diff --git a/pig_solitaire.ipynb b/pig_solitaire.ipynb
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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:51250876cf4d0275d7de2936a3d28351e279f40c0b477d6cbd22ff86e5a52b8d"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "import random\n",
+      "import matplotlib.pyplot as plt\n",
+      "import statistics as st\n",
+      "import seaborn"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 79
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "%matplotlib inline"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "I built a lot of classes here for different players"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player:\n",
+      "    \"\"\"\n",
+      "    Responsibilities:\n",
+      "    * keeps track of points\n",
+      "    * has a strategy\n",
+      "    \"\"\"\n",
+      "    def __init__(self):\n",
+      "        pass\n",
+      "        \n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll == 1:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False\n",
+      "        "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Gordon(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        return True"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Random(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if random.choice([0,1]) == 1:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player17(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 17:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 120
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player18(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 18:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 121
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player19(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 19:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 122
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player20(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 20:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 74
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player21(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 21:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 104
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Player22(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll_points <= 22:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 105
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class FourTurn(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll < 5:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 32
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class FiveTurn(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll < 6:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 134
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class SixTurn(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll < 7:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 138
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class SevenTurn(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll < 8:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 135
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class EightTurn(Player):\n",
+      "    def will_roll(self, roll, roll_points):\n",
+      "        if roll < 9:\n",
+      "            return True\n",
+      "        else:\n",
+      "            return False"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 132
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "My game class handles the playing of the game Pig Solitaire"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "class Game:\n",
+      "    \"\"\"\n",
+      "    Responsibilities:\n",
+      "    * rolls dice\n",
+      "    * handles outcome of dice rolls\n",
+      "    * iterates over player rolls in turns\n",
+      "    * iterates over turns for game\n",
+      "    * \n",
+      "    \n",
+      "    Collaborators:\n",
