This video explains the minimax algorithm with alpha-beta pruning, focusing on a worked example to illustrate its application in game trees. The presenter, John Levine, details how Max (maximizing player) and Min (minimizing player) interact, the concept of utility, and the recursive nature of the max-value and min-value functions. The video contrasts the basic minimax approach with the efficiency gains provided by alpha-beta pruning, demonstrating how it prunes unnecessary branches of the search tree.
Here are some notes based on the video lecture:
Minimax Algorithm Basics:
max_value calls min_value, and min_value calls max_value, down to the terminal nodes.Parameters for max_value and min_value:
state: The current state of the game.alpha: The best alternative for Max on the current path (initialized to negative infinity).beta: The best alternative for Min on the current path (initialized to positive infinity).Minimax Without Alpha-Beta Pruning (Worked Example):
max_value.min_value and max_value down to terminal nodes (e.g., 4, 8).Minimax With Alpha-Beta Pruning:
alpha is negative infinity, beta is positive infinity.v) with the maximum of its children's values.alpha if a better value (v) is found (alpha = max(alpha, v)).alpha >= beta: If the current best option for Max (alpha) is worse than or equal to the best option for Min (beta) found so far on this path, Min will never choose this path. Stop exploring this branch.v) with the minimum of its children's values.beta if a better value (v) is found (beta = min(beta, v)).alpha >= beta: If the current best option for Min (beta) is worse than or equal to the best option for Max (alpha) found so far on this path, Max will never allow this path. Stop exploring this branch.alpha and beta values are passed down the tree during recursive calls.beta is 8, the condition alpha >= beta (specifically 9 >= 8 in this context, considering the perspective of the parent Min node) leads to pruning because Min would never choose a path that could lead to a score of 9 if it already has an option that guarantees a score of 8 or less.Efficiency: Alpha-beta pruning significantly reduces the search space compared to basic minimax, especially in deeper game trees. The assignment involves identifying pruning points in a similar example.