Pandas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'1': [1, 2]}\n",
      "{'1': [1, 2]}\n"
     ]
    }
   ],
   "source": [
    "a={}\n",
    "a['1']=[1]\n",
    "a['1'].append(2)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing numpy and pandas libraries\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining a function deal() to deal cards to two players\n",
    "def deal():\n",
    "    # Initialize player hands\n",
    "    p1 = []\n",
    "    p2 = []\n",
    "    \n",
    "    # Initialize and shuffle deck\n",
    "    deck = list(range(1, 14)) * 4\n",
    "    np.random.shuffle(deck)\n",
    "    \n",
    "    # Deal cards to each player\n",
    "    for i in range(len(deck)):\n",
    "        if i % 2:\n",
    "            p2.append(deck.pop(0))\n",
    "        else:\n",
    "            p1.append(deck.pop(0))\n",
    "            \n",
    "    return p1, p2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1, 1.2, 1.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Re-define function to play a single game - No print statements\n",
    "# The code is a modified version of the solution of HW2 uploaded on ELMS\n",
    "def play(games=1):\n",
    "    dict1={}\n",
    "    # Collect statistics\n",
    "    S = {}\n",
    "    S['p1_initial_total']=[]\n",
    "    S['p2_initial_total']=[]\n",
    "    S['ties']=[]\n",
    "    S['largest_Total']=[]\n",
    "    S['winner']=[]\n",
    "    S['p1_final_total']=[]\n",
    "    S['p2_final_total']=[]\n",
    "    \n",
    "    for game_count in range(games):\n",
    "        # Deal cards to players, initialize claim lists\n",
    "        p1, p2 = deal()\n",
    "        p1_claim, p2_claim = [], []\n",
    "        ties=0\n",
    "        largest_total=0\n",
    "        \n",
    "        \n",
    "        # Calculate initial statistics\n",
    "        S['p1_initial_total'].append(sum(p1))\n",
    "        S['p2_initial_total'].append(sum(p2))\n",
    "        \n",
    "        # Play!\n",
    "        k = 1 # round counter\n",
    "        i = 13 # maximum number of rounds\n",
    "        while i > 0:\n",
    "            # Each player plays two cards\n",
    "            p1_play = [p1.pop(0), p1.pop(0)]\n",
    "            p2_play = [p2.pop(0), p2.pop(0)]\n",
    "            i -= 1\n",
    "\n",
    "            # Check for tie, and process accordingly\n",
    "            if sum(p1_play) > sum(p2_play):\n",
    "                # Player 1 wins hand, append cards to claim list\n",
    "                p1_claim.extend(p1_play); p1_claim.extend(p2_play)\n",
    "                if (sum(p1_play)+sum(p2_play))>largest_total:\n",
    "                    largest_total=sum(p1_play)+sum(p2_play)\n",
    "            elif sum(p2_play) > sum(p1_play):\n",
    "                # Player 2 wins hand, append cards\n",
    "                p2_claim.extend(p1_play); p2_claim.extend(p2_play)\n",
    "                if (sum(p1_play)+sum(p2_play))>largest_total:\n",
    "                    largest_total=sum(p1_play)+sum(p2_play)\n",
    "            else:\n",
    "                temp=0\n",
    "                # Tie - Continue to play two cards until a player wins\n",
    "                if i > 0:\n",
    "                    while sum(p1_play[-2:]) == sum(p2_play[-2:]):\n",
    "                        p1_play.extend([p1.pop(0), p1.pop(0)])\n",
    "                        p2_play.extend([p2.pop(0), p2.pop(0)])\n",
    "                        i -= 1\n",
    "                        ties+=1\n",
    "                        temp+=sum(p1_play)+sum(p2_play)\n",
    "                        \n",
    "                        if sum(p1_play[-2:]) > sum(p2_play[-2:]):\n",
    "                            # Player 1 wins hand, append cards to claim list\n",
    "                            p1_claim.extend(p1_play); p1_claim.extend(p2_play)\n",
    "\n",
    "                            if (temp)>largest_total:\n",
    "                                largest_total=temp\n",
    "\n",
    "                        elif sum(p2_play[-2:]) > sum(p1_play[-2:]):\n",
    "                            # Player 2 wins hand, append cards to claim list\n",
    "                            p2_claim.extend(p1_play); p2_claim.extend(p2_play)\n",
    "\n",
    "                            if (temp)>largest_total:\n",
    "                                largest_total=temp\n",
    "\n",
    "                        else:\n",
    "                            # Check for whether game ends in a tie - return cards to respective players\n",
    "                            if i <= 0:\n",
    "                                p1_claim.extend(p1_play)\n",
    "                                p2_claim.extend(p2_play)\n",
    "                                break\n",
    "                else:\n",
    "                    # Game ends in a tie - return cards to respective players\n",
    "                    p1_claim.extend(p1_play)\n",
    "                    p2_claim.extend(p2_play)\n",
    "\n",
    "            # Increment round\n",
    "            k += 1\n",
    "        \n",
    "        # Game over, compile results\n",
    "        S['p1_final_total'].append((sum(p1_claim)))\n",
    "        S['p2_final_total'].append((sum(p2_claim)))\n",
    "        S['ties'].append(ties)\n",
    "        S['largest_Total'].append(largest_total)\n",
    "        if S['p1_final_total'] != S['p2_final_total']:\n",
    "            # One player wins\n",
    "            S['winner'].append(0) if S['p1_final_total'] > S['p2_final_total'] else S['winner'].append(0)\n",
    "        else:\n",
    "            # Game is tied\n",
    "            S['winner'].append(-1)\n",
    "      \n",
    "        # Return results\n",
    "    return S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'p1_initial_total': [214],\n",
       " 'p2_initial_total': [150],\n",
       " 'ties': [0],\n",
       " 'largest_Total': [39],\n",
       " 'winner': [0],\n",
       " 'p1_final_total': [260],\n",
       " 'p2_final_total': [104]}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "{'p1_initial_total': [214],\n",
       " 'p2_initial_total': [150],\n",
       " 'ties': [0],\n",
       " 'largest_Total': [39],\n",
       " 'winner': [0],\n",
       " 'p1_final_total': [260],\n",
