Exercise 4        Name __________________        Score __/14

1. Give the Minimax values for the game tree at right.
2. Give the a-b values for the game tree at right. Show any pruning.
3. Is there any difference in left-to-right or right-to-left pruning?
4. Prove the following assertion: for every game tree, the utility obtained by MAX using minimax decisions against a suboptimal MIN will never be lower than the utility obtained playing against an optimal MIN.
5. Can you come up with a game tree in which MAX can do better using a suboptimal strategy against a suboptimal MIN?
6. What are the SUCCESSOR states of the following, assuming X moved first?
7. Give the Minimax values for the game tree with 3 players at right.