Salinee_Kingbaisomboon-L03-MontyHall.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 3 Assignment - Monty Hall Simulation\n",
    "## Author - Salinee Kingbaisomboon\n",
    "### UW NetID: 1950831"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instructions\n",
    "Simulate the conditional probabilities of the distributions for winning a car vs. a goat for the Monty Hall Problem that includes the following:\n",
    "1. the cases for switching or not switching\n",
    "2. histograms and summary statistics (at least mean and variance) of the results for winning the car or a goat for both strategies: switching or not switching\n",
    "3. comparison of the cases to determine the best strategy\n",
    "4. recommended strategy\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note: \n",
    "Please clearly outline the results and your recommendation with markdown text. Be sure your discussion includes narrative for your figures and tables so it is clear to the reader the importance of each bit of evidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "from __future__ import division \n",
    "\n",
    "import random\n",
    "import numpy\n",
    "import random\n",
    "import pylab as pl\n",
    "import pandas\n",
    "from matplotlib import pyplot\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation Process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- ## Instantiate Global Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulations_numbers_list = [100, 1000, 100000] # list of numbers of realizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- ### Primitive Simulation\n",
    "When we didn't have the calculated conditional probability of monty hall problem beforehand, we have to find the distribution in a primitive approach. Below funtion will simulate and generate the histogram of monty hall's distributions for winning a car vs. a goat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sim_monty_hall_game_primitive(isSwitchedDoor, n_simulations):\n",
    "    number_of_simulations = range(n_simulations)\n",
    "    win_car = [0] * n_simulations # intantiate zero array with length = number of simulation\n",
    "    win_goat = [0] * n_simulations # intantiate zero array with length = number of simulation\n",
    "\n",
    "    for i in number_of_simulations:\n",
    "        door_numbers = [1,2,3] # there are three doors\n",
    "        player_final_door = 0 # first choice of door player select\n",
    "        player_first_door = 0 # final choice of door player select (used when player want to switch the door (isSwitchedDoor = True))\n",
    "    \n",
    "        car_door = random.randint(1,3) # winng door (car's behind) can be 1, 2 or 3\n",
    "        player_first_door = random.randint(1,3) # 1st selected door choice between 1, 2 or 3\n",
    "        door_numbers.remove(car_door) # remove this winning door from selectable list for monty (monty won't select this door)\n",
    "        if player_first_door != car_door : \n",
    "            door_numbers.remove(player_first_door) # monty will open a different door from the player\n",
    "            \n",
    "        monty_opened = random.choice(door_numbers) # monty open whatever door choice left for him\n",
    "        \n",
    "        if isSwitchedDoor == True: # player want to switch the door\n",
    "            door_numbers = [1,2,3]\n",
    "            door_numbers.remove(monty_opened)\n",
    "            door_numbers.remove(player_first_door)\n",
    "            player_final_door = door_numbers[0]\n",
    "        else:\n",
    "            player_final_door = player_first_door # player want to stay with the first choice\n",
    "        \n",
    "        if player_final_door == car_door: # player open the winning door\n",
    "             win_car[i] = 1\n",
    "        elif player_final_door != car_door: # player open the goat door\n",
    "             win_goat[i] = 1\n",
    "                \n",
    "    game_results = pandas.DataFrame({\n",
    "        \"switch_door\": isSwitchedDoor,\n",
    "        \"play\": 1,\n",
    "        \"win\": win_car,\n",
    "        \"lose\": win_goat,\n",
    "    })\n",
    "    game_results.head()\n",
    "     \n",
    "    return game_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Distribution when player didn't switch the door (**Primitive Approach**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure()\n",
    "gs = gridspec.GridSpec(3, 1) # 3 rows, 1 column\n",
    "i = 0 # counter for the subplot\n",
    "for n in simulations_numbers_list:\n",
    "    ax = fig.add_subplot(gs[i, 0])\n",
    "    resultNotSwitch = sim_monty_hall_game_primitive(isSwitchedDoor=False, n_simulations=n)\n",
    "    resultNotSwitch.loc[:,'win'].plot(kind='hist', bins = 10, color='yellow',ax=ax, edgecolor='black')\n",
    "    pl.suptitle(\"Histogram of Probability Distribution when player didn't switch the door (Primitive Approach)\")\n",
    "    ax.set_xlabel(\"0 = Win Goat, 1 = Win Car\")\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Distribution when player decide to switch the door (**Primitive Approach**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure()\n",
