 16–17
  • Once a root is selected, Qwen3.8-27B consolidates its three child explanations, and the numerical evaluation is replaced with Stockfish’s evaluation at 100K nodes.Examples are discarded if the supplied principal variation is worse than the original model’s; iterations usually yield around 250K examples.Source: §B.1 · p. 16

B.2 HYPERPARAMETERS FOR ITERATIVE IMPROVEMENT

  • Initial GPT-5.6-Sol seeding uses 11,250 human-play and 3,750 puzzle positions, retaining 8,602 analyses that recommend legal moves losing at most 10% win rate.The prompting cost was $652.35.Source: §B.2 · pp. 17–18
  • Self-distillation iterations train on 150K–283K examples and use standardized hyperparameters, with each iteration initialized from the selected checkpoint of the preceding iteration.Tables 12 and 13 list the initial-seeding and iterative SFT hyperparameters, respectively.Source: §B.2 · p. 18, Table 13 · p. 18, Table 12 · p. 18

C EVALUATION DETAILS

The evaluation details specify game-based accuracy tests, held-out-position substantiation tests, and LM-annotated coherence evaluations.

C EVALUATION DETAILS

  • Each model plays four games against each of eight opponents, using two opening lines and both colors; frontier-LM games can cost more than $15 each.The opening lines are 1. e4 e5 2. Nf3 Nc6 and 1. d4 d5 2. c4 e6.Source: C EVALUATION DETAILS · p. 18, Table 14 · p. 19
  • Held-out-position substantiation evaluations use Stockfish with 1M nodes of search.Source: C EVALUATION DETAILS · p. 19
  • Coherence evaluations use GPT-5.6-Sol (high) as the LM judge, with Stockfish annotations generated at 1M nodes.Source: C EVALUATION DETAILS · p. 19

D ANALYSIS DETAILS

The HCE seed analyses combine searched continuations and plausible alternatives with feature-based prose. The QUEEN example illustrates a recommended move, critical line, and position evaluation.

D ANALYSIS DETAILS

  • HCE seed explanations combine engine search with templated descriptions of handcrafted evaluation features, considering candidate moves, continuations, inferior lines, and a best move.No frontier language model is used to write the seed explanations.Source: D ANALYSIS DETAILS · p. 19
  • The analysis tree begins with alpha–beta search to three ply, then extends forcing captures and checks, so three ply is not the final explanation length.When the side to move is not in check, the current evaluation may stand without extension; in check, legal escape replies are searched.Source: D ANALYSIS DETAILS · p. 19
  • Maia-suggested plausible mistakes supplement search-preferred moves, and a separate Stockfish judging pass evaluates retained continuations and can insert or extend variations.A move losing at least 10 percentage points in expected win rate relative to the best continuation is considered a mistake; tactical continuations may be extended by up to six rounds.Source: D ANALYSIS DETAILS · pp. 19–20
  • Refutations and supersessions are stated only when retained branches justify the comparison, which establishes preferences within the constructed tree rather than proving all legal continuations.For each narrated move, up to three salient handcrafted feature effects are verbalized using templates, alongside connective descriptions and a concluding critical variation.Source: D ANALYSIS DETAILS · p. 20

E.1 QUEEN

  • The recommended 13. Qc2 line proceeds through 13... Bd6, 14. Rad1, 14... Be6, 15. e4, and 15... dxe4, ending with a slight edge for the player.After 16. fxe4, the position is roughly balanced, with a small edge to the player.Source: §E.1 · p. 21
  • Against 13.e4’s line, which gives the opponent an approximately 0.32-pawn edge, 13.a3 leaves the position approximately equal; the 13.Qc2 evaluation is approximately 0.54 pawns for the player.The 13.a3 line allows adequate counterplay while the player retains a small space advantage.Source: §E.1 · pp. 21–22
  • 13. Qc2 is the recommended best move, with a critical line and an evaluation of approximately 0.54 pawns in the player’s favor.The critical line is Qc2 Bd6 Rad1 Be6 e4 dxe4 fxe4.Source: §E.1 · p. 22

E.2 QUEEN(HCE)

This section presents a chess example identifying Qc2 as White’s best preparation for e4 and defines the prompts and output conventions for structured analysis, chess-token translation, recursive consolidation, and explanation evaluation. The evaluation uses three independent axes: move-number correctness, conceptual hallucinations, and fluency.

