notebooks/At_the_Roulette_Table.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "from datascience import *\n",
    "import matplotlib\n",
    "matplotlib.use('Agg', warn=False)\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "colors = Table.read_table('roulette_wheel.csv').column('Color')\n",
    "pockets = make_array('0','00')\n",
    "for i in np.arange(1, 37):\n",
    "    pockets = np.append(pockets, str(i)) \n",
    "\n",
    "wheel = Table().with_columns(\n",
    "    'Pocket', pockets,\n",
    "    'Color', colors\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### At the Roulette Table ###\n",
    "\n",
    "The distributions above gave us a picture of the entire random sample. But sometimes we are just interested in one or two quantities computed based on the sample.\n",
    "\n",
    "For example, suppose the sample consists of wins and losses in a series of bets. Then we might just be interested in the total amount of money won, rather than the entire sequence of wins and losses.\n",
    "\n",
    "Equipped with our new knowledge about the long-run behavior of chances, let us explore a gambling game. We will simulate betting on roulette, which is popular in gambling centers such as Las Vegas and Monte Carlo.\n",
    "\n",
    "The main randomizer in roulette in Nevada is a wheel that has 38 pockets on its rim. Two of the pockets are green, eighteen black, and eighteen red. The wheel is on a spindle, and there is a small ball on the wheel. When the wheel is spun, the ball ricochets around and finally comes to rest in one of the pockets. That is declared to be the winning pocket."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table `wheel` represents the pockets of a Nevada roulette wheel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0     </td> <td>green</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>00    </td> <td>green</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>red  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>black</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>red  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>black</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5     </td> <td>red  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6     </td> <td>black</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>7     </td> <td>red  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>8     </td> <td>black</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (28 rows omitted)</p"
      ],
      "text/plain": [
       "Pocket | Color\n",
       "0      | green\n",
       "00     | green\n",
       "1      | red\n",
       "2      | black\n",
       "3      | red\n",
       "4      | black\n",
       "5      | red\n",
       "6      | black\n",
       "7      | red\n",
       "8      | black\n",
       "... (28 rows omitted)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wheel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are allowed to bet on several pre-specified collections of pockets displayed on a roulette table. If you bet on \"red,\" you win if the ball comes to rest in one of the red pockets. \n",
    "\n",
    "The bet on red pays even money. That is, it pays 1 to 1. To understand what this means, assume you are going to bet \\$1 on \"red.\" The first thing that happens, even before the wheel is spun, is that you have to hand over your \\$1. If the ball lands in a green or black pocket, you never see that dollar again. If the ball lands in a red pocket, you get your dollar back (to bring you back to even), plus another \\$1 in winnings.\n",
    "\n",
    "The function `red_winnings` takes a color as its argument and returns 1 if the color is red. For all other colors it returns -1. We apply `red_winnings` to the `Color` column of `wheel` to get a new table `bets` that shows the net gain on each pocket if you bet \\$1 on red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def red_winnings(color):\n",
    "    if color == 'red':\n",
    "        return 1\n",
    "    else:\n",
    "        return -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th> <th>Winnings: Red</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0     </td> <td>green</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>00    </td> <td>green</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>7     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>8     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (28 rows omitted)</p"
      ],
      "text/plain": [
       "Pocket | Color | Winnings: Red\n",
       "0      | green | -1\n",
       "00     | green | -1\n",
       "1      | red   | 1\n",
       "2      | black | -1\n",
       "3      | red   | 1\n",
       "4      | black | -1\n",
       "5      | red   | 1\n",
       "6      | black | -1\n",
       "7      | red   | 1\n",
       "8      | black | -1\n",
       "... (28 rows omitted)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bets = wheel.with_column(\n",
    "    'Winnings: Red', wheel.apply(red_winnings, 'Color')\n",