+      "    * Player\n",
+      "    \"\"\"\n",
+      "    def __init__(self, player):\n",
+      "        self.turn = 0\n",
+      "        self.player = player\n",
+      "        self.player_score = 0\n",
+      "    \n",
+      "    def dice_roll(self):\n",
+      "        return random.randint(1, 6)\n",
+      "    \n",
+      "    def roll_success(self, die):\n",
+      "        if die == 1:\n",
+      "            return False\n",
+      "        else:\n",
+      "            return True\n",
+      "    \n",
+      "    def turn_event(self, player):\n",
+      "        #turn_points = 0\n",
+      "        roll = 1\n",
+      "        roll_points = 0\n",
+      "        while True:\n",
+      "            if player.will_roll(roll, roll_points):\n",
+      "                die = self.dice_roll()\n",
+      "                if self.roll_success(die):\n",
+      "                    roll_points += die\n",
+      "                else:\n",
+      "                    return 0\n",
+      "                roll += 1    \n",
+      "            else:\n",
+      "                return roll_points\n",
+      "        \n",
+      "    def complete_game(self):\n",
+      "        for _ in range(7):\n",
+      "            self.player_score += self.turn_event(player)\n",
+      "        return self.player_score\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player()\n",
+      "game = Game(player)\n",
+      "print(game.complete_game())"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "21\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def multiple_games(n, player):\n",
+      "    score_list = []\n",
+      "    for _ in range(n):\n",
+      "        game = Game(player)\n",
+      "        score_list.append(game.complete_game())\n",
+      "    return(score_list)\n",
+      "\n",
+      "player = Player()\n",
+      "print(multiple_games(10, player))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[15, 16, 23, 19, 21, 17, 21, 29, 23, 25]\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "basic_player = Player()\n",
+      "basic_player_1000 = multiple_games(1000, player)\n",
+      "basic_player_mean = st.mean(basic_player_1000)\n",
+      "basic_player_stdev = st.stdev(basic_player_1000)\n",
+      "print(basic_player_mean)\n",
+      "print(basic_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "23.431\n",
+        "5.18576234811538\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(basic_player_1000, bins= 10)\n",
+      "plt.axvline(x=basic_player_mean, color = 'red')\n",
+      "plt.axvline(x=basic_player_mean+basic_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=basic_player_mean-basic_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  23.431\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  5.18576\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of Basic Player\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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3q1+W1DZ069mP7r0G1LqMpcyZ+WqtS5DUjqw06CPi3cCZQG+gLiIAGjPzQ1Wu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\n/x/JmcvKUgG37wAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c35b898>"
+       ]
+      }
+     ],
+     "prompt_number": 80
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Gordon()\n",
+      "gordon_player_1000 = multiple_games(1000, player)\n",
+      "gordon_player_mean = st.mean(gordon_player_1000)\n",
+      "gordon_player_stdev = st.stdev(gordon_player_1000)\n",
+      "print(gordon_player_mean)\n",
+      "print(gordon_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "0.0\n",
+        "0.0\n"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(gordon_player_1000, bins= 10)\n",
+      "plt.axvline(x=gordon_player_mean, color = 'red')\n",
