Monty Hall

monty hall

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 "metadata": {
  "name": "",
  "signature": "sha256:54dd0380143918c25eba34914e70f3100831189ab021b2871dcf92f0b5cce9d3"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!/usr/bin/env python\n",
      "\n",
      "from random import randint, sample\n",
      "\n",
      "def simulate_once(switch_door):\n",
      "    picked_door = randint(0, 2)\n",
      "    door_with_prize = randint(0, 2)\n",
      "\n",
      "    # If picked_door == door_with_prize, there are 2 doors he can choose to open\n",
      "    # otherwise, there's only one.\n",
      "    doors_monty_can_open = set(n for n in range(3) if n not in (picked_door, door_with_prize))\n",
      "    door_monty_opens = sample(doors_monty_can_open, 1)[0]\n",
      "    \n",
      "    if switch_door:\n",
      "        picked_door = list(n for n in range(3) if n not in (picked_door, door_monty_opens))[0]\n",
      "\n",
      "    return picked_door == door_with_prize\n",
      "\n",
      "def main():\n",
      "    n_runs = 100000\n",
      "    n_wins = 0\n",
      "    for i in range(1, n_runs):\n",
      "        if simulate(False):\n",
      "            n_wins += 1\n",
      "\n",
      "    print 'WITHOUT switching', 1.* n_wins/n_runs\n",
      "    n_wins = 0\n",
      "    for i in range(1, n_runs):\n",
      "        if simulate(True):\n",
      "            n_wins += 1\n",
      "\n",
      "    print 'WITH switching', 1.* n_wins/n_runs\n",
      "\n",
      "if __name__ == \"__main__\":\n",
      "    main()\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "WITHOUT switching 0.33341\n",
        "WITH switching"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.66832\n"
       ]
      }
     ],
     "prompt_number": 86
    }
   ],
   "metadata": {}
  }
 ]
}