1. Game Representation:

   • The Minimax algorithm is used for deterministic, two-player, perfect-information games. Examples include chess, tic-tac-toe, and Connect Four.
   • In these games, players take turns making moves, and the outcome depends solely on the current state of the game.

2. Objective:

   • The goal is to find the best move for a player (usually called “Max”) while considering the opponent’s (usually called “Min”) counter-moves.
   • We want to maximize Max’s score and minimize Min’s score.

3. Recursive Evaluation:

   • The algorithm recursively evaluates the game tree. Each node represents a game state (board position).
   • For each node, it computes a value based on the utility of that state (e.g., winning, losing, or drawing).

4. Algorithm Steps:

   • Given the current state, generate all possible legal moves (children).
   • For each child:
     • If it’s Max’s turn, recursively evaluate the child and choose the maximum value.
     • If it’s Min’s turn, recursively evaluate the child and choose the minimum value.
   • Propagate these values up the tree until you reach the root.

5. Pseudocode:

   def minimax(state, depth, is_max):
       if depth == 0 or game_over(state):
           return evaluate(state)  # Evaluate the state (heuristic function)
       
       if is_max:
           best_value = -inf
           for child in generate_children(state):
               value = minimax(child, depth - 1, False)
               best_value = max(best_value, value)
           return best_value
       else:
           best_value = +inf
           for child in generate_children(state):
               value = minimax(child, depth - 1, True)
               best_value = min(best_value, value)
           return best_value
   

6. Heuristic Evaluation Function:

   • The evaluate(state) function assigns a score to a game state. It’s often domain-specific.
   • For chess, it might consider piece values, board control, and king safety.
   • For tic-tac-toe, it could be as simple as counting Xs and Os.

7. Alpha-Beta Pruning (Optimization):

   • Minimax can be slow due to the large search space. Alpha-beta pruning reduces unnecessary evaluations.
   • It maintains two values (alpha and beta) to prune branches that won’t affect the final decision.

Remember, the Minimax algorithm provides optimal play assuming both players play perfectly.