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Uncertain Reasoning in Games

This paper explores advanced techniques in game tree search, focusing on both deterministic and stochastic games with perfect and imperfect information. It highlights classical algorithms like MiniMax and Alpha-Beta pruning, while introducing advanced search methods and statistical evaluations to enhance performance. The effectiveness of transposition tables, iterative deepening, and various evaluation functions are presented, showcasing a 10% performance improvement with BNS. The study also addresses issues in multi-player games and approximations, offering insights into future research directions.

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Uncertain Reasoning in Games

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  1. Uncertain Reasoning in Games Dmitrijs Rutko Faculty of Computing University of Latvia LU and LMT Computer Science Days at Ratnieki, 2011

  2. Game Tree Search • Deterministic / stochastic games • Perfect / imperfect information games

  3. Finite zero-sum games

  4. Game trees

  5. max 8 min 2 8 max 2 7 8 9 1 2 7 4 3 6 8 9 5 4 √ √ √ Χ Χ √ √ √ Χ Χ Classical algorithms • MiniMax • O(wd) • Alpha-Beta • O(wd/2)

  6. Advanced search techniques • Transposition tables • Time efficiency / high cost of space • PVS • Negascout • NegaC* • SSS* / DUAL* • MTD(f)

  7. max ≥5 min <5 ≥5 max <5 ? ≥5 ≥5 1 2 7 4 3 6 8 9 5 4 √ √ Χ Χ Χ √ Χ √ Χ Χ Uncertain Reasoning • O(wd/2) • More cut-offs

  8. Game tree statistical evaluation

  9. Fmin Fmax FX FX FX FX Game tree analytical evaluation Probability density Cumulativedistribution

  10. Fmin Fmax FX FX FX FX Game tree analytical evaluation

  11. Cumulative probability function by level

  12. Probability density function by level

  13. Relative performance (Leaf nodes visited)

  14. Hey! That's My Fish!

  15. Evaluation function Fish Amount (player) – Fish Amount (opponent)

  16. Iterative deepening

  17. Number of positions searched

  18. Relative number of positions searched

  19. Relative time elapsed

  20. Conclusions and Future Work • BNS gives a 10 percent performance improvement • Transposition tables • Different evaluation functions • Multi-player game • Approximation search

  21. Questions ? dim_rut@inbox.lv

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