Enhancing Search Efficiency by Using Move Categorization Based on Game Progress in Amazons

1. Enhancing Search Efficiency by Using Move Categorization Based on Game Progress in Amazons Yoshinori Higashiuchi Saga University, Japan Reijer Grimbergen Yamagata University, Japan Advances in Computer Games 11

2. Outline • Amazons • Move categories in Amazons • Priority ordering of moves • Adjusting category priorities using game progress • Experimental results • Conclusions and future work Advances in Computer Games 11

3. Amazons • Two-player perfect information game • 1010 board with 4 Amazons each • A move consists of • Moving the Amazon like a chess queen • Shooting an arrow like a chess queen • Arrows stay on the board and can not be passed • The player who can not move any of his Amazons loses Advances in Computer Games 11

4. How to do a reasonable search in Amazons? Amazons • Main feature: large number of legal moves • 2176 moves in the initial position • 479 moves on average • Relatively new game • No expert players • No heuristics for good moves Advances in Computer Games 11

5. Improving search in Amazons • Step 1: improving efficiency of - search • Searching good moves first • Best move of previous iteration • Killer moves • History heuristic • Etc… • What are good moves in Amazons? Advances in Computer Games 11

6. Move categories in Amazons Advances in Computer Games 11

7. Move categories in Amazons Amazon and arrow block 3 opponent Amazons Advances in Computer Games 11

8. Move categories in Amazons Amazon and arrow adjacent to opponent, also blocking twice Advances in Computer Games 11

9. Move categories in Amazons Moving the threatened Amazon, also blocking twice Advances in Computer Games 11

10. Move categories in Amazons Blocking the Amazon that just moved with a free Amazon Advances in Computer Games 11

11. Move categories in Amazons • Moves can belong to different categories • Total number of combinations: 6,144 • Theoretically possible: 1,420 Advances in Computer Games 11

12. A i = P i B i Priority ordering of moves • Importance of categories Pi: The realization probability of category i Ai: Number of times a move from category i was played Bi: Number of positions where a move from category i was possible Advances in Computer Games 11

13. Priority ordering of moves Advances in Computer Games 11

14. Priority ordering of moves • We use the 1,420 theoretically possible categories • 11,000 games to find the realization probabilities • Realization probabilities for our four example moves: Advances in Computer Games 11

15. Adjusting category priorities • Step 2: adjusting the probabilities using game progress • The strategic features of Amazons change as the game progresses • Good moves change as the game progresses • Probabilities must change as well • Most basic progress measurement: move number • Grouping probabilities in intervals of 8 moves Advances in Computer Games 11

16. Blocking with the move Advances in Computer Games 11

17. Blocking with the arrow Advances in Computer Games 11

18. Adjusting category priorities Advances in Computer Games 11

19. Experimental results • Three program versions • No Move Categories (NMC) • No Game Progress (NGP) • Game Progress (GP) • Comparing search times to depth 3 • Using 1,521 positions from 30 games • Self-play experiments • Matches of 100 games with 10, 30 and 60 seconds per move Advances in Computer Games 11

20. Experimental results Advances in Computer Games 11

21. Experimental results Advances in Computer Games 11

22. Experimental results Advances in Computer Games 11

23. Experimental results Advances in Computer Games 11

24. Experimental results • Matches between the different versions Advances in Computer Games 11

25. Experimental results • Total self-play results Advances in Computer Games 11

26. Conclusions and future work • Conclusions • Using move categories is better than not using move categories • Using game progress is better than not using game progress • Future work • Investigate different ways to decide realization probabilities • Games against different programs • Different representation of game progress • Using game progress in other games Advances in Computer Games 11