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   "cell_type": "markdown",
   "id": "e29535e2-230e-4ba8-a9c6-d30dce1a6011",
   "metadata": {},
   "source": [
    "# Chapter 9.3 - Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d3528751-32b4-4f83-b9a1-52cea6766425",
   "metadata": {},
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b63d1bde-8a1f-403f-a7ff-16864ced198e",
   "metadata": {},
   "source": [
    "## [Farkle] (https://www.wikihow.com/Play-Farkle)\n",
    "Let's simulate how often some of the higher rolling scores occur on the roll of all 6 dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "30a0cf52-909f-424e-ad51-34fdc2562fd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def farkle_roll():\n",
    "    rolls = make_array()\n",
    "    for _ in range(6):\n",
    "        rolls = np.append(rolls, np.random.randint(1,7))\n",
    "    return np.sort(rolls)\n",
    "\n",
    "farkle_roll()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e7665c2-3e2c-47fa-98e8-70aade69a8c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def farkle_score(roll):\n",
    "    if roll[0] == roll[5]:\n",
    "        return \"Sextuplet\"\n",
    "    elif roll[0] == roll[2] and roll[3] == roll[5]:\n",
    "        return \"2 Triplets\"\n",
    "    elif roll[0] == roll[4] or roll[1] == roll[5]:\n",
    "        return \"Quintuplet\"\n",
    "    elif (roll[0] == roll[3] and roll[4] == roll[5]) or (roll[0] == roll[1] and roll[2] == roll[5]):\n",
    "        return \"Quadruplet + Pair\"\n",
    "    elif roll[0] == roll[3] or roll[1] == roll[4] or roll[2] == roll[5]:\n",
    "        return \"Quadruplet\"\n",
    "    else:\n",
    "        return \"Unknown\"\n",
    "\n",
    "roll = farkle_roll()\n",
    "farkle_score(roll)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d011fc8-c18f-4936-ad58-1c89c10610f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "trials = make_array()\n",
    "for _ in range(10000):\n",
    "    trials = np.append(trials, farkle_score(farkle_roll()))\n",
    "print(\"done\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed40724c-d250-4328-80ea-7dcf1db1d134",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation = Table().with_column(\"Result\", trials)\n",
    "farkle_simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa057b19-1795-402a-a4bd-876560a2d5bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation = farkle_simulation.group(\"Result\")\n",
    "farkle_simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc99ef03-c59c-4e87-b314-da9b5fc26402",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation = farkle_simulation.sort(\"count\")\n",
    "farkle_simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "231abdfc-96c0-4212-aa98-ba87421b67c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "farkle_simulation.barh(\"Result\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de66026f-d464-45c9-a9aa-886fc12c1aa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation = farkle_simulation.with_column(\"Percent\", farkle_simulation.column(\"count\") / sum(farkle_simulation.column(\"count\")))\n",
    "farkle_simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3772a88d-4fd6-45a9-b2a8-a4d82bc48776",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation.set_format(\"Percent\", PercentFormatter)\n",
    "farkle_simulation = farkle_simulation.drop(\"count\")\n",
    "farkle_simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9043bbaf-11f4-44b6-adff-e3e0a3d4440a",
   "metadata": {},
   "outputs": [],
   "source": [
    "farkle_simulation.barh(\"Result\")"
   ]
  }
 ],
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