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   "source": [
    "# The Monty Hall problem (Deutsch: Ziegenproblem)\n",
    "\n",
    "Read about it [on Wikipedia](https://en.wikipedia.org/wiki/Monty_Hall_problem) or [in German as the Ziegenproblem](https://de.wikipedia.org/wiki/Ziegenproblem) and come back. I'll wait.\n",
    "\n",
    "In this notebook, you will write a program to simulated the Monty Hall problem.\n",
    "\n",
    "We are going to make extensive use of the function `random.randint(a, b)`. From its docstring, it returns a `random integer in range [a, b], including both end points.`"
   ]
  },
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    "tags": []
   },
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbgrader": {
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     "grade_id": "cell-8d3e7b29ddec3069",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "0\n",
      "0\n",
      "2\n",
      "0\n",
      "0\n",
      "0\n",
      "0\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    print(random.randint(0,2))"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Q1\n",
    "\n",
    "For your first task, create a function called `sample_not` which takes two positional arguments (call them `not1` and `not2`) and will return a random integer between 0 and 2 (endpoints included) but which is not either of the arguments. The positional arguments will always be integers between 0 and 2 (inclusive)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "# Write your function here\n",
    "def sample_not(not1, not2):\n",
    "    while True:\n",
    "        this_guess = random.randint(0,2)\n",
    "        if this_guess != not1:\n",
    "            if this_guess != not2:\n",
    "                return this_guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-50feeabd1f4f7d07",
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   "source": [
    "# This is a test of the above, do not change this code.\n",
    "assert sample_not(0,1)==2\n",
    "assert sample_not(0,2)==1\n",
    "assert sample_not(1,0)==2\n",
    "assert sample_not(1,2)==0\n",
    "assert sample_not(2,0)==1\n",
    "assert sample_not(2,1)==0\n",
    "assert sample_not(0,1)==2\n",
    "assert sample_not(0,0) in (1,2)\n",
    "assert sample_not(1,1) in (0,2)\n",
    "assert sample_not(2,2) in (0,1)"
   ]
  },
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   "source": [
    "### Q2\n",
    "\n",
    "For your next task, consider the following code:\n",
    "\n",
    "```python\n",
    "\n",
    "# generate what is behind the doors\n",
    "doors = ['goat', 'goat', 'goat']\n",
    "car_door = random.randint(0,2)\n",
    "doors[car_door] = 'car'\n",
    "\n",
    "# Now, the guest makes a first guess.\n",
    "guess1 = random.randint(0,2)\n",
    "\n",
    "# Now, the host opens a door, which is not the guess or the car.\n",
    "host_open_door = sample_not(guess1,car_door)\n",
    "\n",
    "# Based on the variable `do_switch` (which is not set here), the guess will either make a new choice or stay with the original guess.\n",
    "if do_switch:\n",
    "    guess2 = sample_not(guess1,host_open_door)\n",
    "    final_guess = guess2\n",
    "else:\n",
    "    final_guess = guess1\n",
    "\n",
    "# Finally, determine what was behind the door for the final guess.\n",
    "result = doors[final_guess]\n",
    "```\n",
    "\n",
    "Put this code in a function called `run_game` which takes a single argument, `do_switch`, and returns a boolean, indicating a win with `True` or a loss with `False`."