       " 'p2_final_total': [104]}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To play a single game\n",
    "play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'p1_initial_total': [178, 186, 174, 184, 179],\n",
       " 'p2_initial_total': [186, 178, 190, 180, 185],\n",
       " 'ties': [0, 0, 0, 0, 1],\n",
       " 'largest_Total': [40, 39, 44, 41, 48],\n",
       " 'winner': [0, 0, 0, 0, 0],\n",
       " 'p1_final_total': [142, 242, 163, 140, 169],\n",
       " 'p2_final_total': [222, 122, 201, 224, 195]}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "{'p1_initial_total': [178, 186, 174, 184, 179],\n",
       " 'p2_initial_total': [186, 178, 190, 180, 185],\n",
       " 'ties': [0, 0, 0, 0, 1],\n",
       " 'largest_Total': [40, 39, 44, 41, 48],\n",
       " 'winner': [0, 0, 0, 0, 0],\n",
       " 'p1_final_total': [142, 242, 163, 140, 169],\n",
       " 'p2_final_total': [222, 122, 201, 224, 195]}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To play multiple games\n",
    "play(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#To simulate 1000 games and storing the results in a pandas DataFrame\n",
    "outcome=pd.DataFrame(play(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>0</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>195</td>\n",
       "      <td>169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "      <td>0</td>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185</td>\n",
       "      <td>179</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>233</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>205</td>\n",
       "      <td>159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>190</td>\n",
       "      <td>174</td>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>163</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>197</td>\n",
       "      <td>167</td>\n",
       "      <td>1</td>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>234</td>\n",
       "      <td>130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>173</td>\n",
       "      <td>191</td>\n",
       "      <td>2</td>\n",
       "      <td>136</td>\n",
       "      <td>0</td>\n",
       "      <td>164</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>1</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "      <td>299</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>182</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>192</td>\n",
       "      <td>172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>166</td>\n",
       "      <td>198</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "0               189               175     0             46       0   \n",
       "1               179               185     1             59       0   \n",
       "2               185               179     3             64       0   \n",
       "3               180               184     0             41       0   \n",
       "4               190               174     1             60       0   \n",
       "5               197               167     1             61       0   \n",
       "6               173               191     2            136       0   \n",
       "7               189               175     1             66       0   \n",
       "8               182               182     1             49       0   \n",
       "9               166               198     0             38       0   \n",
       "\n",
       "   p1_final_total  p2_final_total  \n",
       "0             195             169  \n",
       "1             179             185  \n",
       "2             233             131  \n",
       "3             205             159  \n",
       "4             163             201  \n",
       "5             234             130  \n",
       "6             164             200  \n",
       "7             299              65  \n",
       "8             192             172  \n",
       "9              94             270  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>0</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>195</td>\n",
       "      <td>169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "      <td>0</td>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185</td>\n",
       "      <td>179</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>233</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>205</td>\n",
       "      <td>159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>190</td>\n",
       "      <td>174</td>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>163</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>197</td>\n",
       "      <td>167</td>\n",
       "      <td>1</td>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>234</td>\n",
       "      <td>130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>173</td>\n",
       "      <td>191</td>\n",
       "      <td>2</td>\n",
       "      <td>136</td>\n",
       "      <td>0</td>\n",
       "      <td>164</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>1</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "      <td>299</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>182</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>192</td>\n",
       "      <td>172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>166</td>\n",
       "      <td>198</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "0               189               175     0             46       0   \n",
       "1               179               185     1             59       0   \n",
       "2               185               179     3             64       0   \n",
       "3               180               184     0             41       0   \n",
       "4               190               174     1             60       0   \n",
       "5               197               167     1             61       0   \n",
       "6               173               191     2            136       0   \n",
       "7               189               175     1             66       0   \n",
       "8               182               182     1             49       0   \n",
       "9               166               198     0             38       0   \n",
       "\n",
       "   p1_final_total  p2_final_total  \n",
       "0             195             169  \n",
