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Implementing the Minimax Algorithm for AI in Python

Learn to code an unbeatable Tic-tac-toe AI using the Minimax algorithm in Python. This tutorial covers theory, implementation, and optimization, ideal for game AI enthusiasts.
Jan 31, 2025  · 14 min read

The Mini-Max algorithm has a rich history in AI, dating back to the 1920s. While the term AI was not used for computer algorithms at that time, the foundational algorithm certainly gave some of the earliest insights into how machines could make optimal decisions in adversarial scenarios. The algorithm was first formalized by John von Neumann in his 1928 paper “Zur Theorie der Gesellschaftsspiele” (On the Theory of Games of Strategy), which laid the groundwork for modern game theory and decision-making algorithms.

In 1997, IBM’s Deep Blue defeated world chess champion Garry Kasparov using the advanced variants of Mini-max. Since then, the algorithm has been the backbone for more sophisticated approaches like Monte Carlo Tree Search (MCTS) and reinforcement learning systems.

In this article, we won’t rebuild the famous Deep Blue for chess but a far simpler version for tic-tac-toe in Python. Along the way, you will gain a strong intuition into how the algorithm works and how to apply it to more complex real-world games.

What is the Minimax Algorithm?

Minimax is usually a decision-making algorithm for two-player games (like chess, tic-tac-toe, or checkers). It allows computers to plan several moves while assuming your opponent will always make their best possible move. In this section, we will look at an overview of the algorithm through the example of tic-tac-toe.

Overview of the Minimax algorithm

In a real-world tic-tac-toe, every time it’s your turn, you try to make the best move possible while assuming your opponent will also play their best. This is exactly what the Minimax algorithm does — it helps a computer make the best possible move by thinking ahead about all possible moves.

The Minimax algorithm gets its name from how it works:

  • “Mini” represents the opponent trying to minimize your score
  • “Max” represents you trying to maximize your score

When it’s your turn, you want to make moves that give you the best chance of winning (maximizing). When it is your opponent’s turn, you assume they’ll make moves that give you the worst outcome (minimizing).

The importance of Minimax in AI

Minimax is highly important in artificial intelligence for several reasons:

  1. It helps computers make smart decisions in two-player games
  2. It’s the foundation for many modern game-playing AI systems
  3. It teaches computers how to think ahead and plan moves

The coolest part? This same idea is used in lots of real-world applications:

  • Video game AI opponents
  • Strategy games like chess and checkers
  • Even some business decision-making tools

While Minimax might sound complicated, it’s really just teaching a computer to think like a careful player who considers both their moves and their opponent’s moves before making a decision.

Understanding the Minimax Algorithm

Let’s break down how Minimax works using a simple tic-tac-toe example. Imagine you’re playing as X, and the computer is O.

How the computer thinks

When it’s the computer’s turn, it follows these steps:

  1. Look at all possible moves it can make
  2. For each move, it imagines what you might do next
  3. It keeps thinking ahead until it reaches an end point (like someone winning or a tie)
  4. It picks the move that gives it the best chance of winning

Scoring the game

The computer can use a simple scoring system:

  • +10 points if the computer wins
  • -10 points if you win
  • 0 points if it’s a tie

Think of it like a tree of possibilities:

  • At the top is the current game board
  • Each branch is a possible move
  • At the bottom are all the possible results

Taking turns

The computer switches between two modes of thinking:

1. Maximizing mode (computer’s turn):

  • Looks for moves that get the highest score
  • Tries to win or force a tie

2. Minimizing mode (player’s turn):

  • Assumes you’ll make moves that get the lowest score
  • Prepares for your best possible moves

A simple example

Let’s say it’s the computer’s turn (X) in this game:

A sample state in a tic-tac-toe game to be solved with mini-max algorithm

The computer will:

  1. See it has 3 empty spots to choose from
  2. For each empty spot, it imagines all possible future moves
  3. Picks the move that leads to its best outcome
  4. In this case, it should select the bottom-middle corner to block your win

This way of thinking ahead helps the computer play a perfect game of tic-tac-toe every time!

Minimax Algorithm Pseudocode

Let’s break down how to write the Minimax algorithm step by step. Don’t worry if you’re new to pseudocode — think of it as writing out the steps in plain English before we turn it into actual code!

