Question

I’ve implemented Negamax as it can be found on wikipedia, which includes alpha/beta pruning.

However, it seems to favor a losing move, which is an invalid result to my knowledge.

The game is Tic-Tac-Toe, I’ve abstracted most of the game play so it should be rather easy to spot an error within the algorithm.

#include <list>
#include <climits>
#include <iostream>

//#define DEBUG 1

using namespace std;

struct Move {
    int row, col;

    Move(int row, int col) : row(row), col(col) { }
    Move(const Move& m) { row = m.row; col = m.col; }
};

struct Board {
    char player;
    char opponent;
    char board[3][3];

    Board() { }

    void read(istream& stream) {
        stream >> player;
        opponent = player == 'X' ? 'O' : 'X';

        for(int row = 0; row < 3; row++) {
            for(int col = 0; col < 3; col++) {
                char playa;

                stream >> playa;
                board[row][col] = playa == '_' ? 0 : playa == player ? 1 : -1;
            }
        }
    }

    void print(ostream& stream) {
        for(int row = 0; row < 3; row++) {
            for(int col = 0; col < 3; col++) {
                switch(board[row][col]) {
                    case -1:
                        stream << opponent;
                        break;

                    case 0:
                        stream << '_';
                        break;

                    case 1:
                        stream << player;
                        break;

                }
            }
            stream << endl;
        }
    }

    void do_move(const Move& move, int player) {
        board[move.row][move.col] = player;
    }

    void undo_move(const Move& move) {
        board[move.row][move.col] = 0;
    }

    bool isWon() {
        if (board[0][0] != 0) {
            if (board[0][0] == board[0][1] &&
                    board[0][1] == board[0][2])
                return true;

            if (board[0][0] == board[1][0] &&
                    board[1][0] == board[2][0])
                return true;
        }

        if (board[2][2] != 0) {
            if (board[2][0] == board[2][1] &&
                    board[2][1] == board[2][2])
                return true;

            if (board[0][2] == board[1][2] &&
                    board[1][2] == board[2][2])
                return true;
        }

        if (board[1][1] != 0) {
            if (board[0][1] == board[1][1] &&
                    board[1][1] == board[2][1])
                return true;

            if (board[1][0] == board[1][1] &&
                    board[1][1] == board[1][2])
                return true;

            if (board[0][0] == board[1][1] &&
                    board[1][1] == board[2][2])
                return true;

            if (board[0][2] == board [1][1] &&
                    board[1][1] == board[2][0])
                return true;
        }

        return false;
    }

    list<Move> getMoves() {
        list<Move> moveList;

        for(int row = 0; row < 3; row++)
            for(int col = 0; col < 3; col++)
                if (board[row][col] == 0)
                    moveList.push_back(Move(row, col));

        return moveList;
    }
};

ostream& operator<< (ostream& stream, Board& board) {
    board.print(stream);
    return stream;
}

istream& operator>> (istream& stream, Board& board) {
    board.read(stream);
    return stream;
}

int evaluate(Board& board) {
    int score = board.isWon() ? 100 : 0;

    for(int row = 0; row < 3; row++)
        for(int col = 0; col < 3; col++)
            if (board.board[row][col] == 0)
                score += 1;

    return score;
}

int negamax(Board& board, int depth, int player, int alpha, int beta) {
    if (board.isWon() || depth <= 0) {
#if DEBUG > 1
        cout << "Found winner board at depth " << depth << endl;
        cout << board << endl;
#endif
        return player * evaluate(board);
    }

    list<Move> allMoves = board.getMoves();

    if (allMoves.size() == 0)
        return player * evaluate(board);

    for(list<Move>::iterator it = allMoves.begin(); it != allMoves.end(); it++) {
        board.do_move(*it, -player);
        int val = -negamax(board, depth - 1, -player, -beta, -alpha);
        board.undo_move(*it);

        if (val >= beta)
            return val;

        if (val > alpha)
            alpha = val;
    }

    return alpha;
}

void nextMove(Board& board) {
    list<Move> allMoves = board.getMoves();
    Move* bestMove = NULL;
    int bestScore = INT_MIN;

    for(list<Move>::iterator it = allMoves.begin(); it != allMoves.end(); it++) {
        board.do_move(*it, 1);
        int score = -negamax(board, 100, 1, INT_MIN + 1, INT_MAX);
        board.undo_move(*it);

#if DEBUG
        cout << it->row << ' ' << it->col << " = " << score << endl;
#endif

        if (score > bestScore) {
            bestMove = &*it;
            bestScore = score;
        }
    }

    if (!bestMove)
        return;

    cout << bestMove->row << ' ' << bestMove->col << endl;

#if DEBUG
    board.do_move(*bestMove, 1);
    cout << board;
#endif

}

int main() {
    Board board;

    cin >> board;
#if DEBUG
    cout << "Starting board:" << endl;
    cout << board;
#endif

    nextMove(board);
    return 0;
}

Giving this input:

O
X__
___
___

The algorithm chooses to place a piece at 0, 1, causing a guaranteed loss, do to this trap(nothing can be done to win or end in a draw):

XO_
X__
___

I’m pretty sure the game implementation is correct, but the algorithm should be aswell.

EDIT: Updated evaluate and nextMove.

EDIT2: Fixed first problem, there still seem to be bugs though

Answer 1

Your evaluate function counts the empty spaces, and does not recognize a winning board.

EDIT:
There’s also a relatively minor problem in nextMove. The line should be

int score = -negamax(board, 0, -1, INT_MIN + 1, INT_MAX);

Fix that (and evaluate), and the code chooses the right move.

EDIT:

This fixes it:

if (board.isWon() || depth <= 0) {
#if DEBUG > 1
  cout << "Found winner board at depth " << depth << endl;
  cout << board << endl;
#endif
  return -100;                                                      
}

Almost all of these problems stem from not being clear about the meaning of score. It is from the point of view of player. If negamax is evaluating the position of player 1, and player 1 cannot win, the score should be low (e.g. -100); if negamax is evaluating the position of player -1, and player -1 cannot win, the score should be low (e.g. -100). If evaluate() can’t distinguish the players, then returning a score of player * evaluate(board) is just wrong.