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Choosing Subgames: Minimax Strategies and Temperature-Bounded Search

This paper explores the problem of choosing subgames to play, focusing on strategies such as minimax sorting moves and temperature-bounded search. It discusses previous and recent work, recent experiments, and new results. The paper also raises questions for future work.

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Choosing Subgames: Minimax Strategies and Temperature-Bounded Search

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

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

  3. 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? Problem Description

  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. 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 Sum of Means vs Hostrat Rollouts

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

  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?

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