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Development of the Best Tsume- Go Solver Akihiro Kishimoto

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

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

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Previous Work on Tsume-Go GoTools [Wolf:1994] 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

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Previous Work on Shogi Tsume-shogi solvers 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

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TsumeGo Explorer Search-based approach 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 Enhancements –Connections to safe stones –Forced moves –Simulation –Evaluation function to initialize proof and disproof numbers

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

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Forced Moves Forced attacker moves Forced attacker moves Forced defender moves

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Simulation [Kawano:96] Where to apply? Where to apply? P1 P2 A4 P5 Df-pn(r) P3P4 Simulation A4 Df-pn (r) wins OR nodeAND node

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Heuristic Initialization (1 / 2) Problem of df-pn based search 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 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)

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Heuristic Initialization (2 / 2) Heuristic distance to make two eyes Heuristic distance to make two eyes Heuristic distance to break eye spaces

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Problem of Heuristic Initialization Standard Df-pn Standard Df-pn Df-pn with heuristic initialization 1 11 Leaf nodes th.pn = Leaf nodes th.pn = 7 Result in more expansions of interior nodes pn OR nodeAND node

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Non-Uniform Threshold Control Compute average of evaluation values Compute average of evaluation values Use as a unit to increase thresholds Use as a unit to increase thresholds Achieve 20% node reduction for harder problems Achieve 20% node reduction for harder problems –Ratio of reexpanded node 45% ->33% Example 6 68 th.pn = 8 + (6 + 8) / 2 = 15 pn OR nodeAND node

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

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Performance in Wolf’s Test Collection # of Problems Execution # of Problems Execution Solved Time Solved Time GoTools 418 1,235 GoTools 418 1,235 TsumeGo Explorer TsumeGo Explorer Total Problems 418 Total Problems 418

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

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Comparison on Each Problem Wolf’s Test Problems

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

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

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

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Lessons Learned (2 / 2) Black to live 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)

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Summary Conclusions Conclusions –Successfully developed the best solver Future work 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

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

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