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
Plausible Move Generator Set for Shogi

• 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

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
  N20,30,40,50.
• 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

Version NG Accuracy Savings
PMG-ALL 81 99.4 23.7
PMG-MMA 144 98.8 46.5
PMG-50 178 98.6 51.2
PMG-40 231 98.1 54.2
PMG-30 401 96.7 59.2
PMG-20 892 92.7 68.0
12
Move Ordering Test
13
Search Comparison Test

• Performance in 298 tactical shogi problems from
  Shukan Shogi

Cat Total FW All MMA N50 N40 N30 N20
1 50 17 21 22 21 23 23 22
2 50 9 8 13 12 12 13 10
3 50 10 10 11 11 12 10 11
4 50 9 7 8 8 9 9 8
5 50 5 4 4 4 4 5 7
6 48 4 5 6 6 6 6 6
Tot 298 54 55 64 62 66 66 64
14
Self Play Experiment
No Vers. 1 2 3 4 5 6 7 P Res
1 N20 X 10-10 11-9 11-9 11-9 16-4 17-3 5.5 76-44
2 N30 10-10 X 11-9 13-7 10-10 16-4 20-0 5 80-40
3 MMA 9-11 9-11 X 12-8 12-8 15-5 20-0 4 77-43
4 N40 9-11 7-13 8-12 X 11-9 18-2 19-1 3 72-48
5 N50 9-11 10-10 8-12 9-11 X 17-3 18-2 2.5 71-49
6 All 4-16 4-16 5-15 2-18 3-17 X 16-4 1 34-86
7 FW 3-17 0-20 0-20 1-19 2-18 4-16 X 0 10-110
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.