Solver Class

Negamax solver with alpha-beta pruning for perfect Connect 4 play

The Solver class implements a Negamax algorithm with alpha-beta pruning to find the optimal move in any Connect 4 position. It can determine whether a position is winning, losing, or drawn with perfect play.

Overview

What is Negamax?

Negamax is a variant of the Minimax algorithm for zero-sum games. Instead of alternating between maximizing and minimizing players, Negamax always maximizes from the current player’s perspective by negating the score when recursing to the opponent’s turn.

Key principle: The value of a position for player A = -(value for player B)

What is Alpha-Beta Pruning?

Alpha-Beta is an optimization that skips branches that won’t affect the final decision:

• Alpha: The best score the current player is guaranteed (lower bound)
• Beta: The worst score the opponent will allow (upper bound)
• If alpha >= beta, we can prune (skip) the rest of the branch

This can reduce the search space exponentially while guaranteeing the same result as full Minimax.

Move Ordering

Alpha-Beta works best when good moves are found first. In Connect 4, center columns typically offer more winning opportunities, so the solver tries them first using the COLUMN_ORDER constant.

Constants

COLUMN_ORDER

static constexpr int COLUMN_ORDER[7] = {3, 2, 4, 1, 5, 0, 6};

Defines the order in which columns are evaluated, from center to edges (0-indexed).

Order: Column 3 (center), then 2, 4, 1, 5, 0, 6 (edges)

This ordering improves alpha-beta pruning efficiency by finding strong moves early.

Public Methods

solve()

int solve(const Position& pos);

Finds the game-theoretic value of a position assuming both players play perfectly.

pos · const Position&

The position to analyze

Returns: int - Score from the current player’s perspective:

• Positive: Current player can force a win
• Zero: Game is a draw with perfect play
• Negative: Opponent can force a win

Score Interpretation: The magnitude indicates how many moves until the game ends. For example:

• +10: Current player wins in 10 moves
• -5: Opponent wins in 5 moves
• 0: Perfect play leads to a draw

Example:

Position pos;
Solver solver;

// Set up some position
pos.make_move(3);
pos.make_move(3);

// Solve the position
int score = solver.solve(pos);

if (score > 0) {
    std::cout << "Winning position!\n";
} else if (score < 0) {
    std::cout << "Losing position!\n";
} else {
    std::cout << "Draw with perfect play!\n";
}

From main.cpp:107-139, here’s how solve() is used to find the best move:

Solver solver;
int best_col = -1;
int best_score = -1000;

std::cout << "Analyzing...\n";

for (int col = 0; col < Position::WIDTH; col++) {
    if (pos.can_play(col)) {
        // Try this move
        Position next = pos;
        next.make_move(col);

        // Get the score (negate because we're looking from opponent's view)
        int score = -solver.solve(next);

        std::cout << "  Column " << (col + 1) << ": score " << score << "\n";

        if (score > best_score) {
            best_score = score;
            best_col = col;
        }
    }
}

// Output result
std::string result;
if (best_score > 0) result = "WIN";
else if (best_score < 0) result = "LOSE";
else result = "DRAW";

std::cout << "bestmove " << (best_col + 1) << " score " << best_score 
          << " (" << result << ")\n";
std::cout << "Nodes analyzed: " << solver.get_node_count() << "\n";

get_node_count()

unsigned long long get_node_count() const;

Returns the number of positions analyzed during the most recent solve operation.

Returns: unsigned long long - Total nodes visited

Use cases:

• Benchmarking solver performance
• Understanding search depth
• Analyzing pruning efficiency

Example:

Solver solver;
solver.solve(pos);
std::cout << "Positions analyzed: " << solver.get_node_count() << std::endl;

From main.cpp:139:

std::cout << "Nodes analyzed: " << solver.get_node_count() << "\n";

reset_node_count()

void reset_node_count();

Resets the node counter to zero. Call this before each solve operation if you want to measure a single search.

Example:

Solver solver;

// First analysis
solver.reset_node_count();
solver.solve(pos1);
std::cout << "First solve: " << solver.get_node_count() << " nodes\n";

// Second analysis
solver.reset_node_count();
solver.solve(pos2);
std::cout << "Second solve: " << solver.get_node_count() << " nodes\n";

Complete Usage Example

Here’s the complete handle_go() function from main.cpp that demonstrates all solver functionality:

void handle_go(Position& pos) {
    // Check for immediate wins first (fast path)
    for (int col = 0; col < Position::WIDTH; col++) {
        if (pos.can_play(col) && pos.is_winning_move(col)) {
            std::cout << "bestmove " << (col + 1) << " score WIN (immediate)\n";
            return;
        }
    }
    
    // Check if game is already over
    if (pos.nb_moves() == Position::WIDTH * Position::HEIGHT) {
        std::cout << "Game is a draw - no moves available\n";
        return;
    }

    // Use the solver to find the best move
    Solver solver;
    int best_col = -1;
    int best_score = -1000;

    std::cout << "Analyzing...\n";

    for (int col = 0; col < Position::WIDTH; col++) {
        if (pos.can_play(col)) {
            // Try this move
            Position next = pos;
            next.make_move(col);

            // Get the score (negate because we're looking from opponent's view)
            int score = -solver.solve(next);

            std::cout << "  Column " << (col + 1) << ": score " << score << "\n";

            if (score > best_score) {
                best_score = score;
                best_col = col;
            }
        }
    }

    // Output result
    std::string result;
    if (best_score > 0) result = "WIN";
    else if (best_score < 0) result = "LOSE";
    else result = "DRAW";

    std::cout << "bestmove " << (best_col + 1) << " score " << best_score 
              << " (" << result << ")\n";
    std::cout << "Nodes analyzed: " << solver.get_node_count() << "\n";
}

Performance Considerations

• The solver uses a TranspositionTable internally to cache position evaluations
• Move ordering via COLUMN_ORDER significantly improves pruning efficiency
• Alpha-beta pruning can reduce the search space by orders of magnitude
• The node count helps measure the effectiveness of these optimizations

Implementation Details

The solver uses a private negamax() method that implements the core recursive search:

int negamax(Position pos, int alpha, int beta);

This method:

1. Checks the transposition table for cached results
2. Evaluates terminal positions (wins/draws)
3. Recursively explores moves in COLUMN_ORDER
4. Updates alpha/beta bounds
5. Prunes branches when alpha >= beta
6. Caches the result in the transposition table