Step-by-step explanation

The Minimax function needs three main things to work:

  1. The current game board
  2. The depth (how many moves ahead we’re looking)
  3. Whether it’s the maximizing player’s turn (computer) or the minimizing player’s turn (human)

Here’s what the basic pseudocode looks like:

function minimax(board, depth, isMaximizingPlayer):
   # First, check if the game is over
   if game is won:
       return +10 if computer wins, -10 if human wins
   if game is tied:
       return 0

   # If it's the computer's turn (maximizing)
   if isMaximizingPlayer:
       bestScore = -infinity
       for each empty spot on board:
           make the move
           score = minimax(board, depth + 1, false)
           undo the move
           bestScore = max(score, bestScore)
       return bestScore

   # If it's the human's turn (minimizing)
   else:
       bestScore = +infinity
       for each empty spot on board:
           make the move
           score = minimax(board, depth + 1, true)
           undo the move
           bestScore = min(score, bestScore)
       return bestScore

While most pseudocode examples read in English and are perfectly understandable, the one above is different as it uses recursion. Recursion is when a function calls itself over and over to solve a bigger problem. Think of it like looking in a mirror that reflects another mirror — you see the same image repeated many times, getting smaller each time.

In our Minimax algorithm, we need recursion because we’re trying to look at all possible future moves in the game. Each time the function calls itself, it’s looking at the next move that could happen. 

This helps us figure out the best move by checking every possible way the game could play out, like a really smart player thinking “If I do this, then they might do that, then I could do this…” and so on until the game ends. To learn more about recursion, you can read our separate recursion tutorial.

Illustrative example

Let’s see how this works in a simple game situation:

1. Starting Position:

A sample state in a tic-tac-toe game to be solved with mini-max algorithm

2. The computer thinks:

  • “If I place X in any empty spot…”
  • “What would the human do next?”
  • “And what could I do after that?”
  • “Which move gives me the best final score?”

3. For each empty spot, the computer:

  • Makes a move
  • Checks if game is over
  • If not over, imagines the human’s best move
  • Keeps going until it finds an ending
  • Picks the move with the highest score

Think of it like chess — you’re always thinking “If I move here, they’ll move there, then I can move here…” but the computer can think about ALL possible moves at once!

The cool thing about this algorithm is that it always finds the best move possible, assuming both players play perfectly. It’s like having a crystal ball that shows you all the possible futures of the game!

Implementing Minimax for Tic-tac-toe Step-by-step

In this section, we will build an unbeatable tic-tac-toe AI powered by the Mini-max algorithm in pure Python. We will break down the implementation in simple steps and explain the intuition behind each one and how it fits into the bigger picture of the game.

Step 1: Defining a TicTacToe class

First, we define a class that holds all the necessary logic and methods we need to play a tic-tac-toe game with our computers:

class TicTacToe:
   def __init__(self):
       # Initialize empty board (using ' ' for empty squares)
       self.board = [" " for _ in range(9)]
       self.human_player = "O"
       self.ai_player = "X"

   def print_board(self):
       """Print the current state of the board"""
       for i in range(0, 9, 3):
           print(f"{self.board[i]} | {self.board[i+1]} | {self.board[i+2]}")
           if i < 6:
               print("---------")

   def available_moves(self):
       """Returns list of available moves (indices of empty squares)"""
       return [i for i, spot in enumerate(self.board) if spot == " "]

Above, the __init__ method initializes a new game board as a list of 9 empty spaces (represented by spaces " "), with indices 0-8 representing the board positions from left to right, top to bottom. It also sets up two player symbols - "O" for the human player and "X" for the AI.

The print_board method provides a way to visualize the current state of the board. It prints the 3x3 grid with dividing lines between rows, showing each player's moves in their respective positions.

The available_moves method returns a list of all valid moves that can still be made. It does this by checking which positions on the board are still empty (contain a space " ") and returning their indices. This will be crucial for the minimax algorithm to know which moves it can consider.

These methods form the foundation that we’ll build upon to create our AI player using the minimax algorithm.

Let’s test them quickly:

>>> game = TicTacToe()
>>> game.print_board()
  |   | 
---------
  |   | 
---------
  |   |

>>> game.available_moves()
[0, 1, 2, 3, 4, 5, 6, 7, 8]

As expected, we have an empty board at the moment and all moves are available.

