MiniMax

1
Mini-Max

• Winter 2005
• Lab 05/06 Lecture Supplement
• Jan. 21, 2005

2
Mini-Max

• Search strategy used in two player games
• Using AND-OR graphs
• Alternating levels of (my move / OR) and
  (opponents move / AND)
• Both my moves and opponents moves try to
  maximize each players outcome
• Scoring
• My move maximize my score (max level)
• Opponents move maximize own score
• i.e. minimize the players score (min level)

3
Mini-Max Drawbacks

• Exponential search time (expanding all nodes in
  the tree)
• Usually fixed depth of the tree cant see over
  the fixed depth (horizon effect)

4
Mini-Max Example

• Example slides follow
• Note that the algorithm would need to follow some
  kind of recursive strategy to visit the nodes in
  the bottom-up order.
• We have simplified this by working on one whole
  level at a time.

5
max
min
max
min
max
3
5
2
7
10
4
2
3
6
1
1) Final configuration scores computed by a
heuristic from game configurations at themaximum
depth value.
6
max
min
max
min
1
4
3
2
2
3
max
3
5
2
7
10
4
2
3
6
1
2) Compute min values of the final configuration
values.
7
max
min
max
3
4
2
3
min
1
4
3
2
2
3
max
3
5
2
7
10
4
2
3
6
1
3) Compute max values of the children.
8
max
min
3
2
max
3
4
2
3
min
1
4
3
2
2
3
max
3
5
2
7
10
4
2
3
6
1
4) Compute min values of the children.
9
max
3
min
3
2
max
3
4
2
3
min
1
4
3
2
2
3
max
3
5
2
7
10
4
2
3
6
1
5) Finally, compute our max score value.
10
max
3
min
3
2
max
3
4
2
3
min
1
4
3
2
2
3
max
3
5
2
7
10
4
2
3
6
1
So, the selected node represents the next best
move for the player in order to maximize the
players chances of winning.