In a game playing search tree, up to which depth α−β pruning can be applied?
(A) Root (0) level
(B) 6 level
(C) 8 level
(D) Depends on utility value in a breadth-first order
Choose the correct answer from the options given below:

Correct option is A

Alpha-Beta Pruning Overview:
Alpha-beta pruning is an optimization technique for the minimax algorithm used in game-playing AI to ignore branches of the search tree that cannot influence the final decision. The depth to which alpha-beta pruning can be applied depends on:
1. The structure of the game tree.
2. The utility values at different levels of the tree.
Analysis of the Question:
(A) Root (0) level: Alpha-beta pruning starts at the root level, but it is primarily applied as the algorithm traverses deeper into the tree.
(B) 6 levels: Alpha-beta pruning can work up to any level of the tree, including the 6th level, provided that utility values are available at the leaf nodes.
(C) 8 levels: Similarly, pruning can extend to the 8th level or further, depending on the size of the tree and computational resources.
(D) Depends on utility value in a breadth-first order: This option is misleading because alpha-beta pruning is applied in a depth-first traversal, not breadth-first.
Correct Answer Analysis:
(B) 6 level: Correct. Pruning can apply up to the 6th level.
(C) 8 level: Correct. Pruning can also apply up to the 8th level or deeper if the tree allows.
Thus, the correct answer is: (a) (B) and (C) only.
Information Booster:
1. Alpha-Beta Pruning Principles:
· Alpha: Best value that the maximizer currently guarantees.
· Beta: Best value that the minimizer currently guarantees.
2. Benefits of Alpha-Beta Pruning:
· Reduces the number of nodes evaluated.
· Allows deeper exploration of the game tree within the same computational resources.
3. Depth-First Traversal: Alpha-beta pruning operates on a depth-first traversal of the game tree, ensuring early termination of unpromising branches.
Additional Knowledge:
· Utility values are used to evaluate leaf nodes of the game tree.
· Breadth-first search is not applicable to alpha-beta pruning as it is not optimal for evaluating game trees.