Comment: I forgot to add a np.quantile(results, [0.025,0.975]) to get the confidence interval in the end

cs166-14.1-pcw.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Task 1:\n",
    "\n",
    "# Sadly, I did the first reading before playing and got to the 20% of current balance recommendation\n",
    "# from the formula it presents for the Kelly Criterion, so I did that (unoriginal, I know).\n",
    "\n",
    "from IPython.display import Image\n",
    "Image(\"result.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implementation\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "results = []\n",
    "num_sims = 10000\n",
    "for i in range(num_sims):\n",
    "    balance = 250\n",
    "    for i in range(20):\n",
    "        if np.random.random() < 0.6:\n",
    "            balance += balance*0.2 # gain the worth of your bet - 20% of your balance\n",
    "        else:\n",
    "            balance -= balance*0.2 # lose 20% of your balance\n",
    "    results.append(balance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sbsrj0yWtkPSwpGvzr5Eiabc83pmnT6ss46xcvqbO/32YmVmLG8iZy0eA6k9+fwa4JCJm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\nMzMrzsnFzMyK+//0UKWAMtd/SwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e586834160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting results \n",
    "plt.hist(results,bins=20)\n",
    "plt.title('Coin flip game balance after 20 flips, 10000 runs, Kelly Criterion')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "552.4630442393152"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean outcome - amazingly similar to my instance of playing the game :)\n",
    "np.mean(results)"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}