1. Choose A Subgame to Play by Zhichao “Leaf” Li January 27 th, 2004

2. Choose a Subgame to Play Problem Description Previous Work Recent Work Recent Experiments Some New Results Future Experiments and Work

3. Problem Description Given a Game with Several Subgames Subgame 1: 0 | -1 Subgame 2: 0 | -2 || -3 Subgame 3: 5 || 2 | 0 Problem: Choose Which Subgame to Play?

4. Privious Work Minimax Sort Moves by Temperatures Prune Moves by Incentives Hotstrat Thermostrat Depth-bounded Alphabeta Search use Hotstrat Rollouts

5. Recent Work Minimax Iterative Deepening Try Playing ‘Best Move’ First Static Evaluation Hotstrat Rollouts Static Function: Sum of Means of Subgames (with/without half Highest Temperature bonus) Temperature-bounded Alphabeta Search

6. Sort Moves in Minimax (2-level) IncentivePruning = off Temp = Sort by Temperature Best = Play Best Move first Run Time in 2-Level Games 2 3 4 5 6 7 8 9 Temp Best No No 0 0 0 1 3 15 92 1612 No Yes 0 0 0 1 2 9 44 270 Yes No 0 0 0 1 1 5 26 134 Yes Yes 0 0 0 1 1 6 32 159

7. Sort Moves in Minimax (3-level) IncentivePruning = off Temp = Sort by Temperature Best = Play Best Move first Run Time in 3-Level Games 2 3 4 5 6 Temp Best No No 0 1 6 55 997 No Yes 0 1 2 16 143 Yes No 0 1 1 12 101 Yes Yes 0 1 1 13 117

8. Sum of Means vs Hostrat Rollouts When use Sum of Means as static function, could not tell with or without t/2 bonus better Sum of Means is faster than Hotstrat Rollouts, but Sum of Means is not as precise as Hotstrat Rollouts

9. Sum of Means vs Hostrat Rollouts 100 2-level 5-Subgame Games: no t/2 with t/2 hotstrat rollouts MinMin - DepMin 66 99 21 MinDep - MinMin 105 102 14 100 3-level 5-Subgame Games: no t/2 with t/2 hotstrat rollouts MinMin - DepMin 201 243 88 MinDep - MinMin 172 151 59

10. Temperature-bounded Alphabeta Search Set a Temperature Bound, when the highest temperature is lower than it, stop search Now, we set the bound = Highest Temperature * Factor (=0.8) What Factor should be as best?

11. Depth-bounded vs Temperature -bounded use static evaluation, Depth-bounded is better than Temperature-bounded; use hotstrat rollouts, temperature-bounded is better in most cases

12. Future Work How to set the bound for Temperature- bounded search? Other methods to improve Alphabeta search? Try to apply the strategies on some practical endgames Others?