       "1             179             185  \n",
       "2             233             131  \n",
       "3             205             159  \n",
       "4             163             201  \n",
       "5             234             130  \n",
       "6             164             200  \n",
       "7             299              65  \n",
       "8             192             172  \n",
       "9              94             270  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To display the first 10 rows\n",
    "outcome.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>990</th>\n",
       "      <td>174</td>\n",
       "      <td>190</td>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>103</td>\n",
       "      <td>261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>184</td>\n",
       "      <td>180</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>136</td>\n",
       "      <td>228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>992</th>\n",
       "      <td>187</td>\n",
       "      <td>177</td>\n",
       "      <td>1</td>\n",
       "      <td>47</td>\n",
       "      <td>0</td>\n",
       "      <td>210</td>\n",
       "      <td>154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>993</th>\n",
       "      <td>176</td>\n",
       "      <td>188</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>139</td>\n",
       "      <td>225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>139</td>\n",
       "      <td>225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>174</td>\n",
       "      <td>190</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>167</td>\n",
       "      <td>197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>176</td>\n",
       "      <td>188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>181</td>\n",
       "      <td>183</td>\n",
       "      <td>0</td>\n",
       "      <td>43</td>\n",
       "      <td>0</td>\n",
       "      <td>212</td>\n",
       "      <td>152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>195</td>\n",
       "      <td>169</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>215</td>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>213</td>\n",
       "      <td>151</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>249</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "990               174               190     0             45       0   \n",
       "991               184               180     0             40       0   \n",
       "992               187               177     1             47       0   \n",
       "993               176               188     1             45       0   \n",
       "994               179               185     0             40       0   \n",
       "995               174               190     2             64       0   \n",
       "996               180               184     0             39       0   \n",
       "997               181               183     0             43       0   \n",
       "998               195               169     0             39       0   \n",
       "999               213               151     0             38       0   \n",
       "\n",
       "     p1_final_total  p2_final_total  \n",
       "990             103             261  \n",
       "991             136             228  \n",
       "992             210             154  \n",
       "993             139             225  \n",
       "994             139             225  \n",
       "995             167             197  \n",
       "996             176             188  \n",
       "997             212             152  \n",
       "998             215             149  \n",
       "999             249             115  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>990</th>\n",
       "      <td>174</td>\n",
       "      <td>190</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>103</td>\n",
       "      <td>261</td>\n",
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       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>184</td>\n",
       "      <td>180</td>\n",
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       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>136</td>\n",
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       "    <tr>\n",
       "      <th>992</th>\n",
       "      <td>187</td>\n",
       "      <td>177</td>\n",
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       "      <td>47</td>\n",
       "      <td>0</td>\n",
       "      <td>210</td>\n",
       "      <td>154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>993</th>\n",
       "      <td>176</td>\n",
       "      <td>188</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>139</td>\n",
       "      <td>225</td>\n",
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       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>139</td>\n",
       "      <td>225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>174</td>\n",
       "      <td>190</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>167</td>\n",
       "      <td>197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>176</td>\n",
       "      <td>188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>181</td>\n",
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       "      <td>0</td>\n",
       "      <td>43</td>\n",
       "      <td>0</td>\n",
       "      <td>212</td>\n",
       "      <td>152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>195</td>\n",
       "      <td>169</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>215</td>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>213</td>\n",
       "      <td>151</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>249</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "990               174               190     0             45       0   \n",
       "991               184               180     0             40       0   \n",
       "992               187               177     1             47       0   \n",
       "993               176               188     1             45       0   \n",
       "994               179               185     0             40       0   \n",
       "995               174               190     2             64       0   \n",
