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Development of the Best Tsume-Go Solver

Development of the Best Tsume-Go Solver. Akihiro Kishimoto kishi@cs.ualberta.ca. Today’s Talk. My and Martin’s effort to develop Tsume-Go Explorer Apply ideas behind one-eye solver to tsume-Go. Crucial stones are given Attacker tries to capture all crucial stones

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Development of the Best Tsume-Go Solver

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  1. Development of the Best Tsume-Go Solver Akihiro Kishimoto kishi@cs.ualberta.ca

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

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

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

  8. Forced attacker moves Forced defender moves Forced Moves

  9. wins A4 Df-pn (r) Df-pn(r) Simulation Simulation [Kawano:96] • Where to apply? P1 A4 P2 P3 P4 P5 OR node ANDnode

  10. 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 Heuristic Initialization (1 / 2) P1 P2 Leaf node pn(P2) = 1 dn(P2) = 1 pn(P2) = evalPN(P2) dn(P2) = evalDN(P2)

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

  12. Standard Df-pn Df-pn with heuristic initialization Problem of 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 ANDnode pn

  13. 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 Non-Uniform Threshold Control 6 6 8 th.pn = 8 + (6 + 8) / 2 = 15 OR node pn ANDnode 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 418 1,235 TsumeGo Explorer 418 448 Total Problems 418

  16. Performance in One-Eye Problems Execution # of Problems Time Solved (119 Probs.) GoTools 119 957 TsumeGo Explorer 142 47 Total Problems 148

  17. Comparison on Each ProblemWolf’s Test Problems

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

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

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

  21. 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) Lessons Learned (2 / 2)

  22. Summary • Conclusions • Successfully developed the best solver • Future work • 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. Solved if Black plays first 750 seconds 16 million nodes Unsolved if White plays first Next Target!

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