The Algorithmic Mind: Building AI That Beats Me at My Own Games

After a brief calculation—thousands of positions evaluated in milliseconds—a red piece slides diagonally across the board, capturing three of my pieces in a devastating combo. I built this opponent myself, and yet it consistently outplays me.

In another window, numbers rapidly fill empty cells in a sudoku grid. Green highlights flash across successful placements, while red marks indicate the algorithm's backtracking—a visual representation of computational thinking unfolding in real time. There's something mesmerizing about watching the machine "think" through a problem space, testing hypotheses and revising its approach.

These projects mark my entry point into the world of artificial intelligence and algorithmic problem-solving. What began as experimental weekend builds evolved into a profound appreciation for algorithmic elegance. In today's AI landscape—where attention gravitates toward neural networks with billions of parameters and inscrutable decision-making processes—these transparent, deterministic algorithms provided me with something far more valuable: understanding.

The beauty of minimax and backtracking isn't just their effectiveness, but their transparency. Every decision is traceable, every evaluation explainable. This clarity stands in stark contrast to the black-box nature of many contemporary AI systems, where even their creators cannot fully explain specific outcomes. It's worth remembering that these classical approaches form the fundamental building blocks upon which more complex systems are built—the minimax principle underpins game-theoretical approaches in reinforcement learning, while constraint satisfaction techniques like backtracking provide the backbone for scheduling and optimization libraries that power everything from delivery routing to compiler design.

I share these implementations not just as coding exercises, but as invitations to experience the same intellectual spark that ignited my journey into algorithmic thinking. Sometimes the most profound insights come not from the latest research papers, but from implementing the elegant solutions discovered decades ago and watching them execute, one logical step at a time.

The Architecture of Decision-Making: Checkers AI

My checkers implementation follows a modular architecture that separates game mechanics from AI decision-making. This separation is more than architectural cleanliness—it reflects the fundamental distinction between the rules of a game (its mechanics) and strategies for playing it (its meta-game). The board doesn't "know" about strategy, just as the AI doesn't need to understand how pieces are rendered on screen.

The Minimax Algorithm: Looking into the Future

At the heart of the checkers AI lies the minimax algorithm—a recursive approach to adversarial search that models the fundamental back-and-forth nature of two-player games. Minimax works by simulating possible future game states to a certain depth, assuming optimal play from both sides.

Here's the core implementation:

def minimax(position, depth, max_player, game):

    if depth == 0 or position.winner() != None:

        return position.evaluate(), position

    if max_player:

        maxEval = float('-inf')

        best_move = None

        for move in get_all_moves(position, WHITE, game):

            evaluation = minimax(move, depth-1, False, game)[0]

            maxEval = max(maxEval, evaluation)

            if maxEval == evaluation:

                best_move = move

        return maxEval, best_move

    else:

        minEval = float('inf')

        best_move = None

        for move in get_all_moves(position, RED, game):

            evaluation = minimax(move, depth-1, True, game)[0]

            minEval = min(minEval, evaluation)

            if minEval == evaluation:

                best_move = move

    return minEval, best_move

This elegant recursion captures something profound about strategic thinking: the interdependent nature of decision-making in adversarial contexts. When I evaluate a move, I must consider your optimal response, which depends on my subsequent optimal response, and so on—a recursive descent into the game tree.

The Heuristic Evaluation Function: Value Judgment

While minimax provides the search framework, the AI's "intelligence" largely stems from how it evaluates board positions. My implementation uses a straightforward heuristic:

def evaluate(self):

    return self.white_left - self.red_left + (self.white_kings * 0.5 - self.red_kings * 0.5)

This captures two key strategic principles:

1. Material advantage: Having more pieces than your opponent

2. Piece quality: Kings are more valuable than regular pieces

The weighting factor of 0.5 for kings represents a careful balance. If kings were weighted too heavily, the AI would sacrifice excessive material for promotion opportunities. If weighted too lightly, it would fail to capitalize on the strategic advantage kings provide.

Computational Complexity and Search Depth

The minimax algorithm's time complexity is O(b^d), where b is the branching factor (average legal moves per position) and d is the search depth. In checkers:

• The average branching factor is approximately 8-10

• At depth 4, this means examining around 10,000 positions

• Each additional ply (half-move) increases computational load roughly 10-fold

This exponential growth creates an interesting trade-off between search depth and response time. My implementation uses a fixed depth of 4, which provides strong play while maintaining reasonable performance on modest hardware:

if game.turn == WHITE:

    value, new_board = minimax(game.get_board(), 4, WHITE, game)

game.ai_move(new_board)

The Decision-Making Pipeline

When the AI analyzes a position, it follows a systematic process:

1. Position evaluation: For terminal or maximum-depth positions

2. Move generation: Identifying all legal moves from the current position

3. Recursive evaluation: Calculating the value of each potential move

4. Minimax selection: Choosing the move with the optimal worst-case outcome

This process mirrors how a human might approach the game—considering possibilities, evaluating positions, and selecting the most promising line of play—but with the computer's characteristic exhaustiveness and precision.

