Mini-Max Algorithm in Artificial Intelligence

The Mini-Max algorithm is a decision-making algorithm commonly used in artificial intelligence and game theory. It is used to determine the best move for a player in a two-player, zero-sum game. A zero-sum game is a game in which one player's gain is equal to the other player's loss.

In the Mini-Max algorithm, the player tries to maximize their own score while minimizing their opponent's score. The algorithm works by considering all possible moves and their resulting outcomes, then selecting the move that leads to the best outcome for the player.

Here is a simple example of the Mini-Max algorithm implemented in Python:

def mini_max(depth, node_index, maximizing_player, values, alpha, beta):
  # base case: leaf node is reached
  if depth == 3:
    return values[node_index]
  
  if maximizing_player:
    best_value = -float('inf')
    # loop through all children of the current node
    for i in range(0, 2):
      value = mini_max(depth + 1, node_index * 2 + i, False, values, alpha, beta)
      best_value = max(best_value, value)
      alpha = max(alpha, best_value)
      if beta <= alpha:
        break  # beta cut-off
    return best_value
  else:
    best_value = float('inf')
    # loop through all children of the current node
    for i in range(0, 2):
      value = mini_max(depth + 1, node_index * 2 + i, True, values, alpha, beta)
      best_value = min(best_value, value)
      beta = min(beta, best_value)
      if beta <= alpha:
        break  # alpha cut-off
    return best_value

# test the algorithm
values = [3, 5, 6, 9, 1, 2, 0, -1]
print(mini_max(0, 0, True, values, -float('inf'), float('inf')))  # should output 5

In this example, the mini_max function is a recursive function that takes in the current depth of the tree, the index of the current node, a boolean value indicating whether the maximizing player or the minimizing player is making the move, a list of values for each node in the tree, and alpha and beta values for alpha-beta pruning.

The base case of the function is when the depth of the tree is 3, at which point the function returns the value of the current node. Otherwise, the function loops through all the children of the current node and calculates the best value for either the maximizing player or the minimizing player, depending on the value of the maximizing_player parameter.

Alpha-beta pruning is a technique used to improve the efficiency of the Mini-Max algorithm by pruning off branches of the tree that will not be searched. This is done by keeping track of the best value for the maximizing player (alpha) and the best value for the minimizing player (beta) at each node, and pruning the tree when the value of beta is less than or equal to alpha.

This is just a basic example of the Mini-Max algorithm, and there are many other considerations and optimizations that can be made for more complex games.