f1(s) = (number of white queens) (number of black queens), etc. Other features which ... Othello: human champions refuse to compete against computers, who are ...
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
What does it means?
Involves Animal Behave
A Two-player zero-sum discrete finite deterministic game of perfect information is a quintuplet:
( S , I , N , T , V ) where:
+1 for MAX (=win)
-1 for MIN (=loose)
0 for a draw.
For chess, b ≈ 35, m ≈100 for "reasonable" games exact solution completely infeasible
b … branching factor m … maximum number of moves
doubles possible depth of search doable in the same time
prune that branch
Suppose we have 100 secs, explore 104 nodes/sec106nodes per move
even with pruning not possible to explore the whole search space e.g. for chess!
e.g., depth limit (perhaps add quiescence search)
= estimated desirability of position
Eval(s) = w1 f1(s) + w2 f2(s) + … + wn fn(s)
w1 = 9 with
f1(s) = (number of white queens) – (number of black queens), etc.
Other features which could be taken into account: number of threats, good structure of pawns, measure of safety of the king.
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!
2-player algorithms (minimax, -, cutoff-eval) can be extended to multi-player in a straightforward way:
Expectiminimax next slide
Chance nodes have certain probabibilities.
where P(s) is the probability of reaching s (e.g.
probability of rolling a certain number with the dice)
What makes Game theory interesting in practice?