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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.19446 |
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| _version_ | 1866914170734116864 |
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| author | Gür, Serkan |
| author_facet | Gür, Serkan |
| contents | This paper presents a novel class of information-theoretic strategies for solving the game of Mastermind, achieving state-of-the-art performance among known heuristic methods. The core contribution is the application of a weighted entropy heuristic, based on the Belis-Guias, u framework, which assigns context-dependent utility values to each of the possible feedback types. A genetic algorithm optimization approach discovers interpretable weight patterns that reflect strategic game dynamics. First, I demonstrate that a single, fixed vector of optimized weights achieves a remarkable 4.3565 average guesses with a maximum of 5. Building upon this, I introduce a stage-weighted heuristic with distinct utility vectors for each turn, achieving 4.3488 average guesses with a maximum of 6, approaching the theoretical optimum of 4.3403 by less than 0.2%. The method retains the computational efficiency of classical one-step-ahead heuristics while significantly improving performance through principled information valuation. A complete implementation and all optimized parameters are provided for full reproducibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Quality of Information: A Weighted Entropy Approach to Near-Optimal Mastermind Gür, Serkan Information Theory Computer Science and Game Theory This paper presents a novel class of information-theoretic strategies for solving the game of Mastermind, achieving state-of-the-art performance among known heuristic methods. The core contribution is the application of a weighted entropy heuristic, based on the Belis-Guias, u framework, which assigns context-dependent utility values to each of the possible feedback types. A genetic algorithm optimization approach discovers interpretable weight patterns that reflect strategic game dynamics. First, I demonstrate that a single, fixed vector of optimized weights achieves a remarkable 4.3565 average guesses with a maximum of 5. Building upon this, I introduce a stage-weighted heuristic with distinct utility vectors for each turn, achieving 4.3488 average guesses with a maximum of 6, approaching the theoretical optimum of 4.3403 by less than 0.2%. The method retains the computational efficiency of classical one-step-ahead heuristics while significantly improving performance through principled information valuation. A complete implementation and all optimized parameters are provided for full reproducibility. |
| title | The Quality of Information: A Weighted Entropy Approach to Near-Optimal Mastermind |
| topic | Information Theory Computer Science and Game Theory |
| url | https://arxiv.org/abs/2511.19446 |