实现井字游戏的极大极小算法

我正在尝试为井字游戏实现最小最大算法，在该游戏中，两名玩家都是人类，每次计算机都使用最小最大算法建议最佳移动。但它并不是每次都给出正确的建议。例如：对于以下情况，它没有给出正确的建议：玩家X:1玩家O:2玩家X:5。这是我的代码：

#include <stdio.h>
#include <algorithm>  
#include <string>
using namespace std;
#define inf 1<<20
int posmax, posmin;
char board[15];
void print_board()
{
    int i;
    for (i = 1; i <= 9; i++)
    {   
        printf("%c ",board[i]);
        if (i % 3 == 0)
            printf("n");
    }
    printf("n");
}
int check_win(char board[])
{
    if ((board[1] == 'X' && board[2] == 'X' && board[3] == 'X') ||
        (board[4] == 'X' && board[5] == 'X' && board[6] == 'X') ||
        (board[7] == 'X' && board[8] == 'X' && board[9] == 'X') ||
        (board[1] == 'X' && board[4] == 'X' && board[7] == 'X') ||
        (board[2] == 'X' && board[5] == 'X' && board[8] == 'X') ||
        (board[3] == 'X' && board[6] == 'X' && board[9] == 'X') ||
        (board[1] == 'X' && board[5] == 'X' && board[9] == 'X') ||
        (board[3] == 'X' && board[5] == 'X' && board[7] == 'X'))
    {
        return 1;
    }
    else if((board[1] == 'O' && board[2] == 'O' && board[3] == 'O') ||
            (board[4] == 'O' && board[5] == 'O' && board[6] == 'O') ||
            (board[7] == 'O' && board[8] == 'O' && board[9] == 'O') ||
            (board[1] == 'O' && board[4] == 'O' && board[7] == 'O') ||
            (board[2] == 'O' && board[5] == 'O' && board[8] == 'O') ||
            (board[3] == 'O' && board[6] == 'O' && board[9] == 'O') ||
            (board[1] == 'O' && board[5] == 'O' && board[9] == 'O') ||
            (board[3] == 'O' && board[5] == 'O' && board[7] == 'O'))
    {
        return -1;
    }
    else return 0;
}
int check_draw(char board[])
{
    if ((check_win(board) == 0) && (board[1] != '_') && (board[2] != '_') &&
        (board[3] != '_') && (board[4] != '_') && (board[5] != '_') &&
        (board[6] != '_') && (board[7] != '_') && (board[8] != '_') &&
        (board[9] != '_'))
    {
        return 1;
    }
    else return 0;
}
int minimax(int player, char board[], int n)
{
    int i, res, j;
    int max = -inf;
    int min = inf;
    int chk = check_win(board);
    if (chk == 1)
        return 1;
    else if (chk == (-1))
        return -1;
    else if (chk = check_draw(board))
        return 0;
    for (i = 1; i <= 9; i++)
    {
        if(board[i] == '_')
        {
            if(player == 2)  
            {
                board[i] = 'O';
                res = minimax(1, board, n + 1);
                board[i] = '_';
                if(res < min)
                {
                    min = res;
                    if (n == 0)
                        posmin = i;
                }
            }
            else if (player == 1)
            {
                board[i] = 'X';
                res = minimax(2, board, n + 1);
                board[i] = '_';
                if (res > max)
                {
                    max = res;
                    if (n == 0)
                        posmax = i;
                }
            }
        }
    }
    if (player == 1)
        return max;
    else return min;    
}

// 1 is X, 2 is O
int main()
{
    int i, j, input, opt;
    for(i = 1; i <= 9; i++)
        board[i] = '_';
    printf("Board:n");
    print_board();
    for(i = 1; i <= 9; i++)
    {
        if (i % 2 == 0)
            printf("Player O give input:n");
        else 
            printf("Player X give input:n");
        scanf("%d", &input);
        if (i % 2 != 0)
            board[input] = 'X';
        else
            board[input] = 'O';
        printf("Board:n");
        print_board();
        int chk = check_win(board);
        if (chk == 1)
        {
            printf("Player X wins!n");
            break;
        }
        else if (chk == -1)
        {
            printf("Player O wins!n");
            break;
        }
        else if ((chk == 0) && (i != 9))
        {
            posmax = -1;
            posmin = -1;
            if(i % 2 == 0)
            {
                opt = minimax(1, board, 0);
                printf("Optimal move for player X is %dn", posmax);
            }
            else 
            {
            opt = minimax(2, board, 0);
            printf("Optimal move for player O is %dn", posmin);
            }
        }
        else 
            printf("The game is tied!n");
    }
    return 0;
}