{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = [int(os.popen('rolldice d20').read()) for i in range(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([541., 487., 471., 503., 531., 517., 489., 479., 490., 498., 505.,\n",
       "        503., 488., 484., 515., 478., 522., 476., 533., 490.]),\n",
       " array([ 1.  ,  1.95,  2.9 ,  3.85,  4.8 ,  5.75,  6.7 ,  7.65,  8.6 ,\n",
       "         9.55, 10.5 , 11.45, 12.4 , 13.35, 14.3 , 15.25, 16.2 , 17.15,\n",
       "        18.1 , 19.05, 20.  ]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(res, bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Power_divergenceResult(statistic=31984.521923755903, pvalue=0.0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.chisquare(res)"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}