monty_hall.ipynb

monty_hall.ipynb

{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Monty Hall problem simulation\n\nThis notebook contains a simple simulation of the famous [Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem). The logic of this particular implementation works only for the case of three possible doors."
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "import numpy as np\nimport matplotlib.pylab as plt\n%matplotlib inline",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "randint = np.random.randint\nN = 3 # Don't change N. The logic works only for N == 3",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "def arrange():\n    \"\"\"Arrange the game. Put one care and two goats\"\"\"\n    doors = np.zeros(N, dtype=bool)\n    ix = randint(0, N)\n    doors[ix] = True\n    return doors",
      "execution_count": 3,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def car_print(x, pref=''):\n    \"\"\"Print a nice representation of the game\"\"\"\n    ret = [['🐐', '🚙'][v] for v in x]\n    print (f'{pref:30s}\\t{\"\".join(ret)}')\ncar_print(arrange())",
      "execution_count": 4,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "                              \t🚙🐐🐐\n"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "def sel_print(x, pref=''):\n    \"\"\"Print a nice representation of a selection\"\"\"\n    ret = [['∅', '✓'][v] for v in x]\n    print (f'{pref:30s}\\t{\"\".join(ret)}')",
      "execution_count": 5,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "def make_a_guess():\n    \"\"\"Make a guess\"\"\"\n    return arrange() # Technically, making a guess is identical to arranging a new game",
      "execution_count": 6,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "def check(doors, guess):\n    \"\"\"Check the results\"\"\"\n    success = (doors * guess).sum()\n    return success",
      "execution_count": 7,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Let's see an example"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "doors = arrange()\nguess = make_a_guess()\ncar_print(doors, 'Truth')\nsel_print(guess, 'Guess')\nprint(check(doors, guess))",
      "execution_count": 8,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Truth                         \t🚙🐐🐐\nGuess                         \t✓∅∅\n1\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "doors = arrange()\ncar_print(doors, 'Truth')\nguess = make_a_guess()\nsel_print(guess, 'Guess')\nnot_selected = ~guess\nno_car = ~doors\nmaybe_open = not_selected & no_car\nsel_print(maybe_open, 'What to open')\nto_open = np.zeros(N, dtype=bool)\nix_to_open = np.where(maybe_open)\nix_to_open = ix_to_open[randint(0, len(ix_to_open))]\nto_open = np.zeros(N, dtype=bool)\nto_open[ix_to_open] = True\nsel_print(to_open, 'To open')\nswitch = (~guess) & (~to_open)\nsel_print(switch , 'Switch')\nresult = check(doors, guess) - check(doors, switch)\nprint(f'{\"Result\":30s}{result}')",
      "execution_count": 9,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Truth                         \t🐐🚙🐐\nGuess                         \t∅✓∅\nWhat to open                  \t✓∅✓\nTo open                       \t✓∅✓\nSwitch                        \t∅∅∅\nResult                        1\n"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "def running_mean(x):\n    cumsum = np.cumsum(np.array(x) == -1) \n    return cumsum / (np.arange(1.0, len(x) + 1.0))",
      "execution_count": 10,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "results = []\nfor i in range(30):\n    doors = arrange()\n    guess = make_a_guess()\n    not_selected = ~guess\n    no_car = ~doors\n    maybe_open = not_selected & no_car\n    to_open = np.zeros(N, dtype=bool)\n    ix_to_open = np.where(maybe_open)\n    ix_to_open = ix_to_open[randint(0, len(ix_to_open))]\n    to_open = np.zeros(N, dtype=bool)\n    to_open[ix_to_open] = True\n    switch = (~guess) & (~to_open)\n    result = check(doors, guess) - check(doors, switch)\n    results.append(result)\nplt.figure(figsize=(10, 4))\nplt.title('Results')\nplt.plot(results, 'o')\nplt.figure(figsize=(10, 4))\nplt.title('Cumulative results')\nplt.plot(np.cumsum(results), '-o', color='C1')",
      "execution_count": 11,
      "outputs": [
        {
          "data": {
            "text/plain": "[<matplotlib.lines.Line2D at 0x10d668390>]"
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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            "text/plain": "<matplotlib.figure.Figure at 0x10864f9b0>"
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": "<matplotlib.figure.Figure at 0x10d6556d8>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "version": "3.6.3",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
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