+      "plt.axvline(x=gordon_player_mean+gordon_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=gordon_player_mean-gordon_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  0\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  0\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of Gordon (never stop rolling!)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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SG3rkkYeZNu1Ydt55F/7v//7IS14yif33fxsXXngeixc/ykknncqOO+7EsmXLOPPML3L/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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c368e80>"
+       ]
+      }
+     ],
+     "prompt_number": 81
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Random()\n",
+      "random_player_1000 = multiple_games(1000, player)\n",
+      "random_player_mean = st.mean(random_player_1000)\n",
+      "random_player_stdev = st.stdev(random_player_1000)\n",
+      "print(random_player_mean)\n",
+      "print(random_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "16.443\n",
+        "11.380609354040287\n"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(random_player_1000, bins= 10)\n",
+      "plt.axvline(x=random_player_mean, color = 'red')\n",
+      "plt.axvline(x=random_player_mean+random_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=random_player_mean-random_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  16.443\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  11.3806\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of Random Player (50/50 as to whether he rolls)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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y2mtTueeeMbRs2ZKbb76eKVNeZN999+fss0+pTPSvvTaVIUNOW2+7l18+MuXP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\nP0xp/lNRZBjtAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c4ac898>"
+       ]
+      }
+     ],
+     "prompt_number": 82
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "Enough fooling around.  Let's look at some strategies that make more sense.  The first is no longer continuing to roll once you've hit some set level of points for that turn.  So, once you get at least x points, you want to bank it and quit.  I looked at strategies where that point level equaled 17, 18, 19, 20, 21, and 22."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player17()\n",
+      "player17_player_100000 = multiple_games(100000, player)\n",
+      "player17_player_mean = st.mean(player17_player_100000)\n",
+      "player17_player_stdev = st.stdev(player17_player_100000)\n",
+      "print(player17_player_mean)\n",
+      "print(player17_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.58585\n",
+        "25.857724493788314\n"
+       ]
+      }
+     ],
+     "prompt_number": 123
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player18()\n",
+      "player18_player_100000 = multiple_games(100000, player)\n",
+      "player18_player_mean = st.mean(player18_player_100000)\n",
+      "player18_player_stdev = st.stdev(player18_player_100000)\n",
+      "print(player18_player_mean)\n",
+      "print(player18_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.96332\n",
+        "26.877851453689292\n"
+       ]
+      }
+     ],
+     "prompt_number": 109
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(player18_player_1000, bins= 9)\n",
+      "plt.axvline(x=player18_player_mean, color = 'red')\n",
+      "plt.axvline(x=player18_player_mean+player20_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=player18_player_mean-player20_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  56.963\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  26.878\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of 18Point Player (Stops rolling when he's reached 18 points for the turn)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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dd9tk+4MOOpiDDjoYgOeff4aWLVsCZLV9ly5d6NevHzNnuoKJLCiYEBFppvbf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\nEmECACg5AfmcQwFtmBfrAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c36bc18>"
+       ]
+      }
+     ],
+     "prompt_number": 124
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player19()\n",