Step 2: Implementing methods for making a move and checking board states

Now, let’s add a method for making a move:

class TicTacToe:
   ...
  
   def make_move(self, position, player):
       """Make a move on the board"""
       if self.board[position] == " ":
           self.board[position] = player
           return True
       return False

We’ve added the make_move method which:

  • Takes a position (0–8) and player symbol (“X” or “O”) as input
  • Checks if the selected position is empty (“ “)
  • If empty, places the player’s symbol and returns True
  • If position is already taken, returns False without making any changes

Let’s make a few moves and check the remaining moves:

>>> game = TicTacToe()

>>> game.make_move(0, "X")
>>> game.make_move(1, "O")

>>> game.print_board()
 X | O | 
-----------
   |   | 
-----------
   |   |

>>> game.available_moves()
[2, 3, 4, 5, 6, 7, 8]

Working well. The next step is adding a method for checking if the board is full:

class TicTacToe:
   ...

   def is_board_full(self):
       """Check if the board is full"""
       return " " not in self.board

is_board_full is a boolean method that checks if there are any empty spaces left on the board.

Next, we add a method to check if a winning state is achieved:

class TicTacToe:
   ...

   def check_winner(self):
       """Check if there's a winner. Returns winner symbol or None"""
       # Check rows
       for i in range(0, 9, 3):
           if self.board[i] == self.board[i + 1] == self.board[i + 2] != " ":
               return self.board[i]

       # Check columns
       for i in range(3):
           if self.board[i] == self.board[i + 3] == self.board[i + 6] != " ":
               return self.board[i]

       # Check diagonals
       if self.board[0] == self.board[4] == self.board[8] != " ":
           return self.board[0]
       if self.board[2] == self.board[4] == self.board[6] != " ":
           return self.board[2]

       return None

The check_winner method evaluates the current state of the Tic-tac-toe board to determine if there is a winner. It checks all possible winning combinations:

1. Rows (3 possibilities):

  • Top row (indices 0,1,2)
  • Middle row (indices 3,4,5)
  • Bottom row (indices 6,7,8)

2. Columns (3 possibilities):

  • Left column (indices 0,3,6)
  • Middle column (indices 1,4,7)
  • Right column (indices 2,5,8)

3. Diagonals (2 possibilities):

  • Top-left to bottom-right (indices 0,4,8)
  • Top-right to bottom-left (indices 2,4,6)

For each combination, it checks if all three positions contain the same player symbol (X or O) and are not empty spaces. If a winning combination is found, it returns the winning player’s symbol. If no winner is found after checking all possibilities, it returns None.

Let’s test the function in winning and non-winning states:

game = TicTacToe()

# Winning state
game.make_move(0, "X")
game.make_move(1, "X")
game.make_move(2, "X")

>>> game.print_board()
 X | X | X
-----------
   |   | 
-----------
   |   |

>>> game.check_winner()
'X'

game = TicTacToe()

# Non-winning state
game.make_move(0, "X")
game.make_move(1, "O")
game.make_move(2, "O")
game.make_move(3, "X")

>>> game.print_board()
 X | O | O
-----------
 X |   | 
-----------
   |   |

>>> game.check_winner() is None
True

Finally, we add another boolean method to specify if the game is over or not:

class TicTacToe:
   ...

   def game_over(self):
       """Check if the game is over"""
       return self.check_winner() is not None or self.is_board_full()

The method returns True if either the winner is found or the board is full.

At this point, we have built all the core game mechanics:

  • The board is represented as a list of 9 squares initialized empty
  • print_board() displays the current game state visually
  • available_moves() returns indices of empty squares
  • make_move() places a player's symbol on the board
  • check_winner() examines rows, columns and diagonals for a win in each move
  • is_board_full() determines if no moves remain
  • game_over() combines winner check and full board check

These methods provide the foundation needed to create a playable game, handling all the basic operations like making moves and determining the game state.

Now comes the critical part — giving the computer the “brains” to play the game with Minimax.

Step 3: Implementing Minimax for tic-tac-toe

Now, let’s implement the algorithm for the game in a new method:

class TicTacToe:
   ...

   def minimax(self, depth, is_maximizing):
       """
       Minimax algorithm implementation
       Returns the best score possible for the current board state
       """
       # Base cases
       winner = self.check_winner()
       if winner == self.ai_player:
           return 1
       if winner == self.human_player:
           return -1
       if self.is_board_full():
           return 0

The function takes two parameters:

  • depth - Tracks how many levels deep we are in the recursion. This can be used to limit search depth for very complex games, though for tic-tac-toe we don't need to limit it.
  • is_maximizing - A boolean flag indicating whether we're currently looking for the maximum score (AI's turn) or minimum score (human's turn). This alternates with each recursive call as players take turns.

