NegaMax Algorithm and TicTacToe…What's wrong?

Question

I am new to game tree algorithms, and i've tried to implement a simple tictactoe game which utilizes the NegaMax algorithm to evaluate tile scores for the computer AI player. However, the AI behaves not in a smart way (i can win all the time, because the AI does not block my moves), and i think i implemented the NegaMax algorithm wrongly.

If anyone could help me with the following code, it would be great. I spent such a long time trying different things out, but i never got it to work.

#include <stdlib.h>
#include <stdio.h>
#include <malloc.h>
#include <limits.h>
#include "game_board.h"

/**
 * Constructs a new game board.
 *
 * @param size the size of the board (the length of fields)
 * @return a new GameBoard
 */
GameBoard* game_board_new(int size)
{
    GameBoard* board = (GameBoard*) calloc(1, sizeof(GameBoard));
    board->size = size;
    board->turn = WHITE;
    board->fields = (enum Player*) calloc(size, sizeof(enum Player));
    return board;
}

/**
 * Releases a game board.
 *
 * @param board the GameBoard to release
 */
void game_board_free(GameBoard* board)
{
    free(board->fields);
    free(board);
}

/**
 * Copies a game board.
 *
 * @param original the GameBoard to copy
 * @return a new GameBoard which is copied from the original
 */
GameBoard* game_board_copy(GameBoard* original)
{
    GameBoard* copy;
    int i;

    copy = game_board_new(original->size);
    copy->size = original->size;
    copy->turn = original->turn;

    for (i = 0; i < original->size; i++)
    {
        copy->fields[i] = original->fields[i];
    }

    return copy;
}

/**
 * Returns the winner for the current game or EMPTY if
 * there is no winner, yet.
 *
 * @param board the GameBoard to check
 * @return the winning Player or EMPTY
 */
enum Player game_board_check_winner(GameBoard* board)
{
    enum Player* f;

    f = board->fields;

    // Columns
    if (f[0] != EMPTY && f[0] == f[3] && f[0] == f[6])
        return f[0];
    if (f[1] != EMPTY && f[1] == f[4] && f[1] == f[7])
        return f[1];
    if (f[2] != EMPTY && f[2] == f[5] && f[2] == f[8])
        return f[2];

    // Rows
    if (f[0] != EMPTY && f[0] == f[1] && f[1] == f[2])
        return f[0];
    if (f[3] != EMPTY && f[3] == f[4] && f[4] == f[5])
        return f[3];
    if (f[6] != EMPTY && f[6] == f[7] && f[7] == f[8])
        return f[6];

    // Diagonal
    if (f[0] != EMPTY && f[0] == f[4] && f[4] == f[8])
        return f[0];
    if (f[2] != EMPTY && f[2] == f[4] && f[4] == f[6])
        return f[2];

    return EMPTY;
}

void game_board_toggle_player(GameBoard* board)
{
    if (board->turn == WHITE)
        board->turn = BLACK;
    else if (board->turn == BLACK)
        board->turn = WHITE;
}

int game_board_is_ended(GameBoard* board)
{
    return game_board_check_winner(board) || game_board_is_full(board);
}

static int evaluate(GameBoard* board)
{
    enum Player winner = game_board_check_winner(board);

    if (winner != EMPTY && winner == board->turn)
    {
        return 1;
    }
    else if (winner != EMPTY && winner != board->turn)
    {
        return -1;
    }
    else
    {
        return 0;
    }
}

int negamax(GameBoard* board, int depth)
{
    int bestvalue = INT_MIN;
    int i;
    int value;

    enum Player winner = game_board_check_winner(board);

    if (winner != EMPTY || depth == 0)
        return evaluate(board);

    for (i = 0; i < board->size; i++)
    {
        if (board->fields[i] == EMPTY)
        {
            GameBoard* copy = game_board_copy(board);
            game_board_make_move(copy, i);
            game_board_toggle_player(board);

            value = -negamax(copy, depth-1);
            bestvalue = max(value, bestvalue);

            game_board_free(copy);
        }
    }

    return bestvalue;
}

/**
 * Evaluates the current board according to NegaMax
 * algorithm.
 *
 * @param board the GameBoard to evaluate
 * @return a NegaMax score
 */
int game_board_evaluate(GameBoard* board, int* best_pos)
{
    int i;
    int maxVal;
    int val;

    maxVal = INT_MIN;

    for (i = 0; i < board->size; i++)
    {
        if (board->fields[i] == EMPTY)
        {
            val = negamax(board, 9);
            if (val > maxVal)
            {
                maxVal = val;
                printf("Best move: %i\n", i);
                (*best_pos) = i;
            }
        }
    }

    return maxVal;
}

int game_board_is_full(GameBoard* board)
{
    int i;

    for (i = 0; i < board->size; i++)
    {
        if (board->fields[i] == 0)
        {
            return 0;
        }
    }

    return 1;
}

void game_board_make_move(GameBoard* board, int pos)
{
    board->fields[pos] = board->turn;
}

/**
 * Prints a game board.
 *
 * @param board the GameBoard to print
 */
void game_board_print(GameBoard* board)
{
    int i;

    for (i = 0; i < board->size; i++)
    {
        printf("%i (%i)\t", board->fields[i], i);

        if (i == 2 || i == 5)
            printf("\n");
    }

    printf("\n");
}

Answer 1

In a NegaMax framework the evaluation function has to look different. Try following evaluation function:

int evaluateNegaMax(GameBoard* board)
{
    if (board->turn == MAXPLAYER)
        return evaluate(board);
    else
        return -evaluate(board);
}

The chessprogramming site explains why:

In order for negaMax to work, your Static Evaluation function must return a score relative to the side to being evaluated

Answer 2

Shouldn't

game_board_toggle_player(board);

be

game_board_toggle_player(copy);

?

Answer 3

The usual error is to start with MIN at each level rather than passing values down the tree. I haven't studied your code in detail to compare with the paradigmatic negamax algorithm, but it seems that you may be making that error.