Research map / Learning theory and algorithms / Combinatorial and search optimization
Strength Estimation and Human-Like Strength Adjustment in Games
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes a strength estimator trained with a Bradley-Terry ranking softmax loss on human game records and SE-MCTS, an MCTS variant that biases selection toward actions matching a target strength score, for rank prediction and human-like strength adjustment in Go and chess.
Problem
Estimating a human player's strength from game records without direct interaction, and adjusting AI playing strength so that its moves resemble human play at a target rank rather than just calibrating win rate to 50%.
Approach
A neural strength estimator outputs a per-state-action strength score trained with a Bradley-Terry-style ranking softmax loss over ranks (with an extra weakest rank of random actions); the scores are averaged per rank and used inside MCTS selection via a penalty on the difference between node strength and the target strength.
Key results
- Strength estimator (SE_inf) achieves over 80% rank prediction accuracy with 15 Go games, versus 49% for supervised baselines after 100 games.
- SE_inf-MCTS reaches 51.33% average move-matching accuracy with human Go moves, versus 42.56% for SA-MCTS and 50.35% for vanilla MCTS.
- In chess, SE_inf achieves over 80% rank accuracy with 26 games and SE_inf-MCTS reaches 47.25% move-matching vs 46.56% for MCTS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SE-MCTS rather than strength-index adjustment | MCTS move selection for Go · Go human move prediction (average across ranks) | accuracy: 42.56% ± 0.28% -> 52.87% ± 0.28% | Helped |
| Use SE∞-MCTS rather than strength-index adjustment | MCTS move selection for chess · Chess human move prediction (average across ranks) | accuracy: 40.21% ±0.24% -> 47.25% ±0.24% | Helped |
| Use SE rather than supervised rank classification | Go game rank prediction · Go rank prediction, 100 games | accuracy: 49% -> 97.5% | Helped |
| Add the weakest-rank r∞ training examples (ablation) | SE-MCTS · Go strength adjustment | strength adjustment | Helped |
| Train without the weakest-rank r∞ examples (ablation) | SE-MCTS · Go strength adjustment | strength adjustment | Hurt |
| Train SE on all 11 ranks rather than only 2 or 3 ranks (ablation) | SE rank prediction · Go rank prediction | games needed to exceed 80% accuracy: 38 games (2-rank dataset) and 21 games (3-rank dataset) vs 15 games (all 11 ranks) | Helped |
| Use one action per game instead of all actions (ablation) | SE · Go rank prediction across 20 games | accuracy: 80% -> approximately 60% | Hurt |
| Predict using only the first 50 actions (ablation) | SE · Go rank prediction | accuracy | Hurt |
| Predict using only the last 50 actions (ablation) | SE · Go rank prediction | accuracy | Hurt |
| Use SE-MCTS rather than SE∞-MCTS (ablation) | MCTS strength adjustment · Go strength adjustment | strength adjustment | Hurt |
| Use SE∞-MCTS rather than SE-MCTS (ablation) | MCTS move selection for chess · Chess human move prediction (average across ranks) | accuracy: 38.93%$ .24% -> 47.25% ±0.24% | Helped |
Surprising findings
- The SE network without the extra weakest rank (r_infty) fails to adjust strength effectively, despite accurate rank prediction.
- Vanilla MCTS achieves higher human move-matching accuracy than SA-MCTS, which is a strength-adjustment baseline.
Limitations
- Strength estimator relies on human game records for training.
- Bradley-Terry model cannot capture intransitivity between players.
Experimental setup
Datasets: FoxWeiqi Go game records Lichess chess game records
Benchmarks: FoxWeiqi Go query dataset Lichess chess query dataset
Metrics: rank prediction accuracy move matching accuracy with human actions win rate against baseline Elo rating
Baselines: MCTS SA-MCTS SL-sum SL-vote
Builds on: AlphaZero Bradley-Terry model MiniZero SA-MCTS strength index
Closest papers by meaning
- Human-Aligned Chess With a Bit of Search (ICLR 2025 · similarity 0.87)
- Maia-2: A Unified Model for Human-AI Alignment in Chess (NeurIPS 2024 · similarity 0.87)
- Designing Skill-Compatible AI: Methodologies and Frameworks in Chess (ICLR 2024 · similarity 0.84)
- Mastering Board Games by External and Internal Planning with Language Models (ICML 2025 · similarity 0.82)
- A Unified Perturbation Framework for Analyzing Leaderboard Stability and Manipulation (NeurIPS 2026 · similarity 0.81)
- AssistanceZero: Scalably Solving Assistance Games (ICML 2025 · similarity 0.81)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.