Python计算斗牛游戏的概率
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：
- 把牌中的JQK都拿出来
- 每个人发5张牌
- 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__ = '[email protected]'
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()
如果有错误，欢迎指正。