    "    )\n",
    "bets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you decide to bet \\$1 on red.  What might happen?\n",
    "\n",
    "Here is a simulation of 1 spin.\u001f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th> <th>Winnings: Red</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>14    </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Pocket | Color | Winnings: Red\n",
       "14     | red   | 1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_spin = bets.sample(1)\n",
    "one_spin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The color of the spin is the value in the `Color` column.  Regardless of your bet, the outcome might be red, green, or black.  To see how often those events happen, we can simulate many of these single spins and draw a bar chart of the colors we see.  (We could call this an *empirical bar chart*.)\n",
    "\n",
    "To do that, we can use a `for` loop. We have chosen 5,000 repetitions here, but you can change that when you run the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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xdr23unDhQsXGxjqsKAAAXF25AfvPf/5TWVlZGj16tC5fvlxqf2FhoUaNGqXPP/+8wvci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\nsAAAGEDAAgBgAAELAIAB/wduB0CkAez6bwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a955748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_simulations = 5000\n",
    "\n",
    "colors = make_array()\n",
    "winnings_on_red = make_array()\n",
    "\n",
    "for i in np.arange(num_simulations):\n",
    "    spin = bets.sample(1)\n",
    "    new_color = spin.column(\"Color\").item(0)\n",
    "    colors = np.append(colors, new_color)\n",
    "    new_winnings = spin.column('Winnings: Red')\n",
    "    winnings_on_red = np.append(winnings_on_red, new_winnings)\n",
    "\n",
    "Table().with_column('Color', colors)\\\n",
    "       .group('Color')\\\n",
    "       .barh('Color')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "18 out of 38 pockets are red, and each is equally likely.  So out of 5,000 simulations, we'd expect to see *roughly* (but probably not exactly) $\\frac{18}{38} \\times 5000$, or 2,368, red spins.  The simulation bears that out.\n",
    "\n",
    "In the simulation, we also recorded your winnings.  An empirical histogram of those shows the (approximate) chances of different outcomes of your \\$1 bet on red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4GMePHy/8+9ixY43WIdVqtRCJRKiqqjJedURERGZmcDBmZGSYsg4iIqJ2weBgfPHFF01Z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\nIiLS8X9m3pbMH5tTfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117eeef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Table().with_column('Winnings: Red', winnings_on_red)\\\n",
    "       .hist(bins = np.arange(-1.55, 1.65, .1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only possible outcome of each simulation is that you win \\$1 or lose \\$1, and this is reflected in the histogram.  We can also see that you win slightly less often than you lose.  Do you like this gambling strategy?\n",
    "\n",
    "### Multiple Games\n",
    "Most roulette players stay for more than one spin of the wheel.  Suppose you repeatedly bet \\$1 on red, on 200 separate spins. How much money will you make, in total?\n",
    "\n",
    "Here is a simulation of one set of 200 spins. The table `spins` consists of the results of all 200 bets. Your net gain is the sum of all the +1's and -1's in the `Winnings: Red` column of `spins`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-26"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spins = bets.sample(200)\n",
    "spins.column('Winnings: Red').sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cell a few times. Sometimes your net gain is positive, but more often it seems to be negative.\n",
    "\n",
    "To see more clearly what happens, let us simulate 200 spins many times, just as we did with a single spin.  For each simulation, we will record the total winnings from the 200 spins.  Then we will make a histogram of the 5,000 different simulated total winnings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WVgbZlkqlanBbFuYWBssjhrHy1DVW93+twKr1uwyepy7vz5kIz+eN+/1v6j+DpkT0ZRBN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aab0b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_spins = 200\n",
    "\n",
    "net_gain = make_array()\n",
    "\n",
    "for i in np.arange(num_simulations):\n",
    "    spins = bets.sample(num_spins)\n",
    "    new_net_gain = spins.column('Winnings: Red').sum()\n",
    "    net_gain = np.append(net_gain, new_net_gain)\n",
    "\n",
    "Table().with_column('Net Gain on Red', net_gain).hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the position of 0 on the horizontal axis. That's where you break even. How do you like your chances of making money by using this gambling scheme?\n",
    "\n",
    "If the bet on red isn't appealing, maybe it's worth trying a different bet. A 'split' is a bet on two adjacent numbers on the roulette table, such as 0 and 00. The split pays 17 to 1. \n",
