Python計算斗牛游戲的概率
過年回家，都會約上親朋好友聚聚會，會上經常會打麻將，斗地主，斗牛。在這些游戲中，斗牛是最受歡迎的，因為可以很多人一起玩，而且沒有技術含量，都是看運氣（專業術語是概率）。
斗牛的玩法是：
- 把牌中的JQK都拿出來
- 每個人發5張牌
- 如果5張牌中任意三張加在一起是10的 倍數，就是
有牛。剩下兩張牌的和的10的余數就是牛數。
牌的大小：
4條 > 3條 > 牛十 > 牛九 > …… > 牛一 >沒有牛
而這些牌出現的概率是有多少呢？
由於只有四十張牌，所以采用了既簡單，又有效率的方法枚舉來計算。
計算的結果：
所有牌的組合數：658008
出現四條的組合數:360,概率 :0.05%
出現三條的組合數:25200,概率 :3.83%
出現牛十的組合數:42432,概率 :6.45%
出現牛九或牛八的組合數:87296,概率 :13.27%
出現牛一到牛七的組合數:306112,概率 :46.52%
出現沒有牛的組合數:196608,概率 :29.88%
所以有七成的概率是有牛或以上的，所以如果你經常遇到沒有牛，說明你的運氣非常差或者本來是有牛的，但是你沒有找出來。
Python源代碼：
# encoding=utf-8
__author__ = 'kevinlu1010@qq.com'
import os
import cPickle
from copy import copy
from collections import Counter
import itertools
'''
計算斗牛游戲的概率
'''
class Poker():
'''
一張牌
'''
def __init__(self, num, type):
self.num = num # 牌數
self.type = type # 花色
class GamePoker():
'''
一手牌，即5張Poker
'''
COMMON_NIU = 1 # 普通的牛，即牛一-牛七
NO_NIU = 0 # 沒有牛
EIGHT_NINE_NIU = 2 # 牛九或牛八
TEN_NIU = 3 # 牛十
THREE_SAME = 4 # 三條
FOUR_SAME = 5 # 四條
def __init__(self, pokers):
assert len(pokers) == 5
self.pokers = pokers
self.num_pokers = [p.num for p in self.pokers]
# self.weight = None # 牌的權重，權重大的牌勝
# self.money_weight = None # 如果該牌贏，贏錢的權重
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條
: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條
: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):
'''
計算牌
'''
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，共四十個
: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代表五張牌
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 '所有牌的組合數：%d' % total_num
print '出現四條的組合數:%d,概率 :%.2f%%' % (four_num, four_num * 100 / total_num)
print '出現三條的組合數:%d,概率 :%.2f%%' % (three_num, three_num * 100 / total_num)
print '出現牛十的組合數:%d,概率 :%.2f%%' % (ten_num, ten_num * 100 / total_num)
print '出現牛九或牛八的組合數:%d,概率 :%.2f%%' % (eight_nine_num, eight_nine_num * 100 / total_num)
print '出現牛一到牛七的組合數:%d,概率 :%.2f%%' % (common_num, common_num * 100 / total_num)
print '出現沒有牛的組合數:%d,概率 :%.2f%%' % (no_num, no_num * 100 / total_num)
def main():
game_pokers = get_all_game_poker() # 658008種
print_rate(game_pokers)
main()
如果有錯誤，歡迎指正。