+      "player19_player_100000 = multiple_games(100000, player)\n",
+      "player19_player_mean = st.mean(player19_player_100000)\n",
+      "player19_player_stdev = st.stdev(player19_player_100000)\n",
+      "print(player19_player_mean)\n",
+      "print(player19_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.9802\n",
+        "27.854979572041866\n"
+       ]
+      }
+     ],
+     "prompt_number": 111
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player20()\n",
+      "player20_player_100000 = multiple_games(100000, player)\n",
+      "player20_player_mean = st.mean(player20_player_100000)\n",
+      "player20_player_stdev = st.stdev(player20_player_100000)\n",
+      "print(player20_player_mean)\n",
+      "print(player20_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.87191\n",
+        "28.91087825267011\n"
+       ]
+      }
+     ],
+     "prompt_number": 112
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(player20_player_100000, bins= 9)\n",
+      "plt.axvline(x=player20_player_mean, color = 'red')\n",
+      "plt.axvline(x=player20_player_mean+player20_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=player20_player_mean-player20_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  56.872\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  28.911\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of 20Point Player (Stops rolling when he's reached 20 points for the turn)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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hXbCSrkuXrlx/ffUPLU4FLa1bt+aYY3rx6af/plev49lyy63o0WN3SktL6dSp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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c456978>"
+       ]
+      }
+     ],
+     "prompt_number": 125
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player21()\n",
+      "player21_player_100000 = multiple_games(100000, player)\n",
+      "player21_player_mean = st.mean(player21_player_100000)\n",
+      "player21_player_stdev = st.stdev(player21_player_100000)\n",
+      "print(player21_player_mean)\n",
+      "print(player21_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.84447\n",
+        "29.71856309361244\n"
+       ]
+      }
+     ],
+     "prompt_number": 119
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = Player22()\n",
+      "player22_player_100000 = multiple_games(100000, player)\n",
+      "player22_player_mean = st.mean(player22_player_100000)\n",
+      "player22_player_stdev = st.stdev(player22_player_100000)\n",
+      "print(player22_player_mean)\n",
+      "print(player22_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.77528\n",
+        "30.69314290866636\n"
+       ]
+      }
+     ],
+     "prompt_number": 126
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(player22_player_1000, bins= 9)\n",
+      "plt.axvline(x=player22_player_mean, color = 'red')\n",
+      "plt.axvline(x=player22_player_mean+player22_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=player22_player_mean-player22_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  56.775\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  30.693\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of 22Point Player (Stops rolling when he's reached 22 points for the turn)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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/kFynGgMRERGJKTEQERGRmBIDERERiSkxEBERkZgSAxEREYkpMRA9G14kgfYH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\nElNiICIiIjElBiIiIhL7/0JSfWXMqFfoAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c4dd630>"
+       ]
+      }
+     ],
+     "prompt_number": 127
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "You can get the sense from this overlapping histogram, that we're dealing with pretty similar ranges of data being produced by these strategies:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(player18_player_100000, bins= 9)\n",
