井字游戏(Tic Tac Toe)是大家都很熟悉的一款策略游戏,两个玩家轮流在3x3的棋盘上放置自己的标记(通常是’X’和’O’),目标是在任意方向上(横、竖、斜)连续三个自己的标记。而蒙特卡洛树搜索(MCTS)则是一种广泛用于复杂策略游戏(例如围棋、象棋等)的算法。在本文中,我们将结合这两者,使用MCTS为井字游戏制定策略。
MCTS主要基于四个阶段:
首先,我们定义井字游戏的基础逻辑:
class TicTacToe:
def __init__(self):
self.board = [[' ']*3 for _ in range(3)] # 初始化3x3的棋盘
self.current_player = 'X' # 设置'X'为开始的玩家
def make_move(self, row, col):
if self.board[row][col] == ' ':
self.board[row][col] = self.current_player
if self.check_win(row, col):
return self.current_player
if self.check_draw():
return 'Draw'
self.current_player = 'O' if self.current_player == 'X' else 'X'
return None
def check_win(self, row, col):
# 检查行、列和对角线
return all(self.board[row][i] == self.current_player for i in range(3)) or \
all(self.board[i][col] == self.current_player for i in range(3)) or \
all(self.board[i][i] == self.current_player for i in range(3)) or \
all(self.board[i][2-i] == self.current_player for i in range(3))
def check_draw(self):
return all(cell != ' ' for row in self.board for cell in row)
def display(self):
for row in self.board:
print('|'.join(row))
print('-'*5)
这里,我们创建了一个TicTacToe类,它包含了一个3x3的棋盘、当前玩家和相关的游戏逻辑。
注意:为了简洁和清晰,本文中的代码可能不是最优的或最完整的实现。为了获得完整的项目和更多的优化技巧,请下载完整项目
为了实现MCTS, 我们首先需要定义一个节点(Node)来代表游戏的每一个状态:
class Node:
def __init__(self, game_state, parent=None):
self.game_state = game_state # 当前的游戏状态
self.parent = parent # 父节点
self.children = [] # 子节点
self.visits = 0 # 当前节点被访问的次数
self.value = 0 # 当前节点的价值
def is_fully_expanded(self):
return len(self.children) == 3 * 3 # 井字游戏棋盘大小
def add_child(self, child_state):
child = Node(game_state=child_state, parent=self)
self.children.append(child)
def update(self, result):
self.visits += 1
self.value += result
接下来,我们将定义MCTS的主要逻辑:
import random
class MCTS:
def __init__(self, root):
self.root = root
def search(self, iterations=1000):
for _ in range(iterations):
leaf = self.traverse(self.root) # Selection
child = self.expand(leaf) # Expansion
result = self.simulate(child) # Simulation
self.backpropagate(child, result) # Backpropagation
return self.best_child(self.root)
def traverse(self, node):
while not node.is_fully_expanded():
if not node.children:
return node
node = self.best_uct(node)
return node
def best_uct(self, node):
"""UCT(Upper Confidence Bound for Trees)计算公式."""
uct_values = [(child.value / (child.visits + 1e-10) +
(2 * (2 * log(node.visits) / (child.visits + 1e-10))**0.5))
for child in node.children]
return node.children[uct_values.index(max(uct_values))]
def expand(self, node):
child_state = self.get_random_child_state(node.game_state)
child = Node(game_state=child_state, parent=node)
node.add_child(child)
return child
def simulate(self, node):
game = TicTacToe()
game.board = node.game_state.board
game.current_player = node.game_state.current_player
result = None
while not result:
available_moves = self.get_available_moves(game.board)
row, col = random.choice(available_moves)
result = game.make_move(row, col)
if result == game.current_player:
return 1
elif result == "Draw":
return 0
else:
return -1
def backpropagate(self, node, result):
while node:
node.update(result)
node = node.parent
def best_child(self, node):
child_values = [child.value for child in node.children]
return node.children[child_values.index(max(child_values))]
@staticmethod
def get_random_child_state(game_state):
available_moves = MCTS.get_available_moves(game_state.board)
row, col = random.choice(available_moves)
new_board = [row.copy() for row in game_state.board]
new_board[row][col] = game_state.current_player
return TicTacToeState(board=new_board,
current_player='O' if game_state.current_player == 'X' else 'X')
@staticmethod
def get_available_moves(board):
return [(i, j) for i in range(3) for j in range(3) if board[i][j] == ' ']
这个MCTS
类实现了蒙特卡洛树搜索的主要四个步骤。值得注意的是,我们在模拟步骤中使用了随机策略,并在后向传播中更新了节点的价值。
我们的MCTS实现中还引入了TicTacToeState
这个类,这只是一个简化版的TicTacToe
,只包含棋盘状态和当前玩家。这是为了减少复杂性并更容易地在节点中存储游戏状态。
为了使用MCTS为井字游戏制定策略,我们需要将井字游戏与之前的MCTS实现相结合。下面我们将这两者结合:
class TicTacToeState:
def __init__(self, board=None, current_player='X'):
self.board = board if board else [[' '] * 3 for _ in range(3)]
self.current_player = current_player
def __str__(self):
return "\n".join(["|".join(row) for row in self.board])
def clone(self):
return TicTacToeState(board=[row.copy() for row in self.board], current_player=self.current_player)
def get_next_states(self):
states = []
for i in range(3):
for j in range(3):
if self.board[i][j] == ' ':
new_board = [row.copy() for row in self.board]
new_board[i][j] = self.current_player
next_player = 'O' if self.current_player == 'X' else 'X'
states.append(TicTacToeState(new_board, next_player))
return states
def play_with_mcts():
game = TicTacToe()
while True:
game.display()
if game.current_player == 'X':
row, col = map(int, input("Enter row and column (0-2) separated by a space: ").split())
else:
state = TicTacToeState(game.board, game.current_player)
root = Node(game_state=state)
mcts = MCTS(root)
best_next_step = mcts.search(iterations=1000)
row, col = None, None
for i in range(3):
for j in range(3):
if state.board[i][j] != best_next_step.game_state.board[i][j]:
row, col = i, j
result = game.make_move(row, col)
if result:
game.display()
print(f"Result: {result}")
break
if __name__ == "__main__":
play_with_mcts()
在play_with_mcts
函数中,玩家’X’将手动进行游戏,而玩家’O’将使用MCTS制定策略。使用MCTS的玩家将运行1000次模拟来决定下一步的动作。
蒙特卡洛树搜索是一种高效的搜索算法,尤其适合那些具有大量可能动作和状态的游戏,如围棋。对于井字游戏这样的简单游戏,MCTS可能会显得过于复杂。但通过这种简单的游戏,我们可以更容易地理解和实现MCTS,为处理更复杂的问题打下基础。
总之,蒙特卡洛树搜索提供了一种强大而灵活的方法来处理各种策略决策问题,不仅仅是游戏。希望这篇文章能帮助你理解和实现这一算法,并为你的项目或研究提供指导。
注意:为了简洁和清晰,本文中的代码可能不是最优的或最完整的实现。为了获得完整的项目和更多的优化技巧,请下载完整项目