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Uncertain Reasoning in Games
Dmitrijs RutkoFaculty of Computing
University of Latvia
LU and LMT Computer Science Days at Ratnieki, 2011
Finite zero-sum games
deterministic chance
perfect information chess, checkers, go, othello
backgammon, monopoly, roulette
imperfect information
battleship, kriegspiel, rock-paper-scissors
bridge, poker, scrabble
Classical algorithms
MiniMax O(wd)
Alpha-Beta O(wd/2)
1 2 7 4 3 6 8 9 5 4
2 7 8 9
2 8
8
√ √ √ Χ Χ √ √ √ Χ Χ
max
min
max
Advanced search techniques
Transposition tables Time efficiency / high cost of space
PVS Negascout NegaC* SSS* / DUAL* MTD(f)
Uncertain Reasoning
O(wd/2) More cut-offs
1 2 7 4 3 6 8 9 5 4
<5 ? ≥5 ≥5
<5 ≥5
≥5
√ √ Χ Χ Χ √ Χ √ Χ Χ
max
min
max
Game tree statistical evaluation
Minimax value
Tree count
25 1
26 5
27 11
28 38
29 124
30 206
31 252
32 189
33 111
34 42
35 14
36 7
1000
Conclusions and Future Work
BNS gives a 10 percent performance improvement
Transposition tables Different evaluation functions Multi-player game Approximation search