jhussmann_012313_monty

{
 "metadata": {
  "name": "jhussmann_012313_monty"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import random\n\nparameters = [(7, 3),\n              (7, 4),\n              (7, 5),\n              (8, 3),\n              (8, 4),\n              (8, 5),\n             ]\n\nnum_trials = 100000\n\nfor N, n in parameters:\n    stay_wins = 0\n    switch_wins = 0\n\n    for t in range(num_trials):\n        doors = set(range(N))\n    \n        prize = random.sample(doors, 1)\n        first_pick = random.sample(doors, 1)\n\n        openable_doors = doors - set(prize + first_pick)\n        opened = random.sample(openable_doors, n)\n\n        switchable_doors = doors - set(opened + first_pick)\n        switched_pick = random.sample(switchable_doors, 1)\n    \n        if prize == first_pick:\n            stay_wins += 1\n        if prize == switched_pick:\n            switch_wins += 1\n\n    ratio = float(switch_wins) / stay_wins\n    theoretical_ratio = float(N - 1) / (N - n - 1) \n    print 'N={0}, n={1}\\t {2} {3} {4:.3f} {5:.3f}'.format(N,\n                                                          n,\n                                                          switch_wins,\n                                                          stay_wins,\n                                                          ratio,\n                                                          theoretical_ratio,\n                                                         )",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "N=7, n=3\t 28631 14403 1.988 2.000\nN=7, n=4\t 42844 14208 3.015 3.000"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nN=7, n=5\t 86043 13957 6.165 6.000"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nN=8, n=3\t 21812 12432 1.755 1.750"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nN=8, n=4\t 28901 12493 2.313 2.333"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nN=8, n=5\t 43843 12475 3.514 3.500"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}