我在进行CS50课程的井字游戏项目时
发现使用极小化极大算法时，在某些情况下无法找到最优解

这是我的代码：

"""Tic Tac Toe Player"""import copyimport mathX = "X"O = "O"EMPTY = Nonedef initial_state():    """    Returns starting state of the board.    """    return [[EMPTY, EMPTY, EMPTY],            [EMPTY, EMPTY, EMPTY],            [EMPTY, EMPTY, EMPTY]]board = initial_state()def player(board):    """    Returns player who has the next turn on a board.    """    numO = 0    numX = 0    FirstPlayer = None    for i in range(len(board)):        for j in range(len(board[i])):            if board[i][j] == O:                numO += 1            elif board[i][j] == X:                numX += 1    return X if numO == numX else Odef actions(board):    """    Returns set of all possible actions (i, j) available on the board.    """    possact = set()    for i in range(len(board)):        for j in range(len(board[i])):            if board [i][j] == EMPTY:                possact.add((i, j))    return possactdef result(board, action):    """    Returns the board that results from making move (i, j) on the board.    """    boardcopy = copy.deepcopy(board)    boardcopy[action[0]][action[1]] = player(board)    return boardcopy    def winner(board):    """    Returns the winner of the game, if there is one.    """    for i in range(3):        wonO = True        wonX = True        for j in range(3):            if board[i][j] == O or board[i][j] == EMPTY:                wonX = False            if board[i][j] == X or board[i][j] == EMPTY:                wonO = False        if wonX:            return X        if wonO:            return O    for j in range(3):        wonO = True        wonX = True        for i in range(3):            if board[i][j] == X or board[i][j] == EMPTY:                wonO = False            if board[i][j] == O or board[i][j] == EMPTY:                wonX = False        if wonX:            return X        if wonO:            return O    diag1 = ''    diag2 = ''    j = 2    for i in range(3):      diag1 += str(board[i][i])      diag2 += str(board[i][j])      j -= 1    if diag1 == 'XXX' or diag2 == 'XXX':      return X    elif diag1 == 'OOO' or diag2 == 'OOO':      return Odef terminal(board):    """    Returns True if game is over, False otherwise.    """    if winner(board) == X:        return True    elif winner(board) == O:        return True    for i in range(len(board)):        for j in range(len(board[i])):            if board[i][j] == EMPTY:                return False    return True        def utility(board):    """    Returns 1 if X has won the game, -1 if O has won, 0 otherwise.    """    resB = winner(board)    if resB == X:        return 1    elif resB == O:        return -1    else:        return 0def minimax(board):    """    Returns the optimal action for the current player on the board.    """    if terminal(board):        return None    Max = float("-inf")    Min = float("inf")    if player(board) == X:        return Max_Value(board, Max, Min)[1]    else:        return Min_Value(board, Max, Min)[1]def Max_Value(board, Max, Min):    move = None    if terminal(board):        return [utility(board), None]    v = float('-inf')    for action in actions(board):        test = Min_Value(result(board, action), Max, Min)[0]        Max = max(Max, test)        if test > v:            v = test            move = action        if Max >= Min:            break    return [v, move]def Min_Value(board, Max, Min):    move = None    if terminal(board):        return [utility(board), None]    v = float('inf')    for action in actions(board):        test = Max_Value(result(board, action), Max, Min)[0]        Min = min(Min, test)        if test < v:            v = test            move = action        if Max >= Min:            break    return [v, move]

这是具体情况（电脑扮演O）：第五步的图片
最优解应该是中间底部的格子
但它选择了这个：第六步的图片
电脑最终赢了，但不是以最优方式

为什么极小化极大算法不选择最优解？
我该如何修复这个问题？

回答：

我没有检查你的代码是否正确实现了极小化极大算法，但我可以解释为什么会出现这样的结果。

游戏树中可能有多条路径通向具有相同效用值的节点。极小化极大算法不会区分快速胜利和缓慢胜利；它会选择任何一条能保证胜利的路径。

解决这个问题的一个常见方法是为较慢的胜利分配较低的效用值。例如，将胜利的效用值设为1000 - depth。相反，失败的效用值应设为-1000 + depth，以便算法尽可能延长不可避免的失败。（如果想使用负极大算法，保持评估函数的对称性也是有益的。）