{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The famous [Monty Hall brain teaser](https://en.wikipedia.org/wiki/Monty_Hall_problem):\n",
    "\n",
    "> Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, \"Do you want to pick door No. 2?\" Is it to your advantage to switch your choice?\n",
    "\n",
    "There is a really [fun discussion over at Marilyn vos Savant's site](http://marilynvossavant.com/game-show-problem/).\n",
    "\n",
    "Ok, now to setup the problem, along with some kind of visuals and what not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "# for plots, cause visuals\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# setting up a game\n",
    "\n",
    "There are many ways to do this, but to keep it simple and human comprehensible I'm going to do it one game at a time. \n",
    "\n",
    "First up, a helper function which takes the door number guessed and the door opened up the host to reveal a goat, and returns the switched door:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def switch_door(guess, goat_door_opened):\n",
    "    \"\"\"takes in the guessed door and the goat door opened\n",
    "    and returns the switched door number\"\"\"\n",
    "    doors = [0,1,2]\n",
    "    doors.remove(goat_door_opened)\n",
    "    doors.remove(guess)\n",
    "    return doors[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the actual monty hall function - it takes in a guess and whether you want to switch your guess, and returns True or False depending on whether you win"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def monty_hall(guess=0, switch_guess=False, open_goat_door=True):\n",
    "    \"\"\"sets up 3 doors 0-2, one which has a pize, and 2 have goats.\n",
    "    takes in the door number guessed by the player and whether he/she switched door\n",
    "    after one goat door is revealed\"\"\"\n",
    "    \n",
    "    doors = [door for door in range(3)]\n",
    "    np.random.shuffle(doors)\n",
    "    prize_door = doors.pop()\n",
    "    \n",
    "    goat_door_opened = doors[0]\n",
    "    \n",
    "    if goat_door_opened == guess:\n",
    "        goat_door_opened = doors[1]\n",
    "        \n",
    "    if switch_guess:\n",
    "        return switch_door(guess, goat_door_opened) == prize_door\n",
    "    else:\n",
    "        return guess == prize_door"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to run through a bunch of monty hall games:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33223000000000003"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "no_switch = np.mean([monty_hall(random.randint(0,2), False) for _ in range(100000)])\n",
    "no_switch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not switching doors wins a third of the time, which makes intuitive sense, since we are choosing one door out of three."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66474999999999995"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yes_switch = np.mean([monty_hall(random.randint(0,2), True) for _ in range(100000)])\n",
    "yes_switch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the suprising result, since switching our guess increases the win rate to two third! To put it more graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4xwtG2A7RHYko3WhhC9lVTAixOfvbDtAdiShdYKrtAEKIsiel24sOsB1ACFH2pHR70Sdt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\nUrpCCBEjKV0hhIjR/wNFHyv/i284pgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fda8f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pie([yes_switch, no_switch], labels=[\"Switching win %\", \"Not switching win %\"],\n",
    "       autopct='%1.1f%%', explode=(0, 0.05));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our chances of winning essentially double if we switch our guess once a goat door has been opened.\n",
    "\n",
    "A good [monty hall infographic](https://somethingaweek.wordpress.com/2010/08/19/22-lets-make-a-deal/):\n",
    "\n",
    "<img src=\"images/monty-hall.png\" width=\"75%\">."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# the no reveal month\n",
    "\n",
    "So what if Monty never opens a goat door, and just gives us a change to switch the guessed door? Does the winning % still change?\n",
    "\n",
    "So first we change the switch door function to remove the reveal option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def switch_door_no_revel(guess):\n",
    "    \"\"\"takes in the guessed door\n",
    "    and returns the switched door number\"\"\"\n",
    "    doors = [0,1,2]\n",
    "    doors.remove(guess)\n",
    "    np.random.shuffle(doors)\n",
    "    return doors[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then I removed the revealing the goat door code from the original monty hall function above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def monty_hall_no_reveal(guess=0, switch_guess=False):\n",
    "    \"\"\"sets up 3 doors 0-2, one which has a pize, and 2 have goats.\n",
    "    takes in the door number guessed by the player and whether he/she switched door\n",
    "    \"\"\"\n",
    "    \n",
    "    doors = [door for door in range(3)]\n",
    "    np.random.shuffle(doors)\n",
    "    prize_door = doors.pop()\n",
    "        \n",
    "    if switch_guess:\n",
    "        return switch_door_no_revel(guess) == prize_door\n",
    "    else:\n",
    "        return guess == prize_door"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to run some sims:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "no_switch_no_reveal = np.mean([monty_hall_no_reveal(random.randint(0,2), False) for _ in range(100000)])\n",
    "yes_switch_no_reveal = np.mean([monty_hall_no_reveal(random.randint(0,2), True) for _ in range(100000)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11feeebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar([0,1], [yes_switch_no_reveal, no_switch_no_reveal], tick_label=[\"Switched Guess\",\"Didn't Switch\"], \n",
    "        color=[\"blue\",\"red\"], alpha=0.7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no impact of switching our guess if a goat door hasn't been revealed. Which makes sense to, since whatever door we choose, it has 1/3 probablity of winning. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}