       "996               180               184     0             39       0   \n",
       "997               181               183     0             43       0   \n",
       "998               195               169     0             39       0   \n",
       "999               213               151     0             38       0   \n",
       "\n",
       "     p1_final_total  p2_final_total  \n",
       "990             103             261  \n",
       "991             136             228  \n",
       "992             210             154  \n",
       "993             139             225  \n",
       "994             139             225  \n",
       "995             167             197  \n",
       "996             176             188  \n",
       "997             212             152  \n",
       "998             215             149  \n",
       "999             249             115  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To display the last 10 rows\n",
    "outcome.tail(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Adding a new column to specify the outcome of the game\n",
    "outcome.loc[:,'outcome'] = 'Tie game'\n",
    "outcome.loc[outcome['winner']==0, 'outcome'] = 'Player 1 wins'\n",
    "outcome.loc[outcome['winner']==1, 'outcome'] = 'Player 2 wins'\n",
    "outcome.loc[outcome['winner']==-1, 'outcome'] = 'Tie game'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Adding new columns for the winning total \n",
    "outcome.loc[outcome['p1_final_total']>outcome['p2_final_total'], 'winning_total'] = outcome['p1_final_total']\n",
    "outcome.loc[outcome['p1_final_total']<outcome['p2_final_total'], 'winning_total'] = outcome['p2_final_total']\n",
    "outcome.loc[outcome['p1_final_total']==outcome['p2_final_total'], 'winning_total'] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Adding new columns for the losing total\n",
    "outcome.loc[outcome['p1_final_total']>outcome['p2_final_total'], 'losing_total'] = outcome['p2_final_total']\n",
    "outcome.loc[outcome['p1_final_total']<outcome['p2_final_total'], 'losing_total'] = outcome['p1_final_total']\n",
    "outcome.loc[outcome['p1_final_total']==outcome['p2_final_total'], 'losing_total'] = np.nan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>p1_initial_total</th>\n",
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       "      <td>195</td>\n",
       "      <td>169</td>\n",
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       "    </tr>\n",
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       "      <th>1</th>\n",
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       "      <td>185</td>\n",
       "      <td>Player 1 wins</td>\n",
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       "      <td>179.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185</td>\n",
       "      <td>179</td>\n",
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       "      <td>0</td>\n",
       "      <td>233</td>\n",
       "      <td>131</td>\n",
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       "      <td>233.0</td>\n",
       "      <td>131.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>205</td>\n",
       "      <td>159</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>205.0</td>\n",
       "      <td>159.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>190</td>\n",
       "      <td>174</td>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>163</td>\n",
       "      <td>201</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>201.0</td>\n",
       "      <td>163.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>197</td>\n",
       "      <td>167</td>\n",
       "      <td>1</td>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>234</td>\n",
       "      <td>130</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>234.0</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>173</td>\n",
       "      <td>191</td>\n",
       "      <td>2</td>\n",
       "      <td>136</td>\n",
       "      <td>0</td>\n",
       "      <td>164</td>\n",
       "      <td>200</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>200.0</td>\n",
       "      <td>164.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>1</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "      <td>299</td>\n",
       "      <td>65</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>299.0</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>182</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>192</td>\n",
       "      <td>172</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>192.0</td>\n",
       "      <td>172.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>166</td>\n",
       "      <td>198</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>270</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>270.0</td>\n",
       "      <td>94.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "0               189               175     0             46       0   \n",
       "1               179               185     1             59       0   \n",
       "2               185               179     3             64       0   \n",
       "3               180               184     0             41       0   \n",
       "4               190               174     1             60       0   \n",
       "5               197               167     1             61       0   \n",
       "6               173               191     2            136       0   \n",
       "7               189               175     1             66       0   \n",
       "8               182               182     1             49       0   \n",
       "9               166               198     0             38       0   \n",
       "\n",
       "   p1_final_total  p2_final_total        outcome  winning_total  losing_total  \n",
       "0             195             169  Player 1 wins          195.0         169.0  \n",
       "1             179             185  Player 1 wins          185.0         179.0  \n",
       "2             233             131  Player 1 wins          233.0         131.0  \n",
       "3             205             159  Player 1 wins          205.0         159.0  \n",
       "4             163             201  Player 1 wins          201.0         163.0  \n",
       "5             234             130  Player 1 wins          234.0         130.0  \n",