   ]
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   "cell_type": "code",
   "execution_count": 5,
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     "grade": false,
     "grade_id": "cell-c087e3c1a6e2d2dd",
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   "source": [
    "# Write your function here\n",
    "def run_game(do_switch=True):\n",
    "    # generate what is behind the doors\n",
    "    doors = ['goat', 'goat', 'goat']\n",
    "    car_door = random.randint(0,2)\n",
    "    doors[car_door] = 'car'\n",
    "\n",
    "    # Now, the guest makes a first guess.\n",
    "    guess1 = random.randint(0,2)\n",
    "\n",
    "    # Now, the host opens a door, which is not the guess or the car.\n",
    "    host_open_door = sample_not(guess1,car_door)\n",
    "\n",
    "    # Based on the variable `do_switch` (which is not set here), the guess will either make a new choice or stay with the original guess.\n",
    "    if do_switch:\n",
    "        guess2 = sample_not(guess1,host_open_door)\n",
    "        final_guess = guess2\n",
    "    else:\n",
    "        final_guess = guess1\n",
    "\n",
    "    # Finally, determine what was behind the door for the final guess.\n",
    "    result = doors[final_guess]\n",
    "    win = result=='car'\n",
    "    return win"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-a3750cd0c13cf6c0",
     "locked": true,
     "points": 1,
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     "solution": false,
     "task": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "do_switch: True, wins: 207, count: 300\n",
      "do_switch: False, wins: 100, count: 300\n"
     ]
    }
   ],
   "source": [
    "# This is a test of the above, do not change this code.\n",
    "count = 300\n",
    "for do_switch in (True, False):\n",
    "    wins = 0\n",
    "    for i in range(count):\n",
    "        this_run_win = run_game(do_switch)\n",
    "        assert(type(this_run_win)==bool)\n",
    "        wins += int(this_run_win)\n",
    "    print('do_switch: %s, wins: %d, count: %d'%(do_switch, wins, count))\n",
    "    if do_switch:\n",
    "        assert  abs(wins/count - 2/3) < 0.1\n",
    "    else:\n",
    "        assert abs(wins/count - 1/3) < 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
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     "locked": true,
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    "tags": []
   },
   "source": [
    "Note the above results. You have numerically simulated the Monty Hall problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-054774247e7bc87a",
     "locked": true,
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    "tags": []
   },
   "source": [
    "## Q3\n",
    "\n",
    "Make a new game where there are 100 doors and the host opens 98 of them after the initial guess. Make a new function called `run_game_100`, and any other functions you need, which plays a single round of this game. Again, this function should take an argument `do_switch`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-718f81e609214623",
     "locked": false,
     "schema_version": 3,
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     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Write your code here\n",
    "def sample_not_list(n,not_list):\n",
    "    while True:\n",
    "        this_guess = random.randint(0,n-1)\n",
    "        if this_guess not in not_list:\n",
    "            return this_guess\n",
    "            \n",
    "def run_game_100(do_switch=True):\n",
    "    n_doors = 100\n",
    "    n_open = 98\n",
    "    doors = ['goat']*n_doors\n",
    "    car_door = sample_not_list(n_doors,[])\n",
    "    doors[car_door] = 'car'\n",
    "\n",
    "    guess1 = sample_not_list(n_doors,[])\n",
    "    host_list = []\n",
    "    for i in range(n_open):\n",
    "        host_open_door = sample_not_list(n_doors,host_list+[guess1]+[car_door])\n",
    "        host_list.append(host_open_door)\n",
    "\n",
    "    if do_switch:\n",
    "        guess2 = sample_not_list(n_doors,host_list+[guess1])\n",
    "        final_guess = guess2\n",
    "    else:\n",
    "        final_guess = guess1\n",
    "\n",
    "    result = doors[final_guess]\n",
    "    win = result=='car'\n",
    "    return win"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-0b76bb5440f73c22",
     "locked": true,
     "points": 1,
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     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "do_switch: True, wins: 992, count: 1000\n",
      "do_switch: False, wins: 7, count: 1000\n"
     ]
    }
   ],
   "source": [
    "# This is a test of the above, do not change this code.\n",
    "count = 1000\n",
    "for do_switch in (True, False):\n",
    "    wins = 0\n",
    "    for i in range(count):\n",
    "        this_run_win = run_game_100(do_switch)\n",
    "        assert(type(this_run_win)==bool)\n",
    "        wins += int(this_run_win)\n",
    "    print('do_switch: %s, wins: %d, count: %d'%(do_switch, wins, count))\n",
    "    if do_switch:\n",
    "        assert abs(wins/count - 0.99) < 0.02\n",
    "    else:\n",
    "        assert abs(wins/count - 0.01) < 0.02"
   ]
  }
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