reddit probability - 3 balls.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_context('poster')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def roll(n = 3):\n",
    "    return np.random.choice(np.arange(n),size = 1)[0]\n",
    "\n",
    "# test:\n",
    "res = np.array([roll() for _ in range(int(1e5))])\n",
    "fig,ax = plt.subplots(figsize = (8,4))\n",
    "_=ax.hist(res,bins = 100,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p(bob wins) = 0.331\n",
      "p(emma wins) = 0.330\n"
     ]
    }
   ],
   "source": [
    "n_sim = int(1e5)\n",
    "n = 3\n",
    "bob = np.random.choice(np.arange(n),size = n_sim,)\n",
    "emma = np.random.choice(np.arange(n-1),size = n_sim,)\n",
    "\n",
    "game = np.random.choice(np.arange(n),size = n_sim,)\n",
    "\n",
    "match_bob = np.sum(bob == game,) / n_sim\n",
    "match_emma = np.sum(emma == game,) / n_sim\n",
    "\n",
    "print(f'p(bob wins) = {match_bob:.3f}')\n",
    "print(f'p(emma wins) = {match_emma:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I can also just list out all the possibilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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