       "6             164             200  Player 1 wins          200.0         164.0  \n",
       "7             299              65  Player 1 wins          299.0          65.0  \n",
       "8             192             172  Player 1 wins          192.0         172.0  \n",
       "9              94             270  Player 1 wins          270.0          94.0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "      <th>outcome</th>\n",
       "      <th>winning_total</th>\n",
       "      <th>losing_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>0</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>195</td>\n",
       "      <td>169</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>195.0</td>\n",
       "      <td>169.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "      <td>0</td>\n",
       "      <td>179</td>\n",
       "      <td>185</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>185.0</td>\n",
       "      <td>179.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185</td>\n",
       "      <td>179</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>233</td>\n",
       "      <td>131</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>233.0</td>\n",
       "      <td>131.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>180</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>205</td>\n",
       "      <td>159</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>205.0</td>\n",
       "      <td>159.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>190</td>\n",
       "      <td>174</td>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>163</td>\n",
       "      <td>201</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>201.0</td>\n",
       "      <td>163.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>197</td>\n",
       "      <td>167</td>\n",
       "      <td>1</td>\n",
       "      <td>61</td>\n",
       "      <td>0</td>\n",
       "      <td>234</td>\n",
       "      <td>130</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>234.0</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>173</td>\n",
       "      <td>191</td>\n",
       "      <td>2</td>\n",
       "      <td>136</td>\n",
       "      <td>0</td>\n",
       "      <td>164</td>\n",
       "      <td>200</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>200.0</td>\n",
       "      <td>164.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>189</td>\n",
       "      <td>175</td>\n",
       "      <td>1</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "      <td>299</td>\n",
       "      <td>65</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>299.0</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>182</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>192</td>\n",
       "      <td>172</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>192.0</td>\n",
       "      <td>172.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>166</td>\n",
       "      <td>198</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>270</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>270.0</td>\n",
       "      <td>94.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "0               189               175     0             46       0   \n",
       "1               179               185     1             59       0   \n",
       "2               185               179     3             64       0   \n",
       "3               180               184     0             41       0   \n",
       "4               190               174     1             60       0   \n",
       "5               197               167     1             61       0   \n",
       "6               173               191     2            136       0   \n",
       "7               189               175     1             66       0   \n",
       "8               182               182     1             49       0   \n",
       "9               166               198     0             38       0   \n",
       "\n",
       "   p1_final_total  p2_final_total        outcome  winning_total  losing_total  \n",
       "0             195             169  Player 1 wins          195.0         169.0  \n",
       "1             179             185  Player 1 wins          185.0         179.0  \n",
       "2             233             131  Player 1 wins          233.0         131.0  \n",
       "3             205             159  Player 1 wins          205.0         159.0  \n",
       "4             163             201  Player 1 wins          201.0         163.0  \n",
       "5             234             130  Player 1 wins          234.0         130.0  \n",
       "6             164             200  Player 1 wins          200.0         164.0  \n",
       "7             299              65  Player 1 wins          299.0          65.0  \n",
       "8             192             172  Player 1 wins          192.0         172.0  \n",
       "9              94             270  Player 1 wins          270.0          94.0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To preview the first 10 rows of the modified DataFrame\n",
    "outcome.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The frequency for the three outcomes: \n",
      "Player 1 wins    1000\n",
      "Name: outcome, dtype: int64\n",
      "The frequency for the three outcomes: \n",
      "Player 1 wins    1000\n",
      "Name: outcome, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "#To summarize the frequency of the three outcomes\n",
    "print('The frequency for the three outcomes: ')\n",
    "print(outcome['outcome'].value_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "      <th>outcome</th>\n",
       "      <th>winning_total</th>\n",
       "      <th>losing_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [p1_initial_total, p2_initial_total, ties, largest_Total, winner, p1_final_total, p2_final_total, outcome, winning_total, losing_total]\n",
       "Index: []"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
       "      <th>outcome</th>\n",
       "      <th>winning_total</th>\n",
       "      <th>losing_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [p1_initial_total, p2_initial_total, ties, largest_Total, winner, p1_final_total, p2_final_total, outcome, winning_total, losing_total]\n",
