1 An Open Boundary Safety-of- Territory Solver for the Game of Go Author: Xiaozhen Niu, Martin Mueller Dept of Computing Science University of Alberta Presented by: Xiaozhen Niu

2 Outline Introduction Open Boundary Safety-of-Territory Solver Forward Pruning Techniques Experimental Results Conclusions and Future Work

3 Introduction Problem: In real games, most territories are not fully enclosed Safety solver 1.0 has several restrictions: The region has to be completely enclosed Does not consider external liberties Goal: estimating the safety of open boundary territories!

4 Example White plays first

5 Open Boundary Safety-of- Territory Solver New features of safety solver 2.0 Input parameters and goal setting Board partitioning Multiple searches for related goals

6 New Features Safety solver 2.0 has following new features: Search goals customized by different parameters Multi-searches to provide solutions for different goals Integration with full-board play in Explorer

7 Input parameters (1) A set of points (area) The color of the defender and attacker The color of the first player Boundary safe or territory safe?

8 Input parameters (2) Handle Seki External Liberties Who is the ko winner?

9 Search Goal Setting Safety solver 2.0 concentrates on proving area safe locally Does not consider connection problems Default search goal: Prove territory safe Handle seki Count external liberties No ko winner needs to be set initially

10 Board Partitioning Zone computing Zone merging

11 Zone Computing Use heuristic territory evaluation to partition the board into zones Zones are computed by using dividers, potential dividers

12 Zone Merging Two zones are related if they share one or more common boundary blocks Safety solver 2.0 extends the merging algorithm for enclosed zones by dealing with dividers

13 Example

14 Multiple Searches for Related Goals Switching which player plays first

15 Multiple Searches for Related Goals (2) Determining when external liberties affect the safety status of an area

16 Integration with Explorer Generate defending or invading move for zones Set move values by heuristics

17 Forward Pruning Techniques Two techniques for the defender: External moves Inner eyes

18 External Moves In a 12 interior points zone. Generate 20 moves for the attacker and 16 moves for the defender

19 Inner Eyes Inner eyes can be pruned for the defender

20 Experimental Results Two test sets. Set one: most from classic Guan Zi Pu. 60 main problem and 60 modified problems that has some external liberties added Set two: 20 problems from computer game play records

21 Test Set 1: Correctness Test Four Examples from set 1

22 Test Set 2: Game Play Test Goal: to test whether Explorer enhanced by the safety solver 2.0 is able to play the correct defending or invading move

23 Conclusions Safety solver 2.0 can provide evaluations for the safety status of open boundary areas Major limitation: size of the open area (current: 15)

24 Future Work: Flexible time control scheme using heuristics to select suitable problems to solve Get best try move Integrate other tactical solvers Measure playing strength improvements