8 주 강의 Game Playing

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

Contingency problems The opponent introduces uncertainty 마이티에서는 co-work 이 필요 고스톱에서는 co-work 방지가 필요 Hard to solve  in chess, possible nodes, different legal positions Time limits  how to make the best use of time to reach good decisions Pruning, heuristic evaluation function

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

Mini-max algorithm (AND-OR tree)

상대방의 관점

Negmax Knuth and Moore (1975) F(n) = f(n), if n has no successors F(n) = max{-F(n 1 ), …, -F(n k )}, if n has successors n 1, …, n k

The Negmax formalism

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  w 1 f 1 +w 2 f 2 + ….+w n f n

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

Alpha-beta pruning Eliminate unnecessary evaluations Pruning

Alpha-beta pruning Alpha cutoff Beta cutoff

Negmax representation

Example

Games with Chance Chance nodes  expected value Backgammon, 윷놀이 Expectimax value

A backgammon position

Comparision A 1 A A 1 A MAX DICE MIN

숙제 5.6, 5.8, 5.11, 5.15, 5.16, 5.17