三个红包的问题，让“蟒蛇”来帮你解决
本帖最后由 Highway 于 2014-2-24 13:11 编辑三个红包的问题，我大概是二十年前在《读者》上看到过。当时杂志的某个角落里就藏着答案：“第二次你应该更新你的选择！”。
当时和宿舍里的朋友们讨论过这个问题，大家认为《读者》给的答案也许有问题，都觉得当裁判/主持人/面试官 拿走一个选择以后，情况起了变化，成了“二选一”的问题，你不改初衷或是改变主意应该无所谓，都是50%的中彩几率。
这个问题现在又给翻腾出来了，大家七嘴八舌的，我也没仔细看。直到 @夏翁 老剑客给出了一段程序以后，我才觉得是不是也该用程序验证一下这个问题了。因计算机可以很方便的进行随机模拟。
严格的说，现在计算机产生的“随机数”不是100%真正的随机数，但是对绝大多数的情况已经是足够好了，所以我们就不再这个细节上纠缠了。以前我在西西河做信息版版主的时候，没事儿也爱弄几句程序说明个问题啥的，那时候多数是用Java或C#，今天换个花样，用一把“蟒蛇（Python）”，也算是与时俱进吧！
http://www.python.org/static/community_logos/python-logo-master-v3-TM-flattened.png
程序的语法大家不必细究，看看这个流程就行了（我没有仔细看题，我认为操作过程大概是这样的）。
1. 准备三个红包，随便挑一个作为放钱的真红包
2. 你先来选一个
3. 裁判拿走一个（分两种情况，1：他知道红包的情况，特意拿走一个空的。2，他也不知情，随便从你挑剩的两个红包中拿走一个）
4. 你再次选择（也分两种情况，1：坚持不变，2：换一下选择）
5. 对答案，揭底！
我编了一个小程序，测试了四种可能的情况（Step 3和4的四种组合），其结果显示:
1. 如果裁判知情，拿走一个空包，那你更换选择永远是对的，中彩几率基本上可以增加一倍
2. 裁判如果不知情，随便拿走一个包，那你换不换选择都一样，都只有1/3的中彩概率。
这个结果你能接受吗？
程序贴在下面，大家自己可以改动这玩。如果觉得我的流程有问题，欢迎指出！# -*- coding: utf-8 -*-
import random
def tryYourLuck(changeMind=False, judgeKnowAnswer=True, printDetail=False):
removedOne = None
yourFirstPick = None
yourFinalPick = None
realBonusBag = None
# 1. 准备三个红包
bonusBags = ['Bag_A', 'Bag_B','Bag_C']
realBonusBag = random.sample(bonusBags, 1)
# 2. 作出第一次选择
yourFirstPick = random.sample(bonusBags, 1)
# 3. 裁判拿走一个红包
if judgeKnowAnswer: # 他知情，故意拿走一个空的
for aBag in bonusBags:
if aBag != realBonusBag and aBag != yourFirstPick:
removedOne = aBag
break
else: #他不知情，瞎拿
for aBag in bonusBags:
if aBag != yourFirstPick:
removedOne = aBag
break
# 4. 作出最后选择
if changeMind: # 改变主意
yourFinalPick =
else: # 不变
yourFinalPick = yourFirstPick
# 5. 揭谜底
if printDetail:
print 'Bouns bag: %s, First pick: %s, removed one: %s, Final pick: %s, you win: %s' % \
(realBonusBag, yourFirstPick, removedOne, yourFinalPick, \
str(yourFinalPick == realBonusBag))
return 1 if yourFinalPick == realBonusBag else 0
def main():
#1. 先热身两下，看看程序运行怎么回事儿
print 'Do some demo first'
for count in xrange(10):
tryYourLuck(changeMind=False, judgeKnowAnswer=True, printDetail=True)
print '\nChange Parameter and try again.'