+      "plt.hist(player20_player_100000, bins= 9)\n",
+      "plt.hist(player22_player_100000, bins= 9)\n",
+      "plt.figtext(x=.67, y=.75, s=\"blue: Player 18\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"green: Player 20\")\n",
+      "plt.figtext(x=.67, y=.55, s=\"red: Player 22\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of 22Point Player (Stops rolling when he's reached 22 points for the turn)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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vxX06/fpdQN++5/Hss2GIaVV9JiobIVJeftJJvfjmm6/p1+98XnvtZTp37rpx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\nJszMzKyQfwB3H44j1LZ1dgAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c4d2780>"
+       ]
+      }
+     ],
+     "prompt_number": 128
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "This boxplot gives a good comparison of the different point-based strategies:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.boxplot([player17_player_100000,\n",
+      "             player18_player_100000,\n",
+      "             player19_player_100000,\n",
+      "             player20_player_100000,\n",
+      "             player21_player_100000,\n",
+      "             player22_player_100000])\n",
+      "plt.ylim(0, 200)\n",
+      "plt.title(\"17/18/19/20/21/22 Point Player\")\n",
+      "plt.ylabel(\"ratio\")\n",
+      "plt.xticks(range(1,7), [\"17Point\", \"18Point\", \"19Point\", \"20Point\", \"21Point\", \"22Point\"])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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AGCGgo+vK2DbVbTFox2dXE8QxksHBCzoqUc+YMVlSvxYsWDP2iUJXEdCBArr3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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c46f048>"
+       ]
+      }
+     ],
+     "prompt_number": 131
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "But don't we want a lame bar graph of the mean values?"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.bar(.5, player17_player_mean, .8)\n",
+      "plt.bar(1.5, player18_player_mean, .8)\n",
+      "plt.bar(2.5, player19_player_mean, .8)\n",
+      "plt.bar(3.5, player20_player_mean, .8)\n",
+      "plt.bar(4.5, player21_player_mean, .8)\n",
+      "plt.bar(5.5, player22_player_mean, .8)\n",
+      "plt.xlabel(\"Point Based Strategies\")\n",
+      "plt.ylabel(\"Mean Value\")\n",
+      "plt.xticks(range(1,7), [\"17Point\", \"18Point\", \"19Point\", \"20Point\", \"21Point\", \"22Point\"])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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+       "text": [
+        "<matplotlib.figure.Figure at 0x10c561d68>"
+       ]
+      }
+     ],
+     "prompt_number": 163
+    },
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "I also wanted to look at strategies that involved stopping rolls once you reached a set amount of rolls.  I did less graphing with these as it became clear from the mean data (mean data!  grrrrr) that these were producing consistently lower point totals than the point-based strategies:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = FourTurn()\n",
+      "FourTurn_player_100000 = multiple_games(100000, player)\n",
+      "FourTurn_player_mean = st.mean(FourTurn_player_100000)\n",
+      "FourTurn_player_stdev = st.stdev(FourTurn_player_100000)\n",
+      "print(FourTurn_player_mean)\n",
+      "print(FourTurn_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "54.03187\n",
+        "21.90178694047159\n"
+       ]
+      }
+     ],
+     "prompt_number": 115
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = FiveTurn()\n",
+      "FiveTurn_player_100000 = multiple_games(100000, player)\n",
+      "FiveTurn_player_mean = st.mean(FiveTurn_player_100000)\n",
+      "FiveTurn_player_stdev = st.stdev(FiveTurn_player_100000)\n",
+      "print(FiveTurn_player_mean)\n",
+      "print(FiveTurn_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.27551\n",
+        "26.42954387513705\n"
+       ]