       "Index: []"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To display the rows in your DataFrame that contain the 'Tie game' outcomes\n",
    "outcome[outcome['outcome']=='Tie game']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    991.000000\n",
       "mean     225.329970\n",
       "std       31.396022\n",
       "min      183.000000\n",
       "25%      200.000000\n",
       "50%      220.000000\n",
       "75%      245.000000\n",
       "max      338.000000\n",
       "Name: winning_total, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    991.000000\n",
       "mean     225.329970\n",
       "std       31.396022\n",
       "min      183.000000\n",
       "25%      200.000000\n",
       "50%      220.000000\n",
       "75%      245.000000\n",
       "max      338.000000\n",
       "Name: winning_total, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To provide descriptive statistics for the winning_total column\n",
    "outcome.winning_total.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>p1_initial_total</th>\n",
       "      <th>p2_initial_total</th>\n",
       "      <th>ties</th>\n",
       "      <th>largest_Total</th>\n",
       "      <th>winner</th>\n",
       "      <th>p1_final_total</th>\n",
       "      <th>p2_final_total</th>\n",
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       "      <th>winning_total</th>\n",
       "      <th>losing_total</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>211</td>\n",
       "      <td>153</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>338</td>\n",
       "      <td>26</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>338.0</td>\n",
       "      <td>26.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>154</td>\n",
       "      <td>210</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>331</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>331.0</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>585</th>\n",
       "      <td>161</td>\n",
       "      <td>203</td>\n",
       "      <td>4</td>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>329</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>329.0</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>159</td>\n",
       "      <td>205</td>\n",
       "      <td>2</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>37</td>\n",
       "      <td>327</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>327.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>147</td>\n",
       "      <td>217</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>323</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>323.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>157</td>\n",
       "      <td>207</td>\n",
       "      <td>1</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>323</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>323.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>685</th>\n",
       "      <td>211</td>\n",
       "      <td>153</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>0</td>\n",
       "      <td>322</td>\n",
       "      <td>42</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>322.0</td>\n",
       "      <td>42.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>660</th>\n",
       "      <td>162</td>\n",
       "      <td>202</td>\n",
       "      <td>3</td>\n",
       "      <td>145</td>\n",
       "      <td>0</td>\n",
       "      <td>49</td>\n",
       "      <td>315</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>315.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>659</th>\n",
       "      <td>159</td>\n",
       "      <td>205</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>51</td>\n",
       "      <td>313</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>313.0</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>621</th>\n",
       "      <td>207</td>\n",
       "      <td>157</td>\n",
       "      <td>1</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>313</td>\n",
       "      <td>51</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>313.0</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "72                211               153     0             41       0   \n",
       "200               154               210     1             45       0   \n",
       "585               161               203     4             67       0   \n",
       "243               159               205     2             72       0   \n",
       "13                147               217     0             39       0   \n",
       "497               157               207     1             70       0   \n",
       "685               211               153     1             74       0   \n",
       "660               162               202     3            145       0   \n",
       "659               159               205     1             45       0   \n",
       "621               207               157     1             54       0   \n",
       "\n",
       "     p1_final_total  p2_final_total        outcome  winning_total  \\\n",
       "72              338              26  Player 1 wins          338.0   \n",
       "200              33             331  Player 1 wins          331.0   \n",
       "585              35             329  Player 1 wins          329.0   \n",
       "243              37             327  Player 1 wins          327.0   \n",
       "13               41             323  Player 1 wins          323.0   \n",
       "497              41             323  Player 1 wins          323.0   \n",
       "685             322              42  Player 1 wins          322.0   \n",
       "660              49             315  Player 1 wins          315.0   \n",
       "659              51             313  Player 1 wins          313.0   \n",
       "621             313              51  Player 1 wins          313.0   \n",
       "\n",
       "     losing_total  \n",
       "72           26.0  \n",
       "200          33.0  \n",
       "585          35.0  \n",
       "243          37.0  \n",
       "13           41.0  \n",
       "497          41.0  \n",
       "685          42.0  \n",
       "660          49.0  \n",
       "659          51.0  \n",
       "621          51.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "      <td>154</td>\n",