In the function body, we start by defining the base cases: If the game is won by the AI (winner == ai_player), we return 1 as this is the best possible outcome for the AI. If the human wins (winner == human_player), we return -1 as this is the worst outcome for the AI. If the board is full with no winner, we return 0 for a draw.

def minimax(self, depth, is_maximizing):
   ...

   # if it is the maximizing player's turn (AI), we want to maximize the score
   if is_maximizing:
       best_score = float("-inf")
       for move in self.available_moves():
           # Make a calculating move
           self.board[move] = self.ai_player
           # Recursively call minimax with the next depth and the minimizing player
           score = self.minimax(depth + 1, False)
           # Reset the move
           self.board[move] = " "
           # Update the best score
           best_score = max(score, best_score)
       return best_score

When is_maximizing is True, we're simulating the AI's turn and want to find the move that leads to the highest possible score. We start by setting best_score to negative infinity so any real score will be better. Then for each available move, we:

  1. Place the AI’s symbol on the board temporarily
  2. Recursively evaluate what would happen if we made this move by calling minimax with is_maximizing=False (since it would be the human's turn next)
  3. Undo the temporary move to restore the board state
  4. Keep track of the highest score we’ve seen so far using max()

This lets us check every possible move the AI could make. For each move, we look at what could happen next, all the way until someone wins or the game is tied. Then we work backwards to find which first move gives the AI the best chance to win.

Now, let’s do the minimizing part for the human:

def minimax(self, depth, is_maximizing):
   ...

   # if it is the maximizing player's turn (AI), we want to maximize the score
   if is_maximizing:
       ...

   else:
       # if it is the minimizing player's turn (human), we want to minimize the score
       best_score = float("inf")
       for move in self.available_moves():
           # Make a calculating move
           self.board[move] = self.human_player
           # Recursively call minimax with the next depth and the maximizing player
           score = self.minimax(depth + 1, True)
           # Reset the move
           self.board[move] = " "
           # Update the best score
           best_score = min(score, best_score)
       return best_score

When is_maximizing is False, we're simulating the human player's turn and want to find the move that leads to the lowest possible score (since a high score means the AI wins). We start with best_score as positive infinity so any real score will be lower. For each available move, we:

  1. Place the human’s symbol on the board temporarily
  2. Recursively evaluate what would happen by calling minimax with is_maximizing=True (since it would be the AI's turn next)
  3. Undo the temporary move to restore the board state
  4. Keep track of the lowest score we’ve seen using min()

This simulates the human player trying to make the best moves to prevent the AI from winning. The human wants to minimize the score since positive scores represent AI victories. By alternating between maximizing and minimizing turns, the algorithm can determine the optimal move sequence for both players.

Step 4: Finding the best move for AI using Minimax

Now that we have the algorithm ready, we need another method that uses the minimax method to determine the best move for the AI after each human move:

class TicTacToe:
   ...

   def get_best_move(self):
       """Find the best move for AI using minimax"""
       best_score = float("-inf")
       best_move = None

       for move in self.available_moves():
           # Make a calculating move
           self.board[move] = self.ai_player
           # Recursively call minimax with the next depth and the minimizing player
           score = self.minimax(0, False)
           # Reset the move
           self.board[move] = " "

           # Update the best score
           if score > best_score:
               best_score = score
               best_move = move

       return best_move

The get_best_move method is responsible for determining the optimal move for the AI player using the minimax algorithm. It works by:

1. Starting with negative infinity as the best score and no move selected

2. For each available move on the board:

  • Temporarily placing the AI’s symbol in that position
  • Using minimax to evaluate how good that move is by simulating the rest of the game
  • Undoing the temporary move
  • If this move leads to a better score than what we’ve seen before, updating both the best score and best move

3. Finally returning the move that led to the highest score

This approach ensures the AI will pick the move that gives it the best chance of winning, assuming the human player also plays optimally. The method considers all possible future game states and chooses the path that maximizes the AI’s chances while minimizing the human’s chances of winning.

