Turn-Based Games. sources: http://www.game-research.com/ www.gamespot.com Wikipedia.org Russell & Norvig AI Book; Chapter 5 (and slides) My own. H é ctor Mu ñ oz-Avila. Turn-Based Strategy Games. Early strategy games was dominated by turn-based games Derivate from board games Chess
Chess, Go, rock-paper-scissors
Yes (if tree is finite)
Yes (against an optimal opponent)
evaluationFunction(state)Minimax algorithm with Imperfect Decisions
EF(state) = w1f1(state) + w2f2(state) + … + wnfn(state)
EF(n) = Utility(n)
If EF(state) > 3 then is almost-certain that blacks win
doubles depth of search
α is the value of the best (i.e., highest-value) choice found so far at any choice point along the path for max
If v is worse than α, max will avoid it
prune that branch
Define β similarly for minWhy is it called α-β?
Suppose we have 100 secs, explore 104 nodes/sec106nodes per move
e.g., depth limit (perhaps add quiescence search)
= estimated desirability of position
Eval(s) = w1 f1(s) + w2 f2(s) + … + wn fn(s)
f1(s) = (number of white queens) – (number of black queens), etc.
MinimaxCutoff is identical to MinimaxValue except
Does it work in practice?
bm = 106, b=35 m=4
4-ply lookahead is a hopeless chess player!