for count in xrange(10):
tryYourLuck(changeMind=True, judgeKnowAnswer=False, printDetail=True)
# 2. 开始计数统计
testCount = 1000000
winCount = 0
loseCount = 0
for count in xrange(testCount):
result = tryYourLuck(changeMind=False, judgeKnowAnswer=True, printDetail=False)
if result ==1:
winCount +=1
else:
loseCount +=1
print '\nCASE 1: If you do not change mind and judge know which one is empty to remove'
print 'then you win %d times and you lose %d times' %(winCount, loseCount)
winCount = 0
loseCount = 0
for count in xrange(testCount):
result = tryYourLuck(changeMind=True, judgeKnowAnswer=True, printDetail=False)
if result ==1:
winCount +=1
else:
loseCount +=1
print '\nCASE 2: If you change mind and judge know which one is empty to remove'
print 'then you win %d times and you lose %d times' %(winCount, loseCount)
winCount = 0
loseCount = 0
for count in xrange(testCount):
result = tryYourLuck(changeMind=False, judgeKnowAnswer=False, printDetail=False)
if result ==1:
winCount +=1
else:
loseCount +=1
print '\nCASE 3: If you do not change mind and judge does not know which one is empty to remove'
print 'then you win %d times and you lose %d times' %(winCount, loseCount)
winCount = 0
loseCount = 0
for count in xrange(testCount):
result = tryYourLuck(changeMind=True, judgeKnowAnswer=False, printDetail=False)
if result ==1:
winCount +=1
else:
loseCount +=1
print '\nCASE 4: If you change mind and judge does not knows which one is empty to remove'
print 'then you win %d times and you lose %d times' %(winCount, loseCount)
if __name__ == "__main__":
main()
本帖最后由 Highway 于 2014-2-24 11:00 编辑
运行的时候，先弄弄参数，把过程打出来，你可以检查一下程序是不是按你设计的来运行。然后再开始做大量的模拟和统计。
运行的结果是>>>
Do some demo first
Bouns bag: Bag_A, First pick: Bag_A, removed one: Bag_B, Final pick: Bag_A, you win: True
Bouns bag: Bag_C, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_C, you win: True
Bouns bag: Bag_A, First pick: Bag_A, removed one: Bag_B, Final pick: Bag_A, you win: True
Bouns bag: Bag_B, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_C, you win: False
Bouns bag: Bag_C, First pick: Bag_A, removed one: Bag_B, Final pick: Bag_A, you win: False
Bouns bag: Bag_A, First pick: Bag_A, removed one: Bag_B, Final pick: Bag_A, you win: True
Bouns bag: Bag_B, First pick: Bag_A, removed one: Bag_C, Final pick: Bag_A, you win: False
Bouns bag: Bag_B, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_B, you win: True
Bouns bag: Bag_B, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_B, you win: True
Bouns bag: Bag_C, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_B, you win: False
Change Parameter and try again.
Bouns bag: Bag_C, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_C, you win: True
Bouns bag: Bag_B, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_C, you win: False
Bouns bag: Bag_C, First pick: Bag_A, removed one: Bag_B, Final pick: Bag_C, you win: True
Bouns bag: Bag_B, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: True
Bouns bag: Bag_A, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: False
Bouns bag: Bag_A, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: False
Bouns bag: Bag_C, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: False
Bouns bag: Bag_B, First pick: Bag_B, removed one: Bag_A, Final pick: Bag_C, you win: False
Bouns bag: Bag_B, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: True
Bouns bag: Bag_A, First pick: Bag_C, removed one: Bag_A, Final pick: Bag_B, you win: False
CASE 1: If you do not change mind and judge know which one is empty to remove
then you win 33208 times and you lose 66792 times
CASE 2: If you change mind and judge know which one is empty to remove
then you win 666444 times and you lose 333556 times
CASE 3: If you do not change mind and judge does not know which one is empty to remove
then you win 333512 times and you lose 666488 times
CASE 4: If you change mind and judge does not knows which one is empty to remove
then you win 333080 times and you lose 666920 times Highway 发表于 2014-2-24 10:30 static/image/common/back.gif
运行的时候，先弄弄参数，把过程打出来，你可以检查一下程序是不是按你设计的来运行。然后再开始做大量的模 ...
没细看代码，光看答案，case 2 和 case 4 好像重复。
照道理，如果评判随机拿走红包的话，似乎概率应该是一致的。。。。。 懒厨 发表于 2014-2-24 10:37 static/image/common/back.gif
没细看代码，光看答案，case 2 和 case 4 好像重复。
照道理，如果评判随机拿走红包的话，似乎概率应该 ...
谢谢提醒，最后一个Case是和第二个重复了，程序改过来了，结论也变了{:229:} {:200:}{:201:}{:218:}{:224:} 能不能直接发红包。。。。。 哈哈，编程狂人轧叔也来了{:232:} 原题裁判/主持人/面试官拿走一个空包是假设条件，现在大家把它当成默认条件，解题思路错了
假设条件下，是三选一的题目再加提示
默认条件下，是二选一的题目 本帖最后由 常挨揍 于 2014-2-24 12:52 编辑
再啰嗦一句
“我”选择一个红包，分为A组，中奖概率是1/3，
剩下的两个红包，分为B组，中奖概率是2/3，
无论红包是否打开，无论裁判把红包“拿”到哪儿去，AB两组的中奖概率是不会变的
凯文史派西《21点》里面也用了这个段子 赞！跟夏教授一样都是认真的人。{:222:}
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