封筒の話（さらに続き）

ここで、封筒に入れる金額は、ホストは以下のように決定します。ホストは、さいころを5か6が出るまで連続して振ります。この時、1〜4の目が出た数をn とします。

「この時、1〜4の目が出た回数をn とします」と読まないといけないのね。
しかしでかい方をあけた確率が0.6になってる。変すぎ。

[nori@shinano]~/Desktop/study/python/hack% python two2envelopes.py 100000
[1, 16685, 16685, 33370, 0] 2.0 0.0
[2, 27613, 55226, 60634, 16606] 1.09792489045 0.601383406367
[4, 18749, 74996, 82270, 11287] 1.09699183956 0.60200544029
[8, 12305, 98440, 107588, 7441] 1.09292970337 0.604713531085
[16, 8234, 131744, 144736, 4948] 1.09861549672 0.600923002186
[32, 5508, 176256, 194928, 3283] 1.10593681917 0.596042120552
[64, 3664, 234496, 263456, 2141] 1.1234989083 0.584334061135
[128, 2399, 307072, 337280, 1442] 1.09837432263 0.60108378491
[256, 1624, 415744, 453248, 985] 1.09020935961 0.606527093596
[512, 1074, 549888, 599808, 651] 1.09078212291 0.606145251397
[1024, 729, 746496, 821760, 437] 1.10082304527 0.599451303155
[2048, 469, 960512, 1048576, 284] 1.09168443497 0.605543710021
[4096, 296, 1212416, 1374208, 171] 1.13344594595 0.577702702703
[8192, 197, 1613824, 1667072, 127] 1.03299492386 0.644670050761
[16384, 162, 2654208, 3072000, 91] 1.15740740741 0.561728395062
[32768, 96, 3145728, 3342336, 60] 1.0625 0.625
[65536, 79, 5177344, 6324224, 41] 1.22151898734 0.518987341772
[131072, 39, 5111808, 5111808, 26] 1.0 0.666666666667
[262144, 27, 7077888, 7864320, 16] 1.11111111111 0.592592592593
[524288, 21, 11010048, 11796480, 13] 1.07142857143 0.619047619048
['sum', 99970, 40770819, 44700102]

修正後のコード

import sys
import random

class Die:
  def roll(self):
    r = random.randint(1, 6)
    assert r > 0
    assert r < 7
    return r
  def odd(self):
    return bool(random.randint(0, 1))

die = Die()

class Envelope:
  def __init__(self):
    r = die.roll()
    n = 0
    while r < 5:
      n += 1
      r = die.roll()
    self.values = (1 << n, 1 << (n + 1))
    self.first_opend = die.odd()

  def open(self):
    return self.values[self.first_opend]

  def swap(self):
    return self.values[not self.first_opend]
    

def experiment(t):
  result = {}
  for i in range(t):
    e = Envelope()
    v = e.open()
    s = e.swap()
    r = result.get(v, None)
    if r is None:
      r = [0, 0, 0, 0] #occurence, none-swap case, swap case, respectivly
    r[0] += 1
    r[1] += v
    r[2] += s
    r[3] += int(e.first_opend)
    result[v] = r
  return result

r = experiment(int(sys.argv[1]))

xs = [[i, r[i][0], r[i][1], r[i][2], r[i][3]] for i in r]
xs.sort(key=lambda x: x[0])

total = ['sum', 0, 0, 0]
for i in range(20):
  r=xs[i]
  total[1] += r[1]
  total[2] += r[2]
  total[3] += r[3]
  print r, 1.0*r[3]/r[2], 1.0*r[4]/r[1]
print total