Let’s test it on a sample game state:

game = TicTacToe()

# Make a couple of moves
game.make_move(0, "X")
game.make_move(1, "O")

# Print the board

>>> game.print_board()
X | O | 
---------
  |   | 
---------
  |   |

>>> game.get_best_move()
3

# AI moves
>>> game.make_move(3, "X")

# I move
>>> game.make_move(4, "O")
>>> game.print_board()
X | O | 
---------
X | O | 
---------
  |   |

# Get the best move for AI
>>> game.get_best_move()
6

As you can see, the AI found the winning combination based on my moves (it was a dummy state but this proves our algorithm is working).

Step 5: Implementing a game loop

Now that we have implemented and tested our minimax algorithm, let’s create a game loop that allows us to play against the AI.

class TicTacToe:

   ...

   def play_game(self):
       """Main game loop"""
       print("Welcome to Tic Tac Toe!")
       print("You are 'O' and the AI is 'X'")
       print("Enter positions (0-8) as shown below:")
       print("0 | 1 | 2")
       print("---------")
       print("3 | 4 | 5")
       print("---------")
       print("6 | 7 | 8")
       print("\n")

The play_game method starts by displaying a welcome message and instructions to the player. It shows that the human player uses ‘O’ and the AI uses ‘X’. It then prints out a numbered grid (0–8) to show the player which number corresponds to which position on the board. This makes it easy for players to know exactly which number to input for their desired move.

# ... the rest of the class
def play_game(self):
   ...

   # Randomly decide who goes first
   import random

   ai_turn = random.choice([True, False])

   while not self.game_over():
       self.print_board()

       if ai_turn:
           print("\nAI's turn...")
           move = self.get_best_move()
           self.make_move(move, self.ai_player)
       else:
           while True:
               try:
                   move = int(input("\nYour turn (0-8): "))
                   if 0 <= move <= 8 and self.make_move(move, self.human_player):
                       break
                   else:
                       print("Invalid move! Try again.")
               except ValueError:
                   print("Please enter a number between 0 and 8!")

       ai_turn = not ai_turn

After displaying the initial instructions, the game enters its main loop. The game randomly decides who goes first — either the AI or the human player — using random.choice([True, False]). This creates an element of fairness and unpredictability at the start of each game.

The main game loop continues until game_over() returns True (either someone has won or the board is full). During each turn, the current state of the board is displayed using print_board().

If it’s the AI’s turn (ai_turn is True), the program:

  1. Prints a message indicating the AI is thinking
  2. Calls get_best_move() to determine the optimal move using the minimax algorithm
  3. Makes the move by placing the AI’s symbol (‘X’) in the chosen position

If it’s the human’s turn (ai_turn is False), the program:

1. Enters a loop to get valid input from the player2. Prompts for a move number between 0–83. Validates the input is:

  • A valid integer (using try/except)
  • Within the valid range 0–8
  • Points to an empty position on the board

4. Keeps asking until valid input is received. Makes the move by placing the player’s symbol (‘O’) in the chosen position

After each turn, ai_turn is flipped using not to alternate between players. This creates the back-and-forth flow of the game, with each player taking turns until someone wins or the game ends in a draw.

The input validation ensures the game can’t crash from invalid user input and provides helpful error messages to guide the player to enter correct moves. This creates a robust and user-friendly game experience.

def play_game(self):
   ...
   # Game over
   self.print_board()
   winner = self.check_winner()
   if winner == self.ai_player:
       print("\nAI wins!")
   elif winner == self.human_player:
       print("\nCongratulations! You win!")
   else:
       print("\nIt's a tie!")

When the game ends, the final board state is displayed using print_board() and the winner is determined by check_winner(). The game can end in three ways:

  1. AI wins — If check_winner() returns the AI's symbol ('X'), indicating the AI has achieved a winning line
  2. Human wins — If check_winner() returns the human's symbol ('O'), indicating the player has achieved a winning line
  3. Draw/Tie — If neither player has won but the board is full, meaning no more moves are possible

The appropriate message is displayed to announce the game outcome. This provides clear feedback to the player about how the game concluded.

Step 6: Putting everything together

Now, it is time to put all the code we wrote so far into a Python script with the following if/main clause at the very end:

# Start the game
if __name__ == "__main__":
   game = TicTacToe()
   game.play_game()

This allows the game to start as soon as you run the script with python script.py. If you got lost among all the explanations and code blocks, you can find the full code for the game in this GitHub gist.

