Plausible Move Generation Using Move Merit Analysis with Cut-off Thresholds in Shogi

1. Plausible Move Generation Using Move Merit Analysis with Cut-off Thresholds in Shogi Reijer Grimbergen(Electrotechnical Laboratory)

2. Contents • Full-width search and plausible move generation • Why plausible move generation in shogi? • A set of plausible move generators for shogi • Move Merit Analysis • Cut-off thresholds • Experimental results • Related work • Conclusions

3. Full-width Search and Plausible Move Generation • Full-width search • World championship level programs in chess, checkers and Othello. • Plausible Move Generation • Important in the early days of chess research. • Good alternative in domains where full-width search can not search deep enough: • Large average number of legal moves (e.g. Go, Shogi). • Single agent search problems with extremely long solution sequences (e.g. Sokoban).

4. Why Plausible Move Generation in Shogi? • High average branching factor (80) compared to chess (35). • Average branching factor increases as the game progresses. • Time constraints are strict.

5. Legal Moves in Shogi

6. Positional improvement Defend pins Tie improvement Defend undefended pieces Defend against exchange Cover squares in own camp Develop pieces Defend against positional improvement Pin piece Cover squares in enemy camp Avoid development Goal Capture Material Promote Piece Threat Check Attack king Attack material Discovered attack Threaten promotion Defend threat Defend checks Defend king Defend material Defend discovered attacks Defend against promotion Plausible Move Generator Set for Shogi

7. Move Merit Analysis • In this approach it is possible that moves are generated by more than one PMG. • Knowledge about which PMGs generated a move is used for analyzing the merit of a move. • Move Merit Analysis: Every PMG gives a value to the generated move based on the importance of the PMG. • E.g.: Winning a rook is more important than improving the position. • Possible performance improvements: • Move ordering is improved, aiding alpha-beta search. • Additional cuts are possible: discard all moves with a negative MMA value.

8. Cut-Off Thresholds • MMA values can be used for further cuts. • Cut-off thresholds: • Take the best N moves after MMA based move ordering. • Investigated N = 20, 30, 40, 50.

9. Experiments • Compare the behavior of: • PMG-All: Generate all moves from the plausible move generator set. • PMG-MMA: Generate all moves with a positive MMA value. • PMG-N: MMA based cut-off thresholds for N=20,30,40,50. • Experiments: • Plausible move generation test. • Move ordering test. • Search comparison test. • Self play experiment.

10. Plausible Move Generation Test (1)

11. Plausible Move Generation Test (2) • Savings and accuracy of PMG-All, PMG-MMA and PMG-N in 12097 test positions:

12. Only very few moves are ordered low by MMA Move Ordering Test

13. Only for PMG-MMA there is a significant improvement Search Comparison Test • Performance in 298 tactical shogi problems from Shukan Shogi:

14. Plausible move generation better than full-width search Move merit analysis important Self Play Experiment

15. Related work • IS Shogi • 10 Plausible move generators. • Strict ordering. • Kanazawa Shogi • Only plausible move generation in some special cases. • YSS • 30 Plausible move generators. • Plausible move generation related to search depth. • Kakinoki Shogi • 8 Plausible move generators. • Generate only tactical moves.

16. Conclusions • Plausible move generation can be an important alternative to full-width search. • Plausible move generation with move merit analysis significantly improves the performance of a shogi program. • Move merit analysis is vital for this method of plausible move generation. • There is some indication that by using cut-off thresholds the performance can be further improved.