1. Development of the Best Tsume-Go Solver
Akihiro Kishimoto

2. Today’s Talk My and Martin’s effort to develop Tsume-Go Explorer
Apply ideas behind one-eye solver to tsume-Go

3. Problem Description Crucial stones are given
Attacker tries to capture all crucial stones
Defender tries to live
Make two eyes
Seki
Play restricted to region
Example

4. Previous Work on Tsume-Go
GoTools [Wolf:1994]
Best tsume-Go solver for 15 years
Powerful rules for life/death detection
A lot of Go-knowledge written by hand
Naïve search algorithm
Limited to problems with 14 empty points

5. Previous Work on Shogi Tsume-shogi solvers
Powerful search algorithms [Nagai:2002]
A lot of shogi-specific knowledge
Simpler than Go-knowledge
Surpass best human players
Can solve problems over 100 moves

6. TsumeGo Explorer Search-based approach Enhancements
Df-pn(r) [Kishimoto & Mueller:2003, 2004]
Simple methods to detect terminal node
One or two point eyes, seki, no eye space enough to live
Enhancements
Connections to safe stones
Forced moves
Simulation
Evaluation function to initialize proof and disproof numbers

7. Connections to Safe Stones
Consider attacker’s connections [Mueller:97]
Promote unsafe stones to safe
Detect dead status earlier
Example

8. Forced Moves
Forced attacker moves
Forced defender moves

9. Simulation [Kawano:96] Where to apply? P1 A4 A4 Df-pn (r) wins P2 P3
OR node
AND node

10. Heuristic Initialization (1 / 2)
Problem of df-pn based search
Hates capturing stones
Apparently has large proof and disproof numbers
Use evaluation function to initialize proof and disproof numbers P1 P2
Leaf node
pn(P2) = 1 dn(P2) = 1
pn(P2) = evalPN(P2)
dn(P2) = evalDN(P2)

11. Heuristic Initialization (2 / 2)
Heuristic distance to make two eyes
Heuristic distance to break eye spaces 15 4 2 4 15 2 1 2 3 2 4 2 1 5 5 2 3

12. Problem of Heuristic Initialization
Standard Df-pn
Df-pn with heuristic initialization 6 1 6 6 1 1
th.pn = 7
th.pn = 2
Leaf nodes
Leaf nodes
Result in more expansions of interior nodes
OR node pn
AND node pn

13. Non-Uniform Threshold Control
Compute average of evaluation values
Use as a unit to increase thresholds
Achieve 20% node reduction for harder problems
Ratio of reexpanded node 45% ->33%
Example 6 6 8
th.pn = 8 + (6 + 8) / 2 = 15
OR node pn
AND node pn

14. Comparison with GoTools
Conditions
Athlon 2800XP+ 5 minutes/per problem
300 MB TT for Tsume-Go Explorer
Test suites
Hard 418 problems in Wolf’s collection
148 one-eye problems created by Martin

15. Performance in Wolf’s Test Collection
# of Problems Execution
Solved Time
GoTools ,235
TsumeGo Explorer
Total Problems

16. Performance in One-Eye Problems
Execution
# of Problems Time
Solved (119 Probs.)
GoTools
TsumeGo Explorer
Total Problems

17. Comparison on Each Problem Wolf’s Test Problems

18. Comparison on Each Problem One-Eye Problems (1 / 2)
Plots on problems solved by both programs

19. Comparison on Each Problem One-Eye Problems
Plot on problems solved only by TsumeGo Explorer

20. Lessons Learned (1 / 2) White to kill
GoTools’ knowledge work for small problems
GoTools solves statically
TsumeGo Explorer needs 3,159 nodes

21. Lessons Learned (2 / 2) Black to live
Need better search algorithm for harder problems
GoTools cannot solve within 5 minutes
TsumeGo Explorer needs 0.73 seconds (22,616 nodes)

22. Summary Conclusions Future work Successfully developed the best solver
Solve larger problems
Limited to between 22 and 27 empty points
C.f. GoTools 14 empty points
Solve open-boundary positions
Integration with the game-playing program

23. Next Target! Solved if Black plays first Unsolved if White plays first
750 seconds
16 million nodes
Unsolved if White plays first