cmkl_assignments/fall-2024/math/mat-204/Game.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MAT-204:00010 - Probability\n",
    "Author: Thanawin Pattanaphol - Date: 23th December 2024 - Description: Basic probability calculations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'PIL'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[3], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m \n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_venn\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m venn3\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pyplot \u001b[38;5;28;01mas\u001b[39;00m plt \n\u001b[1;32m      5\u001b[0m Dat \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mread_csv(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDataLoL.csv\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "File \u001b[0;32m~/.local/lib/python3.12/site-packages/matplotlib_venn/__init__.py:56\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;124;03mVenn diagram plotting routines.\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     53\u001b[0m \u001b[38;5;124;03m                arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.5',color='gray'))\u001b[39;00m\n\u001b[1;32m     54\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m---> 56\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_venn\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_venn2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m venn2, venn2_circles\n\u001b[1;32m     57\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_venn\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_venn3\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m venn3, venn3_circles\n\u001b[1;32m     58\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_venn\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_util\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m venn2_unweighted, venn3_unweighted\n",
      "File \u001b[0;32m~/.local/lib/python3.12/site-packages/matplotlib_venn/_venn2.py:24\u001b[0m\n\u001b[1;32m     21\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mwarnings\u001b[39;00m\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mcollections\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Counter\n\u001b[0;32m---> 24\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01maxes\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Axes\n\u001b[1;32m     25\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpatches\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Circle\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcolors\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ColorConverter\n",
      "File \u001b[0;32m~/.local/lib/python3.12/site-packages/matplotlib/__init__.py:159\u001b[0m\n\u001b[1;32m    155\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mpackaging\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mversion\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m parse \u001b[38;5;28;01mas\u001b[39;00m parse_version\n\u001b[1;32m    157\u001b[0m \u001b[38;5;66;03m# cbook must import matplotlib only within function\u001b[39;00m\n\u001b[1;32m    158\u001b[0m \u001b[38;5;66;03m# definitions, so it is safe to import from it here.\u001b[39;00m\n\u001b[0;32m--> 159\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m _api, _version, cbook, _docstring, rcsetup\n\u001b[1;32m    160\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcbook\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m sanitize_sequence\n\u001b[1;32m    161\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m MatplotlibDeprecationWarning\n",
      "File \u001b[0;32m~/.local/lib/python3.12/site-packages/matplotlib/rcsetup.py:28\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m BackendFilter, backend_registry\n\u001b[1;32m     27\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcbook\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ls_mapper\n\u001b[0;32m---> 28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcolors\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Colormap, is_color_like\n\u001b[1;32m     29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_fontconfig_pattern\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m parse_fontconfig_pattern\n\u001b[1;32m     30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_enums\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m JoinStyle, CapStyle\n",
      "File \u001b[0;32m~/.local/lib/python3.12/site-packages/matplotlib/colors.py:52\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mnumbers\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Real\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mre\u001b[39;00m\n\u001b[0;32m---> 52\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mPIL\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Image\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mPIL\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mPngImagePlugin\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m PngInfo\n\u001b[1;32m     55\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mmpl\u001b[39;00m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'PIL'"
     ]
    }
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   "source": [
    "import pandas as pd \n",
    "from matplotlib_venn import venn3\n",
    "from matplotlib import pyplot as plt \n",
    "\n",
    "Dat = pd.read_csv('DataLoL.csv')\n",
    "\n",
    "num_games = len(Dat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculating the probability by diving the amount of games that blue won\n",
    "# dividing it by the amount of total games\n",
    "# Thus: p = Number of time an event occurs / Total nmumber of possible events\n",
    "prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / num_games\n",
    "print(\"Probability that Blue Team wins:\", prob_blue_wins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins and kills the dragon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Doing a similar calculation with the difference being\n",
    "# the number of time an event occurs now only counts\n",
    "# the number of times blue team wins and kills the dragon\n",
    "\n",
    "prob_blue_wins_dragons = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueDragons'] == 1)]) / num_games\n",
    "print(\"Probability that Blue Team wins and kills the dragon:\", prob_blue_wins_dragons)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins and kills the herald"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Similar calculation but with the number of events that\n",
    "# team blue wins and kills the herald\n",
    "\n",
    "prob_blue_wins_heralds = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueHeralds'] == 1)]) / num_games\n",
    "print(\"Probability that Blue Team wins and kills the herald:\", prob_blue_wins_heralds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Count: All possible cases (Venn Diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declaring variable for each set\n",
    "# Loop through the whole games dataset and if the item-\n",
    "# -matches the condition, add it to the set for that\n",
    "# condition list\n",
    "\n",
    "game_blue_wins, game_blue_dragon, game_blue_herald = set()\n",
    "\n",
    "for game in range(num_games):\n",
    "    if(Dat['blueWins'][game] == 1):\n",
    "        game_blue_wins.add(game)\n",
    "    if(Dat['blueDragons'][game] == 1):\n",
    "        game_blue_dragon.add(game)\n",
    "    if(Dat['blueHeralds'][game] == 1):\n",
    "        game_blue_herald.add(game)\n",
    "\n",
    "venn3([game_blue_wins, game_blue_dragon, game_blue_herald], ('A', 'B', 'C'))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Each possible events (Venn Diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setting the variable for each section of the venn diagram\n",
    "# Use these values to calculate its probability by\n",
    "# diving with the total amount of games\n",
    "# Produce venn diagram of the values\n",
    "\n",
    "count_a = 2055\n",
    "count_b = 1096\n",
    "count_c = 564\n",
    "\n",
    "count_ab = 1770\n",
    "count_ac = 583\n",
    "count_bc = 188\n",
    "\n",
    "count_abc = 522\n",
    "\n",
    "p_a = round(2055 / num_games, 3)\n",
    "p_b = round(1096 / num_games, 3)\n",
    "p_c = round(564 / num_games, 3)\n",
    "\n",
    "p_ab = round(1770 / num_games, 3)\n",
    "p_ac = round(583 / num_games, 3)\n",
    "p_bc = round(188 / num_games, 3)\n",
    "\n",
    "p_abc = round(522 / num_games, 3)\n",
    "\n",
    "venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team does not manage to do any of the events (Outer White Section)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the total amount of the games in the venn diagram\n",
    "# Find the complement of (A ∪ B ∪ C)\n",
    "\n",
    "count_all = count_a + count_b + count_c + count_ab + count_abc + count_ac + count_bc\n",
    "did_not_win_all = num_games - p_all_wins\n",
    "\n",
    "print(\"Probabilty that Blue Team loses, doesn't kill dragons and heralds:\", did_not_win_all / num_games)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins and kills dragon and herald"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The probability of this event is essentially the intersection of\n",
    "# A (Blue Team Wins), B (Kills Dragon) and C (Kills Herald)\n",
    "\n",
    "print(\"Probability that blue team wins, kills dragon and herald:\", p_abc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team does not win but kills dragon and the herald "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Same with above but only with the intersection between\n",
    "# B (Kills Dragon) and C (Kills Herald)\n",
    "\n",
    "print(\"Probability that blue team does not win but kills dragon and the herald :\", p_bc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins but does not kill dragon and herald. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Same with above but only with the A section (Blue Team wins)\n",
    "\n",
    "print(\"Probability that blue team wins without killing the dragon and the herald:\", p_a)"
   ]
  }
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