roulette.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook simulates a simplified version of the game of roulette.  The goal is to understand the various ways in which risk attitudes and value functions might make the game attractive to an individual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, interactive, fixed,FloatSlider,IntSlider\n",
    "\n",
    "\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def roulette_spin():\n",
    "    npockets=[18,18,2]  # black, red, green\n",
    "    roll=numpy.random.random_integers(0,numpy.sum(npockets)-1)\n",
    "    if roll<npockets[0]:\n",
    "        color=0\n",
    "    elif roll<numpy.sum(npockets[:2]):\n",
    "        color=0\n",
    "    else:\n",
    "        color=2\n",
    "    return roll,color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of $1 bet = p(outcome)*u(outcome) = $-0.05\n",
      "Mean outcome over 100 bets (on $1.00 bet): $-6.13 (range: $-100.00 - $215.00)\n"
     ]
    },
    {
     "data": {
      "image/png": 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DFlmSJEmS1KGBF1lJjktyY5Kbk5w6T5u3Jtmc5JokRy61b5LfTbIryX6DHIMk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\n0pmQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f58458368d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outcome=[]\n",
    "first_win=[]\n",
    "\n",
    "bet_value=1\n",
    "bet=0  # bet on specific pocket every time - 35X payoff\n",
    "payoff=35\n",
    "nruns=1000\n",
    "nplays=100 # how many games played at one sitting\n",
    "p_payoff=1/38.\n",
    "\n",
    "print('Expected value of $1 bet = p(outcome)*u(outcome) = $%0.2f'%float(-1*bet_value*(1-p_payoff) + payoff*p_payoff))\n",
    "\n",
    "for i in range(nruns):\n",
    "    o=[]\n",
    "    fw=-1\n",
    "    for j in range(nplays):\n",
    "        r,c=roulette_spin()\n",
    "        if payoff==r and fw<0:\n",
    "            fw=j+1\n",
    "        o.append(payoff*bet_value*(payoff==r) - bet_value)\n",
    "    first_win.append(fw)\n",
    "    outcome.append(numpy.sum(o))\n",
    "print('Mean outcome over %d bets (on $%0.2f bet): $%0.2f (range: $%0.2f - $%0.2f)'%(nplays,\n",
    "                bet_value,numpy.mean(outcome),numpy.min(outcome),numpy.max(outcome)))\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.subplot(1,2,1)\n",
    "_=plt.hist(outcome,20,normed=True)\n",
    "plt.ylabel('frequency')\n",
    "plt.xlabel('Winnings after %d plays'%nplays)\n",
    "plt.subplot(1,2,2)\n",
    "_=plt.hist(first_win,20,normed=True)\n",
    "plt.ylabel('frequency')\n",
    "plt.xlabel('Number of plays to first win')\n",
    "\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see how change in the utilty function and probability weighting function change the attractiveness of the bet.  We use a power utility function and a one-parameter (Prelec) weighting function.  Default values are from Table 11.3 in the Fox & Poldrack Neuroeconomics chapter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def pi(p,gamma):\n",
    "    assert gamma > 0 and gamma <= 1\n",
    "    return numpy.exp(-1*(-1*numpy.log(p))**gamma)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MKya9devWTJ8+3acx6UePOntax8fDO+84N9sMHgxt2miwr6pAabKNMacBe4BO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\n++nWrRu3tryVHzr9wOc/fE7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KSRcJUJ5ekz3CGLPDGBNvjDmv9FgT4Ksy5+wtPdYE+LrM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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f583788abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import HTML\n",
    "from IPython.display import display\n",
    "\n",
    "bet_max=1000\n",
    "label = HTML()\n",
    "\n",
    "def plot_prob_weighting(alpha,gamma,bet_value,lam):\n",
    "    beta=alpha # use same weighting for gains and losses\n",
    "    p=numpy.linspace(0.01,1,99)\n",
    "    plt.figure(figsize=(12,5))\n",
    "    plt.subplot(1,2,1)\n",
    "    o=numpy.linspace(0,bet_max,100)\n",
    "    v_o=o**alpha\n",
    "    plt.plot(o,v_o)\n",
    "    plt.plot(-1*o,-1*v_o*lam)\n",
    "\n",
    "    plt.axis([-1*bet_max,bet_max,-1*bet_max,bet_max])\n",
    "    plt.plot(o,o,color='black')\n",
    "    plt.plot([-1*bet_max,bet_max],[0,0])\n",
    "    plt.plot(-1*o,-1*o,color='black')\n",
    "\n",
    "    plt.plot(bet_value,bet_value**alpha,marker='o',color='red')\n",
    "\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.plot(p,pi(p,gamma))\n",
    "    plt.plot(p,p,color='black')\n",
    "    plt.axis([0,1,0,1])\n",
    "    plt.xlabel('p')\n",
    "    plt.ylabel('pi(p)')\n",
    "    payoff=35*bet_value\n",
    "    p_payoff=1/38.\n",
    "    eu=(payoff**alpha)*pi(p_payoff,gamma) - lam*bet_value**beta\n",
    "    label.value = ('Expected value of $%d bet = $%0.2f'%(bet_value,eu))\n",
    "\n",
    "\n",
    "_=interact(plot_prob_weighting, bet_value=FloatSlider(description='bet amount', min=10, max=bet_max, step=10,value=100),\n",
    "           \n",
    "           alpha=FloatSlider(description='alpha (value function curvature)', min=0.5, max=1, step=0.005,value=0.88),\n",
    "           gamma=FloatSlider(description='gamma (probability weighting)', min=0.5, max=1, step=0.005,value=0.74),\n",
    "           lam=FloatSlider(description='lambda (loss aversion)', min=0.5, max=5, step=0.1,value=2.0)\n",
    "\n",
    "\n",
    "          )\n",
    "display(_, label)\n"
   ]
  }
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