+      }
+     ],
+     "prompt_number": 136
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = SixTurn()\n",
+      "SixTurn_player_100000 = multiple_games(100000, player)\n",
+      "SixTurn_player_mean = st.mean(SixTurn_player_100000)\n",
+      "SixTurn_player_stdev = st.stdev(SixTurn_player_100000)\n",
+      "print(SixTurn_player_mean)\n",
+      "print(SixTurn_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "56.48643\n",
+        "30.402734730906875\n"
+       ]
+      }
+     ],
+     "prompt_number": 139
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(SixTurn_player_100000, bins= 9)\n",
+      "plt.axvline(x=SixTurn_player_mean, color = 'red')\n",
+      "plt.axvline(x=SixTurn_player_mean+SixTurn_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.axvline(x=SixTurn_player_mean-SixTurn_player_stdev, color = 'red', linestyle='dashed')\n",
+      "plt.figtext(x=.67, y=.75, s=\"mean  =  56.486\")\n",
+      "plt.figtext(x=.67, y=.65, s=\"std dev =  30.403\")\n",
+      "plt.xlabel(\"points\")\n",
+      "plt.ylabel(\"frequency\")\n",
+      "plt.title(\"Scores of SixTurn Player (Stops rolling after 6 turns)\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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V3/3uD+ywQzs++ugjJk68g4kT76Ft2xLOO+9MzPbYYluTJt1Jv379OP74U3jx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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10ca37c88>"
+       ]
+      }
+     ],
+     "prompt_number": 141
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = SevenTurn()\n",
+      "SevenTurn_player_100000 = multiple_games(100000, player)\n",
+      "SevenTurn_player_mean = st.mean(SevenTurn_player_100000)\n",
+      "SevenTurn_player_stdev = st.stdev(SevenTurn_player_100000)\n",
+      "print(SevenTurn_player_mean)\n",
+      "print(SevenTurn_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "54.70951\n",
+        "33.57795765606216\n"
+       ]
+      }
+     ],
+     "prompt_number": 137
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "player = EightTurn()\n",
+      "EightTurn_player_100000 = multiple_games(100000, player)\n",
+      "EightTurn_player_mean = st.mean(EightTurn_player_100000)\n",
+      "EightTurn_player_stdev = st.stdev(EightTurn_player_100000)\n",
+      "print(EightTurn_player_mean)\n",
+      "print(EightTurn_player_stdev)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "52.18721\n",
+        "36.15866862744077\n"
+       ]
+      }
+     ],
+     "prompt_number": 133
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.boxplot([FourTurn_player_100000,\n",
+      "             FiveTurn_player_100000,\n",
+      "             SixTurn_player_100000,\n",
+      "             SevenTurn_player_100000,\n",
+      "             EightTurn_player_100000])\n",
+      "plt.ylim(0, 200)\n",
+      "plt.title(\"4/5/6/7/8 Turn Player\")\n",
+      "plt.ylabel(\"ratio\")\n",
+      "plt.xticks(range(1,6), [\"4 Turn\", \"5 Turn\", \"6 Turn\", \"7 Turn\", \"8 Turn\"])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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6TtJpZvZHNb8zdxJ/c62ZHe7uT5nZAknrstf/IGlR7n1HZq+NaNOmHZMoRuOF\nGcy2NbsYSRsY6FR7ezv1XKJly/gsl62nJ3yOly2jjstWtc/yaCcfo3W5X64wEv0a7d/tvlfSw5Mo\nz22SLpB0Vba+Nff6jWZ2tUJX+/GS7pnE3wEAYMoYrct9haQVkk7ObjXrVAj1aZJOkTTmwDgzu0nS\nqyQdYmZ9kv6HpCsl3WJm71F221r29x42s1sUThb2Snqfu0/mWj2mIOZyBzBVjXkfupl9VtL7JM2Q\ntEGh9fxT1RHo7n7eCLvOHOH9V0i6YqzjAgAwWeHSRriMlIJ67vM+T+Ee9JslvVrS6xRa7gAAoEXU\nE+hr3H2LpAclneLud0p6QbnFSg8TngAAylRPoG82s3dL+rWkd5rZyyQdWm6xALQqTk7Ll9qEJ2iM\negJ9mqRDs5b5Ckn/IOmSUksFAADGpZ6Hs8yX9FVJcvePllscYHJSG+QCAPWqJ9AHJD1pZi5pZ/ba\noLu/trxiAQBQrtRuc60n0D8xzGvcHw4AQAsZM9Dd/a4GlCN5qZ0JAgBaC88bBzAujMAuH3cSYCII\ndAAAEkCgIym0HgFMVQQ6AGBKSu3SBoEOAEACCPQGSe1MEADQWgh0AOPCyWn5GAuCiSDQAQBIAIGO\npNB6BDBVEegAgCkptUsbBDoAAAkg0BsktTNBAEBrIdABjAsnp+VjLAgmgkAHACABBDqSQusRwFRF\noAMApqTULm0Q6AAAJKCj2QWYKnp6OtXeLi1b1uySAChKb+8BWrq0+K/R1avbJIXvjTIsWbJXvb27\nSjk2mocWOoBxSa2bcjKWLu14NnyLtHDhoI48svDDSgonC2WchKD5+K8KAJOwcOGgli/vL/y43d1d\nWr+++OOW1epH89FCR1JoPQKYqgh0AMCUlNptrgQ6AAAJ4Bp6gyxf3p9dE2t2STBVVHEENqOvgYmj\nhQ4kqmojsBl9DUwO//eg4cpqOUq0HmtVaQQ2o6+ByaGFjoYrq+Uo0XoEMHXxDYWmKKvlKNF6BFCf\n1GbwpIUOAEACCPQGYcITAECZCHQAABJAoAMAkAAGxQEAWha3udaPFjoAoGVxm2v9aKHXqOJ0mVI1\nJz0BgHpwm2t9aKHXqNp0mRKTngAAaKEPq0rTZUpMegIAoIUOAEASCHQAABJAoAMAkAACHQCABBDo\nAAAkgEAHACABBDoAAAkg0AEASACBDgBAAgh0AAASQKADAJAAAh0AgAQQ6AAAJIBABwAgAQQ6AAAJ\n4HnoaLgOi1xgAAAJDUlEQVRPbf6EztrxHc3vGSznD7S3af5Asce+e3WbfjjrbZI+XehxAaAotNAB\nAEgALXQ03BVzP6cr5n5Oy5f3l3L87u4ubVy/rdBjvrynU5L0pyqnzAAwWQQ6AExQqZePSrh0JHH5\nKGV0uQMAkABa6AAwQWVePirj0pFUvctHDKKtH4Fegy40AEAVNS3QzWylpK2S9kna4+5nmNl8STdL\nOlrSSknnuvvmZpURANBcDKKtXzNb6IOSXu3uG3OvXSTpx+7+OTP7ZLZ9USMLRRcaUlG13iZ6moDJ\nafaguLaa7bMlXZ/9fL2kcxpbHAAAqqnZLfQ7zGyfpK+4+9ckHebua7P9ayUd1rTSARVXtd4mepqA\nyWlmC/3l7n6qpDdJer+ZvSK/090HFUIfAACMoWktdHdfk63Xm9n3JZ0haa2ZHe7uT5nZAknrRjvG\nvHmz1NExrdBytWenON3dXYUeNyrjuGWXuWiNKG/Rx65aHUvV+yxTx8/F9wXfF+PRlEA3s1mSprn7\nNjPrlPR6SZdKuk3SBZKuyta3jnacTZt2FF62gYHQ7bd+fTndlOtLGBRXZpnLUHZ5y6jnqtWxVL3P\nMnW8P74vAr4v9jfaSUKzWuiHSfq+mcUyfMvdbzezeyXdYmbvUXbbWpPKBwBApTQl0N19haRThnl9\no6QzG18iAACqrdm3rQEAgAIQ6AAAJIBABwAgAQQ6AAAJINABAEgAgQ4AQAIIdAAAEkCgAwCQAAId\nAIAEEOgAACSAQAcAIAEEOgAACSDQAQBIQLMen9qy+vrCOU5PT2fhx25vH3pObpFWr27TwoWDhR+3\nLGXWsVROPVetjgFMPQR6g6xe3SZJWriw+GMvXDioJUv2Fn/gCiqrnqljAK2OQK+xbt22Uo7b09Op\n9vY2LVvWX8rxq6SsOpaoZwBTF9fQAQBIAIEOAEACCHQAABJAoAMAkAACvUGWL+/XypXNLkX6qGcA\nUxWBDgBAAgh0AAASQKADAJAAAh0AgAQQ6AAAJICpXxskTEkqLVvW7JKkjXoeUrUHDfEAHAyHhznV\nj0AHMC48AAepSO2zTKADieJBQ0gBD3OqH4EOABNUtcsaEpc2UkagA0CLKasrOByTSxupItABYIK4\nrIFWwm1rDcIc441BPQOYqgh0AOPCSRNSkdpnmUAHACABBDoAAAkg0AGgxaTWFYzGINABAEgAgd4g\nPT2dWry42aVIH/UMYKoi0AGMCydNSEVqn2UCHQCABBDoAAAkgEAHgBaTWlcwGoNABwAgAQR6g3Bf\naWNQzwCmKgIdwLhw0oRUpPZZJtABAEgAgQ4AQAIIdABoMal1BaMxCHQAABJAoDcI95U2BvUMYKoi\n0AGMCydNSEVqn2UCHQCABBDoAAAkgEAHgBaTWlcwGoNABwAgAQR6g3BfaWNQzwCmKgIdwLhw0oRU\npPZZJtABAEgAgQ4AQAIIdABoMal1BaMxCHQAABJAoDcI95U2BvUMYKoi0AGMCydNSEVqn2UCHQCA\nBBDoAAAkgEAHgBaTWlcwGoNABwAgAR3NLkAtM3ujpC9ImibpWne/qslFKsTy5f3q7u7S+vXNLkna\nqGcAU1VLtdDNbJqkL0l6o6STJJ1nZic2t1QA8pj0BKlI7bPcUoEu6QxJj7n7SnffI+mfJL2lyWUC\nAKDltVqgHyGpL7e9KnsNAACMotWuoQ82uwDj0dt7iZYuvbXu97e3t2lgoP5/4pIl56i397KJFC0p\nZdYzdRxQx+Ubbx1LberpoY7HY/x1nNZnuW1wsHUy1MxeKqnX3d+YbV8saSCVgXEAAJSl1Vro90o6\n3swWS1ot6e2SzmtqiQAAqICWuobu7nslfUDSv0p6WNLN7v5Ic0sFAEDra6kudwAAMDEt1UIHAAAT\nQ6ADAJAAAh0AgAS02ij3Ssmmqr1X0ip3X1Kz71OS/mO2ebKkB7Kfv+7uX2pcKavLzFZK2ippn6Q9\n7n5GzX7qeJLMbK6kayW9QGEeiAvd/Ze5/dTxJJiZKcx4GR0r6a/d/Zrce6jjAmS3Ob9L0oCkByX9\nZ3fflduffD0zKG4SzOwjknokdbn72aO8b5u7d43juNPcfV8RZawyM1shqcfdN9bxXup4Aszsekk/\nc/frzKxDUqe7bxnhvdTxJJhZu6Q/SDrD3ftGeA91PAHZrc4/lXSiu+8ys5sl/bO7Xz/C+5OsZ1ro\nE2RmR0p6s6TLJX2kzt9ZLGmpu78w2/6YwhfopWZ2l6T7JP2xpJvM7GxJv5T0GklzJb3H3X9R9L+j\nAtrG82bquH5mNkfSK9z9AunZ20aHDfOa31ss6ngizpT0+Ehhnkcdj9tWSXskzTKzfZJmKZw8jSq1\neuYa+sT9raSPK3TvTNSghqa7HZQ03d1Pd/ers+1p7v4SSR+W9OnJFLaiBiXdYWb3mtl/mcQxqOPh\nHSNpvZl9w8x+bWZfM7NZEzgOdVyfd0i6cYK/Sx2PIuvF+7ykJxUmJdvs7ndM4FCVrmcCfQLM7E8k\nrXP3+zTOFuQw8r9/c82+72XrX0taPMm/U0Uvd/dTJb1J0vvN7BUTPA51PLwOSS+W9GV3f7GkfkkX\nTfBY1PEozGyGpCWSvj2Jw1DHIzCz4xRCdrGkhZIOMrN3TvBwla1nAn1i/oOks7NrvDdJeq2Z3VDH\n7+3V/nU+U/s/kKa/5v1xQMc+TcHLI+6+Jluvl/R9hcfrjoU6rt8qhQGdy7Lt7ygE/Fio4/F7k6Tl\n2We5HtTx+Jwm6d/c/ens0tH3FL6nx5JUPRPoE+Dun3L3Re5+jEI32k/d/fw6fnWtpEPNbL6ZHSDp\nT2r2T7a1nwwzm2VmXdnPnZJerzBydSzUcZ3c/SlJfWZ2QvbSmZIequNXqePxO0/h5L9e1PH4/Luk\nl5rZTDNrU/gsP1zH7yVVzwR6Mca6VWBQktx9j6S/kXSPpNv13A/caMeZarcjHCbp52b2G0m/kvQD\nd799lPdTxxPzQUnfMrP7FW7luWKU91LHE5CdkJ6poe7a0VDHE+Du90u6QeE24ng72ldH+ZUk65nb\n1gAASAAtdAAAEkCgAwCQAAIdAIAEEOgAACSAQAcAIAEEOgAACSDQAQBIAIEOAEAC/j+rXFohMHfs\nAgAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10c8d50f0>"
+       ]
+      }
+     ],
+     "prompt_number": 142
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file
diff --git a/requirements.txt b/requirements.txt
new file mode 100644
index 0000000..60e753d
--- /dev/null
+++ b/requirements.txt
@@ -0,0 +1,3 @@
+ipython[all]
+matplotlib
+seaborn