一步步解析Python斗牛游戏的概率

程序员文章站 2022-04-29 15:49:00

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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()

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