1. Generalized Threats Search Paper Review Paper Author: T. Cazenave Review by: A. Botea

2. Overview Motivation Generalized Threats Generalized Threats Search (GTS) Experimental Results Conclusion

3. Motivation Threat Search works well in games such as Go or Go-Moku GTS: Generalizes the previously published threat algorithms (Abstract Proof Search, Lambda Search, Iterative Widening, Gradual Abstract Proof Search); Can be faster than other threat algorithms;

4. Generalized Trees Binary trees where players can play multiple moves in a row Two players: Left & Right Left branches are Left’s moves Right branches are Right’s moves

5. Generalized Threats (GTs) Generalized Threat: A set of generalized trees with some special properties Can be represented as tuples: o i = #of nodes followed by at most i left branches

6. Examples of GTs

7. Comparison of GTs Partial order relationship:

8. Comparison of GTs (2)

9. Composition of GTs

10. Composition of GTs (2)

11. Verification of GTs Map GT to a concrete move tree so that Left wins Check that: For each left branch there is a winning Left move For each right branch there are no Right moves that prevent Left from winning The local search used to verify a GT can be optimized

12. Optimizing GT verification At nodes that have left branches only: iterative widening At nodes with both left and right branches: divide-and-conquer Use abstract moves Ex. from Atari-Go: if Right strings have >2 liberties, 2-ply search won’t work

13. Generalized Threat Search Alpha-Beta Use GTs to speed-up search Forced moves for Right Ex: move 2 found by a (4,3,0) GT Forced moves for Left Ex: move 5 found by a (3,2,0) GT

14. Example

15. Experimental Results Atari-Go on a 6x6 board Compare: Alpha-Beta Lambda Search Gradual Abstract Proof Search Generalized Threats Search

16. Experimental Results

19. Conclusion Generalized Threat Search: More general than other threat search algorithms Also faster Applied to 6x6 Atari-Go Future Work: try GTS in other games such as Go, LoA, Phutball, Hex, Shogi, and Chess