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Uncertain Reasoning in Games. Dmitrijs Rutko Faculty of Computing University of Latvia. LU and LMT Computer Science Days at Ratnieki, 2011. Game Tree Search. Deterministic / stochastic games Perfect / imperfect information games. Finite zero-sum games. Game trees. max. 8. min. 2. 8. - PowerPoint PPT Presentation
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Uncertain Reasoning in Games
Dmitrijs RutkoFaculty of Computing
University of Latvia
LU and LMT Computer Science Days at Ratnieki, 2011
Game Tree Search
Deterministic / stochastic games Perfect / imperfect information games
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
Game trees
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
Game tree analytical evaluation
FX FXFX FX
Fmin
Fmax
Probability density
Cumulative distribution
Game tree analytical evaluation
FX FXFX FX
Fmin
Fmax
Cumulative probability function by level
Probability density function by level
Relative performance (Leaf nodes visited)
Hey! That's My Fish!
Evaluation function
Fish Amount (player) – Fish Amount (opponent)
Iterative deepening
Number of positions searched
Relative number of positions searched
Relative time elapsed
Conclusions and Future Work
BNS gives a 10 percent performance improvement
Transposition tables Different evaluation functions Multi-player game Approximation search