    "\n",
    "The function `split_winnings` takes a pocket as its argument and returns 17 if the pocket is either 0 or 00. For all other pockets it returns -1.\n",
    "\n",
    "The table `more_bets` is a version of the `bets` table augmented by each pocket's winnings on the 0/00 split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def split_winnings(pocket):\n",
    "    if pocket == '0':\n",
    "        return 17\n",
    "    elif pocket == '00':\n",
    "        return 17\n",
    "    else:\n",
    "        return -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th> <th>Winnings: Red</th> <th>Winnings: Split</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0     </td> <td>green</td> <td>-1           </td> <td>17             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>00    </td> <td>green</td> <td>-1           </td> <td>17             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>red  </td> <td>1            </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>black</td> <td>-1           </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>red  </td> <td>1            </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>black</td> <td>-1           </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5     </td> <td>red  </td> <td>1            </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6     </td> <td>black</td> <td>-1           </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>7     </td> <td>red  </td> <td>1            </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>8     </td> <td>black</td> <td>-1           </td> <td>-1             </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (28 rows omitted)</p"
      ],
      "text/plain": [
       "Pocket | Color | Winnings: Red | Winnings: Split\n",
       "0      | green | -1            | 17\n",
       "00     | green | -1            | 17\n",
       "1      | red   | 1             | -1\n",
       "2      | black | -1            | -1\n",
       "3      | red   | 1             | -1\n",
       "4      | black | -1            | -1\n",
       "5      | red   | 1             | -1\n",
       "6      | black | -1            | -1\n",
       "7      | red   | 1             | -1\n",
       "8      | black | -1            | -1\n",
       "... (28 rows omitted)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "more_bets = wheel.with_columns(\n",
    "    'Winnings: Red', wheel.apply(red_winnings, 'Color'),\n",
    "    'Winnings: Split', wheel.apply(split_winnings, 'Pocket')\n",
    "    )\n",
    "more_bets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below simulates the results of both bets – on red and on the 0/00 split – on 200 spins of the wheel. The code is the same as in the previous simulation, apart from the addition of the lines for the split.  (Note: `num_simulations` and `num_spins` were previously defined as 5,000 and 200, respectively, so we do not need to define them again.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ERFWncdGZmJhY7vb8/HycO3cOhw4dwtixY7UWTJ2ZM2di9+7d2L59Oxo1aoTs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\nRKRz/w/i2PwgoGeCKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2e2b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "net_gain_red = make_array()\n",
    "net_gain_split = make_array()\n",
    "\n",
    "for i in np.arange(num_simulations):\n",
    "    spins = more_bets.sample(num_spins)\n",
    "    new_net_gain_red = spins.column('Winnings: Red').sum()\n",
    "    net_gain_red = np.append(net_gain_red, new_net_gain_red)\n",
    "    new_net_gain_split = spins.column('Winnings: Split').sum()\n",
    "    net_gain_split = np.append(net_gain_split, new_net_gain_split)\n",
    "\n",
    "Table().with_columns(\n",
    "    'Net Gain on Red', net_gain_red,\n",
    "    'Net Gain on Split', net_gain_split\n",
    "    ).hist(bins=np.arange(-200, 200, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The position of 0 on the horizontal axis shows that you are more likely to lose money than to make money, regardless of which bet you choose. In both histograms, less than 50% of the area is to the right of 0.\n",
    "\n",
    "However, the chance of making money is larger for the split bet, as is the chance of making more than \\$50. The gold histogram has plenty of area to the right of \\$50, whereas the blue histogram has almost none. So should you bet on the split instead?\n",
    "\n",
    "That depends on how much risk you are willing to take, because the histograms also show that you are more likely to *lose* more than \\$50 if you bet on the split than if you bet on red. \n",
    "\n",
    "All bets at the roulette table have the same expected net loss per dollar bet (except the line bet, which is worse). But the returns on some bets are more variable than on others. You can go for the big bucks by choosing those bets, as long as you are prepared for the possibility of losing big."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}