    "gs = gridspec.GridSpec(3, 1) # 3 rows, 1 column\n",
    "i = 0 # counter for the subplot\n",
    "for n in simulations_numbers_list:\n",
    "    ax = fig.add_subplot(gs[i, 0])\n",
    "    resultSwitch = sim_monty_hall_game_primitive(isSwitchedDoor=True, n_simulations=n)\n",
    "    resultSwitch.loc[:,'win'].plot(kind='hist', bins = 10, color='blue',ax=ax, edgecolor='black')\n",
    "    pl.suptitle(\"Histogram of Probability Distribution when player decide to switch the door (Primitive Approach)\")\n",
    "    ax.set_xlabel(\"0 = Win Goat, 1 = Win Car\")\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- ### Binomial Sampling Distribution Simulation\n",
    "When we have the theoretical conditional probability values of monty hall problem (from **L03-2-IntroToProbability**), we can use the built in numpy **Binomial Sampling** to generate the sample, find **Means** and **Variance** easily. Below funtion will simulate and generate the histogram of monty hall's distributions for winning a car vs. a goat.\n",
    "\n",
    "***\n",
    "**Note:** The reason I decide to use _Binomial Sampling Distribution_ is that, for Binomial, the result will be ($\\{success, fail \\}$) which is the same type of result when playing monty hall gameshow.\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sim_monty_hall_game_binomial(isSwitchedDoor, simulations_list):\n",
    "    p = 0 # probability to generate the sampling\n",
    "    color = '' # plot different color for switching, not-switching selected door\n",
    "    if isSwitchedDoor:\n",
    "        p = 2/3 # from L03-2-IntroToProbability\n",
    "        color = 'blue'\n",
    "    else:\n",
    "        p = 1/3 # from L03-2-IntroToProbability\n",
    "        color = 'yellow'\n",
    "\n",
    "    binom_samples_win = [numpy.random.binomial(1, p, n) for n in simulations_list] # sample arrays\n",
    "    binom_sample_means = [samples.mean() for samples in binom_samples_win] # Means array\n",
    "    binom_sample_vars = [samples.var() for samples in binom_samples_win] # Variance array\n",
    "    \n",
    "    for i in range(0, len(binom_samples_win)):\n",
    "        pyplot.figure(figsize=(6, 3))\n",
    "        pyplot.hist(binom_samples_win[i], color=color, edgecolor='black')\n",
    "        pyplot.xlabel('0 = Win Goat, 1 = Win Car')\n",
    "        pyplot.ylabel('Frequency')\n",
    "        _ = pyplot.title('Histogram of Probability Distribution when player ' + ('switch' if isSwitchedDoor else 'did not switch') + ' the door (Binomial Sampling Approach) for N = ' + str(simulations_list[i]))\n",
    "        \n",
    "    return pandas.DataFrame({\n",
    "    'SampleMean': binom_sample_means,\n",
    "    'SampleVariance': binom_sample_vars\n",
    "    })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Distribution when player didn't switch the door (**Binomial Sampling Approach**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SampleMean</th>\n",
       "      <th>SampleVariance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.3400</td>\n",
       "      <td>0.224400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.3300</td>\n",
       "      <td>0.221100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.3332</td>\n",
       "      <td>0.222178</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SampleMean  SampleVariance\n",
       "0      0.3400        0.224400\n",
       "1      0.3300        0.221100\n",
       "2      0.3332        0.222178"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "statisticsNotSwitch = sim_monty_hall_game_binomial(isSwitchedDoor=False, simulations_list=simulations_numbers_list)\n",
    "statisticsNotSwitch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Distribution when player decide to switch the door (**Binomial Sampling Approach**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SampleMean</th>\n",
       "      <th>SampleVariance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.69000</td>\n",
       "      <td>0.213900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.67800</td>\n",
       "      <td>0.218316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.66776</td>\n",
       "      <td>0.221857</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SampleMean  SampleVariance\n",
       "0     0.69000        0.213900\n",
       "1     0.67800        0.218316\n",
       "2     0.66776        0.221857"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "statisticsSwitch = sim_monty_hall_game_binomial(isSwitchedDoor=True, simulations_list=simulations_numbers_list)\n",
    "statisticsSwitch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- ## Recommended Strategy\n",
    "Based on the histogram from both **Primitive** and **Binomial Sampling**, we can conclude that the best strategy to win this game is to always switch the door after the first selection. \n",
    "\n",
    "We can clearly see that the theoretical conditional probability values is legit since the histogram plots from binomial bampling are pretty much the same as histogram plots from Primitive approach for both switching or not switching cases.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}