1. Games
CSE 473 – Autumn 2003

2. Alpha-Beta Pruning

3. Alpha-Beta MiniMax MinVal(state, alpha, beta){
if (terminal(state)) return utility(state);
for (s in children(state)){
child = MaxVal(s,alpha,beta);
beta = min(beta,child);
if (alpha>=beta) return child; }
return beta;
alpha = highest value choice along any path for MAX
beta = lowest value choice along any choice for min

4. Alpha-Beta MiniMax MaxVal(state, alpha, beta){
if (terminal(state)) return utility(state);
for (s in children(state)){
child = MinVal(s,alpha,beta);
alpha = max(alpha,child);
if (alpha>=beta) return child; }
return alpha;
alpha = highest value choice along any path for MAX
beta = lowest value choice along any choice for min

5. Alpha-Beta Pruning pruned (1) call MaxVal(B,10,…) (3)
(2) MinVal(C1…) returns 20
(6) beta=15 alpha=20 alpha>=beta true! immediately return to B B
(4) call MinVal(C2,20,…)
pruned
(5) call MaxVal(D,20,…) returns 15

6. Effect of Alpha-Beta Pruning
Best case: reduces number of nodes searched from O(bd) to O(bd/2)
Can double depth of search
Using good static evaluation function to order children gets close to best case in practice

7. Evaluation Functions
eval(s) = w1 * material(s) + w2 * mobility(s) + w3 * king safety(s) + w4 * center control(s) + ...
In practice MiniMax improves accuracy of heuristic eval function
But one can construct pathological games where more search hurts performance! (Nau 1981)

8. Learning Weights

9. Learning New Features Search for common patterns
Logistello (Buro 1997)

10. End-Game Databases Ken Thompson – all 5 piece end-games
Lewis Stiller – all 6 piece end-games
Refuted common chess wisdom: many positions thought to be ties were forced wins – 90% for white!
Is perfect chess a win for white?

11. The MONSTER
White wins in 255 moves
(Stiller, 1991)

12. Deep Blue wins - 1997 (3 wins, 1 loss, 2 draws)
Kasparov vs. Deep Blue
IBM team led by JC Tan
32 RISC processors VLSI chess engines
200 million positions per second
16 plies
Deep Blue wins (3 wins, 1 loss, 2 draws)
Kasparov Speaks!

13. Kasparov vs. Deep Junior
Israeli programmers Amir Ban & Shay Bushinsky
2M positions/sec
8 CPU, 8 GB RAM Win2000
15 plies
Strongest program ever!
Buy it for $100!
Deep Junior – August 2, 2003 Match ends in a 3 / 3 tie!