一步步解析Python斗牛游戏的概率

过年回家，都会约上亲朋好友聚聚会，会上经常会打麻将，斗地主，斗牛。在这些游戏中，斗牛是最受欢迎的，因为可以很多人一起玩，而且没有技术含量，都是看运气（专业术语是概率）。
斗牛的玩法是：

• 1、把牌中的JQK都拿出来
  
• 2、每个人发5张牌
  
• 3、如果5张牌中任意三张加在一起是10的 倍数，就是有牛。剩下两张牌的和的10的余数就是牛数。
  

牌的大小：

4条 > 3条 > 牛十 > 牛九 > …… > 牛一 >没有牛

而这些牌出现的概率是有多少呢？

由于只有四十张牌，所以采用了既简单，又有效率的方法枚举来计算。
计算的结果：

• 所有牌的组合数：658008
• 出现四条的组合数:360,概率 :0.05%
• 出现三条的组合数:25200,概率 :3.83%
• 出现牛十的组合数:42432,概率 :6.45%
• 出现牛九或牛八的组合数:87296,概率 :13.27%
• 出现牛一到牛七的组合数:306112,概率 :46.52%
• 出现没有牛的组合数:196608,概率 :29.88%

所以有七成的概率是有牛或以上的，所以如果你经常遇到没有牛，说明你的运气非常差或者本来是有牛的，但是你没有找出来。

Python源代码：

    # encoding=utf-8
    __author__ = 'kevinlu1010@qq.com'
    import os
    import cPickle

    from copy import copy
    from collections import Counter
    import itertools
    '''
    计算斗牛游戏的概率
    '''

    class Poker():
      '''
      一张牌
      '''

      def __init__(self, num, type):
        self.num = num # 牌数
        self.type = type # 花色


    class GamePoker():
      '''
      一手牌，即5张Poker
      '''
      COMMON_NIU = 1 # 普通的牛，即牛一-牛七
      NO_NIU = 0 # 没有牛
      EIGHT_NINE_NIU = 2 # 牛九或牛八
      TEN_NIU = 3 # 牛十
      THREE_SAME = 4 # 三条
      FOUR_SAME = 5 # 四条

      def __init__(self, pokers):
        assert len(pokers) == 5
        self.pokers = pokers
        self.num_pokers = [p.num for p in self.pokers]
        # self.weight = None # 牌的权重，权重大的牌胜
        # self.money_weight = None # 如果该牌赢，赢钱的权重
        self.result = self.sumary()

      def is_niu(self):
        '''
        是否有牛
        :return:
        '''
        # if self.is_three_same():
        # return 0
        for three in itertools.combinations(self.num_pokers, 3):
          if sum(three) % 10 == 0:
            left = copy(self.num_pokers)
            for item in three:
              left.remove(item)
            point = sum(left) % 10
            return 10 if point == 0 else point

        return 0

      def is_three_same(self):
        '''
        是否3条
        :return:
        '''
        # if self.is_four_same():
        # return 0
        count = Counter([p.num for p in self.pokers])
        for num in count:
          if count[num] == 3:
            return num
        return 0

      def is_four_same(self):
        '''
        是否4条
        :return:
        '''
        count = Counter([p.num for p in self.pokers])
        for num in count:
          if count[num] == 4:
            return num
        return 0

      def sumary(self):
        '''
        计算牌
        '''
        if self.is_four_same():
          return GamePoker.FOUR_SAME
        if self.is_three_same():
          return GamePoker.THREE_SAME
        niu_point = self.is_niu()
        if niu_point in (8, 9):
          return GamePoker.EIGHT_NINE_NIU
        elif niu_point == 10:
          return GamePoker.TEN_NIU
        elif niu_point > 0:
          return GamePoker.COMMON_NIU
        else:
          return GamePoker.NO_NIU

    def get_all_pokers():
      '''
      生成所有的Poker，共四十个
      :return:
      '''
      pokers = []
      for i in range(1, 11):
        for j in ('A', 'B', 'C', 'D'):
          pokers.append(Poker(i, j))

      return pokers


    def get_all_game_poker(is_new=0):
      '''
      生成所有game_poker
      :param pokers:
      :return:
      '''
      pokers = get_all_pokers()
      game_pokers = []

      if not is_new and os.path.exists('game_pokers'):
        with open('game_pokers', 'r') as f:
          return cPickle.loads(f.read())

      for pokers in itertools.combinations(pokers, 5): # 5代表五张牌
        game_pokers.append(GamePoker(pokers))
      with open('game_pokers', 'w') as f:
        f.write(cPickle.dumps(game_pokers))
      return game_pokers


    def print_rate(game_pokers):
      total_num = float(len(game_pokers))
      four_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.FOUR_SAME])
      three_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.THREE_SAME])
      ten_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.TEN_NIU])
      eight_nine_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.EIGHT_NINE_NIU])
      common_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.COMMON_NIU])
      no_num = len([game_poker for game_poker in game_pokers if game_poker.result == GamePoker.NO_NIU])
      print '所有牌的组合数：%d' % total_num
      print '出现四条的组合数:%d,概率 :%.2f%%' % (four_num, four_num * 100 / total_num)
      print '出现三条的组合数:%d,概率 :%.2f%%' % (three_num, three_num * 100 / total_num)
      print '出现牛十的组合数:%d,概率 :%.2f%%' % (ten_num, ten_num * 100 / total_num)
      print '出现牛九或牛八的组合数:%d,概率 :%.2f%%' % (eight_nine_num, eight_nine_num * 100 / total_num)
      print '出现牛一到牛七的组合数:%d,概率 :%.2f%%' % (common_num, common_num * 100 / total_num)
      print '出现没有牛的组合数:%d,概率 :%.2f%%' % (no_num, no_num * 100 / total_num)


    def main():
      game_pokers = get_all_game_poker() # 658008种
      print_rate(game_pokers)


    main()

以上就是Python计算斗牛游戏的概率相关内容，希望对大家的学习有所帮助。