E.2 QUEEN(HCE)

  • Qc2 is best: it supports e4 while preserving bishop flexibility, and the critical line Qc2 Bd6 e4 dxe4 fxe4 leaves White with a modest 0.5-pawn advantage.Black’s best reply is ...Bd6; the alternative ...Ng4 is inferior to e5, while 2. h3 allows ...b5 and roughly equal play.Source: §E.2 · pp. 22–23
  • Rc1 is solid but less flexible than Qc2; after ...b5 2. e4 dxe4 3. fxe4, White keeps space but Black’s queenside counterplay provides compensation.The alternative 2. a3 concedes the initiative, while 2. Qc2 allows ...b4 and ...c5.Source: §E.2 · p. 22
  • Immediate e4 is premature: after ...dxe4 and ...Ng4, the position is approximately equal, while 2. Bc2? allows ...exf3 and a clear Black advantage.After 2. Bxe4 Nxe4 3. fxe4 Bd6, Black obtains the bishop pair and a comfortable game.Source: §E.2 · p. 23

F PROMPTS

  • The seed-analysis prompt requests positional features, candidate moves, a best move and critical line, promising legal root moves, and a numerical evaluation from White’s perspective.The requested output has five labeled fields: analysis, best move, critical line, promising moves, and evaluation.Source: F PROMPTS · p. 23

ALLOWED TOKENS

  • Translation replaces chess references with absolute-color piece, player, square, file, rank, and diagonal tokens, while prose moves use structured tokens for moves, captures, and promotions.The translator resolves abbreviated SAN and natural-language moves from the FEN and variation context.Source: ALLOWED TOKENS · p. 24

MOVE NUMBERS

  • The decoder prompt asks QUEEN to analyze a position, identify its best move and critical line, list promising moves, and evaluate the position.Its output uses five fields and the prescribed absolute machine vocabulary for chess references.Source: MOVE NUMBERS · pp. 24–25
  • For consolidation, child evaluations are from the opponent’s perspective, so the root candidate with the lowest signed opponent evaluation is selected as the mandatory best move.The consolidated analysis restores the root player’s perspective and restarts move numbering from the root.Source: MOVE NUMBERS · p. 25
  • Consolidation synthesizes three child analyses into a root analysis, emphasizing the best candidate and organizing content from general features to concrete plans and variations.It compresses overlap and inferior branches, and excludes any continuation beyond a child line’s mechanically identified truncation boundary.Source: MOVE NUMBERS · pp. 25–26
  • Move-number scores range from 1 for entirely hallucinated moves to 5 for no blunders or illegal moves.Intermediate scores reflect how many moves are correct and whether mistakes change the evaluation of moves near the root position.Source: MOVE NUMBERS · p. 27
  • Conceptual-hallucination scores assess whether claimed themes fit the position, with penalties scaled by their effect on the analysis’s coherence.Examples include falsely calling a move a fork or claiming a development lead that does not exist; structural hallucinations are excluded from this axis.Source: MOVE NUMBERS · pp. 27–28
  • Fluency scores whether explanations justify moves, consider alternatives, and use legible, grammatical English, from absent justification at 1 to fully comprehensible prose at 5.The axes are judged independently, and all three scores are required as integers.Source: MOVE NUMBERS · pp. 28–29
  • Piece-token outputs and reflected-board conventions, including reversed move numbering or light/dark-square labels, are not penalized.The instructions specifically exempt tokens such as <WHITE_ROOK> and <SQUARE_A5>.Source: MOVE NUMBERS · pp. 28–29
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