{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Game:\n",
    "    def __init__(self):\n",
    "        self.stage = ['G','G','C']\n",
    "        self.choice = None\n",
    "        random.shuffle(self.stage)\n",
    "        \n",
    "    def set_choice(self,num):\n",
    "        self.choice = num - 1\n",
    "\n",
    "    \n",
    "    def give_goat(self):\n",
    "        if self.stage[self.choice] == 'C':\n",
    "            goat_idx = list(set([0,1,2]) - set([self.choice]))\n",
    "            return np.random.choice(goat_idx) + 1\n",
    "        else:\n",
    "            copy = self.stage.copy()\n",
    "            copy[self.choice] = 'null'\n",
    "            return copy.index('G') + 1\n",
    "        \n",
    "    def check_win(self):\n",
    "        return True if self.stage[self.choice] == 'C' else False\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run the cell below to PLAY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have Three Choices...\n",
      "1 2 or 3\n",
      "Enter your choice2\n",
      "Now...curtain 1 contains goat\n",
      "Would you like to switch.....yes or no..(in lowercase please)\n",
      "So.......yes or noyes\n",
      "Hurray........\n",
      "Bloody hell...you won a car.....\n",
      "To play again, run this cell again please\n"
     ]
    }
   ],
   "source": [
    "def play_monty_hall():\n",
    "    game = Game()\n",
    "    print('You have Three Choices...')\n",
    "    print('1 2 or 3')\n",
    "    choice = int(input('Enter your choice'))\n",
    "    game.set_choice(choice)\n",
    "    goat = game.give_goat()\n",
    "    print('Now...curtain '+ str(goat)+ ' contains goat' )\n",
    "    print('Would you like to switch.....yes or no..(in lowercase please)')\n",
    "    switch = input()\n",
    "    if switch == 'yes':\n",
    "        choice = list(set([1,2,3]) - set([choice,goat]))[0]\n",
    "        game.set_choice(choice)\n",
    "    if game.check_win():\n",
    "        print('Hurray........')\n",
    "        print('Bloody hell...you won a car.....')\n",
    "    else:\n",
    "        print('bad luck...you get a goat')\n",
    "    print('To play again, run this cell again please')    \n",
    "    \n",
    "    \n",
    "play_monty_hall()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now lets see which of the two choices have a better chance of winning....Switching or sticking to the same..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "def monty_hall_stimulation(total_games,switch = True):\n",
    "    wins = 0\n",
    "    for itr in range(total_games):\n",
    "        game = Game()\n",
    "        choice = np.random.choice([1,2,3])\n",
    "        game.set_choice(choice)\n",
    "        goat = game.give_goat()\n",
    "        switch_choice = list(set([1,2,3]) - set([choice,goat]))[0]\n",
    "        if switch:\n",
    "            game.set_choice(switch_choice)\n",
    "        if game.check_win():\n",
    "            wins+=1\n",
    "            \n",
    "    return (wins / total_games)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([     10,     100,    1000,   10000,  100000, 1000000])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_games = 10**np.arange(1,7)\n",
    "total_games"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choice 1: always switch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "always_switch_scores = {}\n",
    "for curr_itr in total_games:\n",
    "    always_switch_scores[curr_itr] = monty_hall_stimulation(curr_itr,switch = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability of Winning')"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6))\n",
    "plt.plot(list(always_switch_scores.keys()),list(always_switch_scores.values()))\n",
    "est_prob_switch = list(always_switch_scores.values())[-1]\n",
    "plt.axhline(y = est_prob_switch ,c = 'red',label = 'Estimated probability ' + str(est_prob_switch))\n",
    "plt.xscale('log')\n",
    "plt.legend()\n",
    "plt.xlabel('Number of Iterations Used')\n",
    "plt.ylabel('Probability of Winning')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the probability of winning would be 66%...now lets see the case where i don't switch.."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choice 2 Stick to the first guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "do_not_switch_scores = {}\n",
    "for curr_itr in total_games:\n",
    "    do_not_switch_scores[curr_itr] = monty_hall_stimulation(curr_itr,switch = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability of Winning')"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6))\n",
    "plt.plot(list(do_not_switch_scores.keys()),list(do_not_switch_scores.values()))\n",
    "est_prob_do_not_switch = list(do_not_switch_scores.values())[-1]\n",
    "plt.axhline(y = est_prob_do_not_switch ,c = 'red',label = 'Estimated probability - '+ str(est_prob_do_not_switch))\n",
    "plt.xscale('log')\n",
    "plt.legend()\n",
    "plt.xlabel('Number of Iterations Used')\n",
    "plt.ylabel('Probability of Winning')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# so, we have the answer...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Conclusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Winning percentage')"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (6,6))\n",
    "plt.bar(['Always_switch','Never Switch'], [est_prob_switch*100,est_prob_do_not_switch*100])\n",
    "plt.ylim(0,100)\n",
    "plt.ylabel('Winning percentage')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Always switching will have around 66% chance of winning as compared to the 33% when one never switches"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}