Here is a sample game that I played:

❯ python tic-tac-toe.py
Welcome to Tic Tac Toe!
You are 'O' and the AI is 'X'
Enter positions (0-8) as shown below:
0 | 1 | 2
---------
3 | 4 | 5
---------
6 | 7 | 8


  |   | 
---------
  |   | 
---------
  |   | 

Your turn (0-8): 4
  |   | 
---------
  | O | 
---------
  |   | 

AI's turn...
X |   | 
---------
  | O | 
---------
  |   | 

Your turn (0-8): 5
X |   | 
----------
  | O | O
----------
  |   | 

AI's turn...
X |   | 
---------
X | O | O
---------
  |   | 

Your turn (0-8): 6
X |   | 
---------
X | O | O
---------
O |   | 

AI's turn...
X |   | X
---------
X | O | O
---------
O |   | 

Your turn (0-8): 1
X | O | X
---------
X | O | O
---------
O |   | 

AI's turn...
X | O | X
---------
X | O | O
---------
O | X | 

Your turn (0-8): 8
X | O | X
---------
X | O | O
---------
O | X | O

It's a tie!

Remember, since tic-tac-toe is a simple game, there is no chance of beating the AI. It either ends in a tie or you lose!

Formalizing the Mini-max Algorithm

Now, let’s review the general definition of algorithm beyond the simple tic-tac-toe example.

The Minimax algorithm can be formally defined as a recursive function that evaluates positions in a zero-sum game. Let’s break down its formal components and properties.

Mathematical definition

For a game state s, the minimax value V(s) is defined as:

V(s) =
   utility(s)                    if s is terminal
   max(V(s')) for all s' in S    if player = MAX
   min(V(s')) for all s' in S    if player = MIN

Where:

  • s’ represents successor states of s
  • S is the set of all legal moves from state s
  • utility(s) is the evaluation function for terminal states

Key properties

1. Perfect information

  • All players have complete knowledge of the game state
  • No hidden information or chance elements
  • Deterministic outcomes

2. Zero-sum nature

  • One player’s gain is exactly equal to the other player’s loss
  • The sum of utilities for all players is always zero
  • For two-player games, utilities are typically {-1, 0, 1}

3. Optimal play

  • Assumes both players make optimal decisions
  • Guarantees the best possible outcome against perfect play
  • Leads to a Nash equilibrium in game theory terms

Complexity analysis

Time complexity: O(b^m)

  • b = branching factor (number of legal moves at each state)
  • m = maximum depth of the game tree

Space complexity: O(bm)

  • Requires storing the game state at each level
  • Can be optimized with iterative deepening

Evaluation function

For non-terminal states, the evaluation function f(s) should:

  1. Correlate with the probability of winning
  2. Be computationally efficient
  3. Maintain consistent scaling throughout the game

The formal definition:

f(s) = w₁x₁ + w₂x₂ + ... + wₙxₙ

Where:

  • wᵢ are weights for different features
  • xᵢ are feature values from the game state
  • n is the number of features being evaluated

Optimality guarantee

The Minimax algorithm guarantees optimal play under these conditions:

  1. Perfect information
  2. Deterministic outcomes
  3. Complete search to terminal states
  4. Accurate terminal state evaluation

This makes it particularly suitable for games like chess, tic-tac-toe, and checkers, where these conditions are met.

Advanced Variations and Limitations

While Minimax is great for simple games like tic-tac-toe, it has some problems with bigger games. Let’s look at how we can make it better and where it struggles.

Making Minimax faster: Alpha-beta pruning

Imagine you’re playing chess and thinking about your moves. If you’ve found a winning move, you don’t need to check all the other possible moves, right? Alpha-Beta Pruning works the same way — it helps the computer skip-checking moves that we already know won’t be better than what we’ve found.

Think of it like this:

  • You’re shopping for the cheapest candy bar
  • You have $1 to spend
  • If you find a candy bar for 50¢, you can skip looking at any candy bars that cost more than $1
  • This saves you time!

Depth limits: Not looking too far ahead

In big games like chess, there are too many possible moves to check them all. So we add a depth limit:

  1. Only look ahead 4–5 moves instead of all the way to the end
  2. Make a good guess about how good the position is at that point
  3. Choose the best move based on these guesses

You can’t plan every move until the end of the game, but you can plan a few moves ahead!