The Backtracking Mind: Sudoku Solver Visualization

If checkers represents adversarial thinking, sudoku embodies constraint satisfaction—finding a solution that satisfies multiple interlocking rules. My sudoku implementation not only solves puzzles but visualizes the algorithm's cognitive process in real time.

The Recursive Backtracking Algorithm

The core solving mechanism uses a depth-first backtracking approach:

def solve(bo):

    find = find_empty(bo)

    if not find:

        return True

    else:

        row, col = find

        for i in range(1,10):

        if valid(bo, i, (row, col)):

            bo[row][col] = i

            if solve(bo):

                return True

            bo[row][col] = 0

        return False

This algorithm embodies a "guess and check" strategy with systematic backtracking:

1. Find an empty cell

2. Try placing digits 1-9 in that cell

3. For each valid digit, recursively attempt to solve the rest of the puzzle

4. If no solution is found, undo the last placement and try the next digit

Constraint Propagation: The Key to Efficiency

What prevents this approach from devolving into brute-force search is the constant application of constraints through the valid() function:

def valid(bo, num, pos):

    for i in range(len(bo[0])):

        if bo[pos[0]][i] == num and pos[1] != i:

            return False

    for i in range(len(bo)):

        if bo[i][pos[1]] == num and pos[0] != i:

            return False

    box_x = pos[1] // 3

    box_y = pos[0] // 3

    for i in range(box_y*3, box_y*3 + 3):

        for j in range(box_x*3, box_x*3 + 3):

            if bo[i][j] == num and (i,j) != pos:

                return False

    return True

This function embodies the three fundamental constraints of sudoku:

1. Each row must contain numbers 1-9 without repetition

2. Each column must contain numbers 1-9 without repetition

3. Each 3×3 box must contain numbers 1-9 without repetition

These constraints dramatically prune the search space. Without them, we would need to check 9^81 possible configurations. With constraint checking, most sudoku puzzles resolve in milliseconds.

Visualizing the Algorithm's Thought Process

What makes this implementation particularly fascinating is the visualization of the backtracking process:

def solve_gui(self):

    self.update_model()

    find = find_empty(self.model)

    if not find:

        return True

    else:

        row, col = find

        for i in range(1, 10):

        if valid(self.model, i, (row, col)):

            self.model[row][col] = i

            self.cubes[row][col].set(i)

            self.cubes[row][col].draw_change(self.win, True)

            self.update_model()

            pygame.display.update()

            pygame.time.delay(100)

            if self.solve_gui():

                return True

            self.model[row][col] = 0

            self.cubes[row][col].set(0)

            self.update_model()

            self.cubes[row][col].draw_change(self.win, False)

            pygame.display.update()

            pygame.time.delay(100)

        return False

This function creates a visual representation of the algorithm's cognitive process:

• Green highlights indicate cells where a value is being tested

• Red highlights show when the algorithm backtracks after reaching an unsolvable state

• The deliberate delay (100ms) slows the process to human-observable speed

Watching this algorithm work is like peering into the computational mind—systematically testing hypotheses, recognizing dead ends, and methodically exploring the solution space.

The Game Loop: Unifying Interface and Logic

At the architectural center of both projects lies the game loop pattern—a fundamental construct in interactive software:

def main():

    run = True

    clock = pygame.time.Clock()

    game = Game(WIN)

    while run:

        clock.tick(FPS)

        if game.turn == WHITE:

            value, new_board = minimax(game.get_board(), 4, WHITE, game)

            game.ai_move(new_board)

        if game.winner() != None:

            print(game.winner())

            run = False

        for event in pygame.event.get():

            if event.type == pygame.QUIT:

                run = False

            if event.type == pygame.MOUSEBUTTONDOWN:

                pos = pygame.mouse.get_pos()

                row, col = get_row_col_from_mouse(pos)

                game.select(row, col)

         game.update()

    pygame.quit()

This pattern coordinates four essential phases:

1. Input processing: Handling user interactions with the system

2. State updating: Modifying the game state based on input and internal logic

3. Rendering: Transforming the abstract game state into visual representation

4. Timing control: Maintaining consistent frame rates and responsiveness

The elegance of this pattern lies in its separation of concerns while maintaining temporal coherence. Each component performs its specialized function within a synchronized framework.

Performance Optimization: When Algorithms Meet Hardware

Implementing these algorithms requires balancing theoretical elegance with practical performance considerations. Several optimization techniques enhance the responsiveness and scalability of both projects:

In the Checkers AI:

1. Move generation optimization: The get_all_moves() function pre-computes valid moves rather than generating them on demand during search.

2. State copying efficiency: Using deepcopy() only at critical junctures prevents unnecessary object duplication:

   temp_board = deepcopy(board)

   temp_piece = temp_board.get_piece(piece.row, piece.col)

3. Early termination: The search immediately returns upon finding a winning position rather than exploring alternatives.

In the Sudoku Solver:

1. Empty cell selection strategy: The find_empty() function simply returns the first empty cell rather than attempting to find the most constrained cell, privileging implementation simplicity over theoretical optimality.

2. Direct array access: Using direct array indexing rather than getter/setter methods for internal operations reduces function call overhead.

