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()