Where Minimax struggles

Minimax isn’t perfect. Here are its main problems:

1. Too many choices

  • Games like Go have way too many possible moves
  • Even fast computers can’t check them all
  • That’s why we need other methods for really complex games

2. Time problems

  • The more moves ahead you look, the longer it takes
  • In chess, computers can’t look at every possible move
  • They need to be smart about which moves to check

3. Not great for uncertain games

  • Minimax works best when you can see everything
  • It’s not good for card games where you don’t know what cards others have
  • It can’t handle random events well (like dice rolls)

Modern solutions

Today’s game AI often combines Minimax with other cool techniques:

1. Machine learning

  • Computers can learn from watching lots of games
  • This helps them make better guesses about good moves
  • Games like AlphaGo use this to beat human champions

2. Pattern recognition

  • Instead of checking every move, look for patterns
  • Just like how human players recognize good moves
  • This makes the computer much faster

3. Memory bank

  • Remember positions that have been seen before
  • Don’t waste time calculating the same thing twice
  • Like having a cheat sheet of good moves!

The coolest part? These improvements help computers play games almost as well as humans do, and sometimes even better! But remember — even with all these fancy additions, Minimax is still the foundation that makes it all work.

Conclusion

In this tutorial, we’ve explored the Minimax algorithm from its basic concepts to practical implementation. Here’s what we’ve learned:

1. Core concepts

  • How Minimax helps computers make decisions in games
  • The difference between minimizing and maximizing players
  • Why it’s called “minimax” and how it works

2. Implementation skills

  • Building a tic-tac-toe game from scratch
  • Writing the Minimax algorithm in Python
  • Testing and debugging game logic

3. Advanced topics

  • Making the algorithm faster with Alpha-Beta Pruning
  • Handling limitations in complex games
  • Modern improvements using machine learning

What’s Next?

The Minimax algorithm is just one piece of the AI puzzle. If you’re excited to learn more about AI and algorithms, here are some great resources to continue your journey:

1. Related Algorithms

2. Machine Learning Applications

3. Complete Learning Tracks

Remember, whether you’re building a simple game or a complex AI system, understanding algorithms like Minimax gives you a strong foundation for more advanced topics in artificial intelligence. Keep practicing, keep learning, and most importantly, keep coding!

Minimax Algorithm FAQs

How difficult is it to understand and implement the Minimax algorithm?

The Minimax algorithm is relatively straightforward to understand, especially when implemented for simple games like Tic-tac-toe. While the concept of recursion might be challenging for beginners, the basic principle of alternating between maximizing and minimizing moves is intuitive. This tutorial breaks down the implementation into manageable steps, making it accessible for programmers with basic Python knowledge.

Can I use this algorithm for other games besides Tic-tac-toe?

Yes, the Minimax algorithm can be adapted for many two-player, zero-sum games with perfect information, such as Chess, Checkers, or Connect Four. However, for more complex games, you'll need to implement additional optimizations like Alpha-Beta pruning and depth limiting, as the number of possible moves increases exponentially.

How does the AI never lose in Tic-tac-toe?

The Minimax algorithm works by simulating all possible future game states and choosing moves that lead to the best possible outcome. In a simple game like Tic-tac-toe, there are relatively few possible moves, allowing the AI to calculate the optimal move in every situation. Since Tic-tac-toe is a "solved game," perfect play by both sides always leads to a draw, which is why the AI can never lose.

What prior knowledge do I need to follow this tutorial?

You should have basic Python programming knowledge, including:

Understanding of functions and classes

Familiarity with lists and basic data structures

Basic control flow (if statements, loops)

Understanding of recursion is helpful but not required, as the tutorial explains the concept.

Why is this algorithm important for AI development?

The Minimax algorithm is fundamental to understanding game theory and decision-making in AI. It introduces important concepts like recursive tree search, adversarial thinking, and optimal decision-making under perfect information. These principles form the foundation for more advanced AI algorithms used in modern applications, from game playing to strategic planning and decision support systems.


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Author
Bex Tuychiev
LinkedIn

I am a data science content creator with over 2 years of experience and one of the largest followings on Medium. I like to write detailed articles on AI and ML with a bit of a sarcastıc style because you've got to do something to make them a bit less dull. I have produced over 130 articles and a DataCamp course to boot, with another one in the makıng. My content has been seen by over 5 million pairs of eyes, 20k of whom became followers on both Medium and LinkedIn. 

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