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Game Playing: Chess, Go, and Simulation of War

This article explores the challenges and strategies involved in game playing, focusing on chess, go, and war simulation games. It discusses the contingency problems, the importance of co-work and co-work prevention in games like Mighty and Gostop, and the difficulty of solving complex games like chess. The article also delves into topics such as time limits, pruning, heuristic evaluation functions, perfect decisions in two-person games, the mini-max algorithm, and the Negmax algorithm. It concludes with discussions on imperfect decisions, evaluation functions, terminal tests, and alpha-beta pruning.

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Game Playing: Chess, Go, and Simulation of War

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  1. 8주 강의 Game Playing

  2. Games as search problems • Chess, Go • Simulation of war (war game) • 스타크래프트의 전투 • Claude Shannon, Alan Turing  Chess program (1950년대)

  3. Contingency problems • The opponent introduces uncertainty • 마이티에서는 co-work이 필요 • 고스톱에서는 co-work방지가 필요 • Hard to solve  in chess, 35100 possible nodes, 1040 different legal positions • Time limits  how to make the best use of time to reach good decisions • Pruning, heuristic evaluation function

  4. Perfect decisions in two person games • The initial state, A set of operators, A terminal test, A utility function (payoff function) • Mini-max algorithm, • Negmax algorithms

  5. Mini-max algorithm(AND-OR tree)

  6. 상대방의 관점

  7. Negmax • Knuth and Moore (1975) • F(n) = f(n), if n has no successors F(n) = max{-F(n1), …, -F(nk)}, if n has successors n1, …, nk

  8. The Negmax formalism

  9. Imperfect Decisions • utility function  evaluation • terminal test  cutoff test • Evaluation function ::: an estimate of the utility of the game from a given position • Chess  material value (장기도 유사) • Weighted linear function  w1f1+w2f2+….+wnfn

  10. Cutting off search • To set a fixed depth limit, so that the cutoff test succeeds for all nodes at or below depth d  iterative deepening until time runs out  위험이 있을 수 있다 • Quiescent posiiton ::: unlikely to exhibit wild swings in value in near future • Quiescent search :: Non-quiescent search  extra search to find quiescent position • Horizon problem

  11. Alpha-beta pruning • Eliminate unnecessary evaluations • Pruning

  12. Alpha-beta pruning Alpha cutoff Beta cutoff

  13. Negmax representation

  14. Example

  15. Games with Chance • Chance nodes  expected value • Backgammon, 윷놀이 • Expectimax value

  16. A backgammon position

  17. Comparision MAX A A 2 A 1 A 2 1 40.9 1.3 21 2.1 DICE .9 .1 .9 .1 .9 .1 .9 .1 20 30 1 400 MIN 2 3 1 4 20 20 30 30 1 1 400 400 2 2 3 3 1 1 4 4

  18. 숙제 • 5.6, 5.8, 5.11, 5.15, 5.16, 5.17

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