       "      <td>210</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>331</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>331.0</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>585</th>\n",
       "      <td>161</td>\n",
       "      <td>203</td>\n",
       "      <td>4</td>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>329</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>329.0</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>159</td>\n",
       "      <td>205</td>\n",
       "      <td>2</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>37</td>\n",
       "      <td>327</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>327.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>147</td>\n",
       "      <td>217</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>323</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>323.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>157</td>\n",
       "      <td>207</td>\n",
       "      <td>1</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>323</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>323.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>685</th>\n",
       "      <td>211</td>\n",
       "      <td>153</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>0</td>\n",
       "      <td>322</td>\n",
       "      <td>42</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>322.0</td>\n",
       "      <td>42.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>660</th>\n",
       "      <td>162</td>\n",
       "      <td>202</td>\n",
       "      <td>3</td>\n",
       "      <td>145</td>\n",
       "      <td>0</td>\n",
       "      <td>49</td>\n",
       "      <td>315</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>315.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>659</th>\n",
       "      <td>159</td>\n",
       "      <td>205</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>51</td>\n",
       "      <td>313</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>313.0</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>621</th>\n",
       "      <td>207</td>\n",
       "      <td>157</td>\n",
       "      <td>1</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>313</td>\n",
       "      <td>51</td>\n",
       "      <td>Player 1 wins</td>\n",
       "      <td>313.0</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     p1_initial_total  p2_initial_total  ties  largest_Total  winner  \\\n",
       "72                211               153     0             41       0   \n",
       "200               154               210     1             45       0   \n",
       "585               161               203     4             67       0   \n",
       "243               159               205     2             72       0   \n",
       "13                147               217     0             39       0   \n",
       "497               157               207     1             70       0   \n",
       "685               211               153     1             74       0   \n",
       "660               162               202     3            145       0   \n",
       "659               159               205     1             45       0   \n",
       "621               207               157     1             54       0   \n",
       "\n",
       "     p1_final_total  p2_final_total        outcome  winning_total  \\\n",
       "72              338              26  Player 1 wins          338.0   \n",
       "200              33             331  Player 1 wins          331.0   \n",
       "585              35             329  Player 1 wins          329.0   \n",
       "243              37             327  Player 1 wins          327.0   \n",
       "13               41             323  Player 1 wins          323.0   \n",
       "497              41             323  Player 1 wins          323.0   \n",
       "685             322              42  Player 1 wins          322.0   \n",
       "660              49             315  Player 1 wins          315.0   \n",
       "659              51             313  Player 1 wins          313.0   \n",
       "621             313              51  Player 1 wins          313.0   \n",
       "\n",
       "     losing_total  \n",
       "72           26.0  \n",
       "200          33.0  \n",
       "585          35.0  \n",
       "243          37.0  \n",
       "13           41.0  \n",
       "497          41.0  \n",
       "685          42.0  \n",
       "660          49.0  \n",
       "659          51.0  \n",
       "621          51.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Display the rows which has top 10 winning totals\n",
    "outcome.sort_values(by='winning_total', ascending = False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    558\n",
       "1    332\n",
       "2     92\n",
       "3     15\n",
       "4      3\n",
       "Name: ties, dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0    558\n",
       "1    332\n",
       "2     92\n",
       "3     15\n",
       "4      3\n",
       "Name: ties, dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate the frequency of the number of ties in each games\n",
    "outcome['ties'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ties(0) :40.39247311827957\n",
      "Ties(1) :56.69277108433735\n",
      "Ties(3) :104.2\n",
      "Ties(2) :75.83695652173913\n",
      "Ties(4) :95.66666666666667\n",
      "Ties(0) :40.39247311827957\n",
      "Ties(1) :56.69277108433735\n",
      "Ties(3) :104.2\n",
      "Ties(2) :75.83695652173913\n",
      "Ties(4) :95.66666666666667\n"
     ]
    }
   ],
   "source": [
    "#Calculate the mean maximum round total as a function of the number of ties.\n",
    "for i in outcome.ties.unique():\n",
    "    outcome_filter=outcome[outcome.ties==(i)]\n",
    "    print('Ties(' + str(i) + ') :' + str(outcome_filter.largest_Total.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I observe that as the number of ties increase, the mean maximum round total also increases. Here, the number of cards that the winner of a tie-breaking round takes increase, so the round total for this situation will also increase."
   ]
  }
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