alpha-beta pruning – example - depaul...
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Alpha-Beta Pruning – Example
0 5 -3 25-2 32-3 033 -501 -350 1-55 3 2-35
Minimax on a 6-ply gameHorizon depth: h = 6
HeuristicEvaluation
Alpha-Beta Pruning – Example
0 5 -3 25-2 32-3 033 -501 -350 1-55 3 2-35
MAX
MIN
MAX
MIN
MAX
MIN
Alpha-Beta Pruning – Example
MAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
MAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
-3
MAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
-3
MAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
-3
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
-3 3
3
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
-3 3
3
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
5
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
= prunedMAX
MIN
MAX
MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
= prunedMAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
= prunedMAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
0= pruned
MAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
5
0= pruned
MAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
0= pruned
MAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3
0= pruned
MAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3
0= pruned
MAX
MIN
MAX
2MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3
0= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
0= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
0= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
-5
-5
0= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
-5
-5
0= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
-5
-5
1
1
= prunedMAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
-5
-5
2
2
2
2
1
1
= prunedMAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2
Alpha-Beta Pruning – Example
0
0
0
-3 3
3
0
2
2
2
1
1
-3 -5
-5
-5
1
2
2
2
2
1= pruned
MAX
MIN
1MAX
12MIN
MAX
0MIN
0 5 -3 3 -3 -3 0 2 -2 3 5 2 -5 0 1 5 1 - 03 5 55 3-3 2