1 An Improved Safety Solver for Computer Go Presented by: Xiaozhen Niu Date: 2004/02/24

2 Outline n Introduction n Methods for processing regions n Search Enhancements n Experimental Results n Future Work

3 Introduction n Blocks and regions n Definitions n Structure of the safety solver

4 Blocks and Regions n Boundary blocks, interior blocks, merged regions

5 Definitions n Definition 1: A set of blocks is alive under alternating play in a set of regions R if there exist liberty targets LT(b,r) and a strategy S that achieves all these liberty targets in each r of R and: n Definition 2: We call a region r one-vital for a block b if b can achieve a liberty target of one in r, and two-vital if b can achieve a target of two.

6 Structure of the Safety Solver n 1. Call static solver. n 2. Call 2-vital solver for each region (size <30). n 3. Call expend-vital solver for regions that have some safe boundary blocks. n 4. Region Merging. For each small-enough merged region (size <=14), call 2-vital solver. n 5. Call 1-vital and 2-vital solver to deal with weakly dependent regions. n 6. Call expend-vital solver again for those regions for which one or more new safe boundary blocks have been found.

7 Methods for Processing Regions n Region merging. n Strongly and weakly dependent regions n External eyes.

8 Region Merging n Step 1: merge all related regions. n Step 2: handle weakly dependent regions

9 Strongly and Weakly Dependent Regions n Strongly dependent regions (more than 1 common boundary block) and weakly dependent regions (only 1). There are three weakly dependent region R1, R2, and F

10 Weakly Dependent Regions n For one region, the common boundary has X internal liberties. u Type 1: X >1 u Type 2: X=1

11 Weakly Dependent Regions n Type 2: the common boundary block only has 1 internal liberty.

12 External Eye n An external eye of the boundary block will be very helpful to reduce the liberty target for that block.

13 Search Enhancements n Move generation and move ordering n Evaluation function

14 Move Generation and Ordering n Move generation: u forced move n Move ordering: three priorities of attacker’s moves, for attacker’s move: u 1, it is close to empty cutting points u 2, it extends one or more cutting blocks u 3, using following formula to calculate scores, in here f1 = 10, f2 = 30, f3 = 20, f4 = 50, f5 = 100.

15 Evaluation Function u Heuristic evaluation function: NSR is the number of subrigions and NAB is the number of the attacker‘s active blocks, then: u Exact evaluation function: F HasSureLiberties(), quick F StaticSafe(), 5-10 times slower.

16 Experimental Results n Test set 1: 31 games played by amateur dan players. n Test set 2: 27 games played by professional players.

17 Experiment 1 n Overall Comparison of Solvers: u Benson: benson algorithm u Static-1997: static solver in 1997 u Search- 1997: 6 ply limit u Static-2004: current version of static solver u M1: basic 2-vital solver u M2: M1 + consider external eyes u M3: M2 + region merging u M4: M3 + move ordering u M5: M4 + heuristic evaluation function u M6: M5 + weakly dependent regions

18 Test Set 1 n T = 200 seconds

19 Test Set 2 n T = 200 seconds

20 Experiment 2 n Detailed comparison of solvers in test set 1. Static solver can prove 321 out of 802 regions safe, safety solver can prove 227, the remaining 254 have not been solved n We divide 227 regions to four group, very easy, easy, moderate, and hard by the CPU time used.

21 Group 1: Very Easy n Group 1 (25 regions): Most regions in this group is small (size <10). M1 can solve all within a time limit of 0.2s. M2-M6 can solve all within a time limit of 0.1s.

22 Group 2: Easy n Group 2 (62 regions). M3 solves all within 0.5s, M4-M6 solves all within 0.1s.

23 Group 2 Examples

24 Group 3: Moderate n Group 3 (87 regions):

25 Group 3 Examples

26 Group 4: Hard n Group 4 ( 53 regions): there are 20 weakly dependent regions that can not be solved by M1-M5.

27 Group 4 Examples

28 Future Work n An example of unsolved region by a 14-ply search within 200s.

29 Future Work n An example of multiple related regions

30 Future Work n Seki, double Ko. n Move generation, selective search? n Evaluation function.

31 n Thank you!