3. Minimal state preservation: The backtracking implementation modifies and restores the board in place rather than creating copies at each recursion level.

These practical optimizations reflect an important principle in algorithm implementation: theoretical analysis guides design, but empirical performance in context determines success.

Beyond the Surface: What Makes These Implementations Special

These projects transcend mere game implementations to demonstrate several profound computational principles:

1. The Power of Recursive Problem Decomposition

Both the minimax algorithm and backtracking solver use recursion to decompose complex problems into simpler subproblems. This divide-and-conquer approach mirrors how humans tackle complex problems—breaking them down into manageable pieces, solving each piece, and combining the results.

2. The Elegant Balance of Heuristics and Exhaustive Search

The checkers AI balances heuristic evaluation (the simplified board scoring) with systematic tree search. This combination—using approximations to guide exhaustive exploration—appears throughout AI, from classic game-playing systems to modern neural network guidance of Monte Carlo tree search in systems like AlphaGo.

3. The Visual Representation of Abstract Processes

Both projects translate abstract computational processes into visual form, making algorithmic thinking observable. This visualization bridges the gap between the conceptual elegance of algorithms and the tangible experience of watching them work, creating an intuitive understanding that purely mathematical descriptions cannot achieve.

The Enduring Relevance of Classical Algorithms in the Age of Deep Learning

While neural networks and statistical learning dominate today's AI headlines, these classical algorithmic approaches remain profoundly relevant. Their enduring significance stems from several distinct advantages:

Deterministic Reliability and Transparency

Unlike probabilistic models, these algorithms provide guaranteed behavior under consistent inputs. A checkers position evaluated at depth 4 will always return the same move evaluation; a sudoku puzzle will always yield the same solution path. This determinism creates reliability that probabilistic systems cannot match.

The transparency of these approaches—being able to trace exactly why the algorithm made each decision—contrasts sharply with the "black box" nature of neural networks. This explainability is crucial for applications where understanding the reasoning process matters as much as the outcome.

Computational Efficiency at Scale

For well-defined problems with clear rules, classical algorithms often provide extraordinary efficiency. The backtracking sudoku solver can resolve puzzles in milliseconds on modest hardware. The minimax implementation, while facing combinatorial explosion at higher depths, remains manageable for practical gameplay at reasonable depths.

This efficiency stems from the algorithms' ability to leverage problem structure rather than learning it through data. When the rules are known and fixed (as in games like checkers and sudoku), encoding this knowledge directly produces substantial performance advantages.

Educational Value and Transferable Principles

These implementations demonstrate fundamental concepts that transfer across domains:

• State space search appears in robotics path planning, logistics optimization, and scheduling

• Heuristic evaluation informs decision-making from medical diagnosis to financial trading

• Constraint propagation enables everything from compiler optimization to supply chain management

• Recursive decomposition structures approaches to complex system design and analysis

Understanding these principles through concrete implementations creates a foundation for tackling more complex computational problems across disciplines.

The Future: Hybridizing Classical and Modern Approaches

The most promising direction for these classical implementations lies not in replacing them with deep learning approaches, but in creating hybrid systems that leverage the strengths of both paradigms:

1. Learning Evaluation Functions

The static evaluation function in the checkers AI could be replaced or augmented with a trained neural network that captures more nuanced positional understanding. This approach—keeping the minimax search framework but enhancing the evaluation component—has proven highly effective in systems like AlphaZero.

2. Guided Backtracking

The sudoku solver could incorporate learned heuristics to prioritize which cells to fill first and which values to try, potentially reducing the number of backtracking steps required. This guided search maintains the systematic exploration while adding learned intuition about likely successful paths.

3. Dynamic Search Depth Allocation

Rather than using a fixed minimax depth, machine learning could determine which positions deserve deeper analysis, allocating computational resources more efficiently based on position complexity and criticality.

Conclusion: The Algorithmic Aesthetic

There's a certain beauty in watching these algorithms operate—a window into the mathematical structures that underlie complex problem-solving. The checkers piece that sacrifices itself to set up a devastating combination three moves later; the sudoku solver that confidently places digits in a complex region through chain deductions; these moments reveal the elegant patterns of computational thinking.

Beyond their practical utility and educational value, these implementations remind us that algorithms aren't just tools for solving problems—they're expressions of logical beauty, capturing deep patterns in problem-solving that transcend specific applications.

In an AI landscape increasingly dominated by statistical models trained on vast datasets, these classical approaches maintain their relevance by demonstrating the power of precise algorithmic thinking. They remind us that intelligence isn't just about pattern recognition, but about systematic reasoning within well-defined spaces.

Whether you're a seasoned developer or just beginning your journey into computational thinking, implementations like these provide an accessible entry point into the fascinating world of algorithms and AI. They demonstrate that profound computational ideas don't require cutting-edge hardware or massive datasets—just clear thinking expressed through elegant code.

The algorithms may be decades old, but their capacity to illuminate the fundamentals of computational problem-solving remains as powerful as ever.

** A huge shoutout to TechwithTim for significantly enhancing my interest within AI and ML with intuitive ideas and projects, and providing an amazing manual to help create significant portions of my project above.