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": 229,
   "metadata": {},
   "outputs": [],
   "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": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins: 0.4990383642069035\n"
     ]
    }
   ],
   "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": 231,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins and kills the dragon: 0.23200728818706348\n"
     ]
    }
   ],
   "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": 232,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins and kills the herald: 0.11185342646016803\n"
     ]
    }
   ],
   "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": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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 = set()\n",
    "game_blue_dragon = set()\n",
    "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": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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",
    "plt.figure(figsize=(10, 5))\n",
    "venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))\n",
    "\n",
    "plt.text(0.6, -0.5, f'Complement: aaaaa', ha='center', va='center')\n",
    "plt.show()"
   ]
  },
  {
   "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": 240,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilty that Blue Team loses, doesn't kill dragons and heralds: 0.3138981678307521\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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 - count_all\n",
    "prob_did_not_win_all = did_not_win_all / num_games\n",
    "\n",
    "print(\"Probabilty that Blue Team loses, doesn't kill dragons and heralds:\", prob_did_not_win_all)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))\n",
    "\n",
    "plt.text(0.6, -0.5, f'{round(prob_did_not_win_all, 3)}', ha='center', va='center')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability: Blue Team wins and kills dragon and herald"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that blue team wins, kills dragon and herald: 0.053\n"
     ]
    }
   ],
   "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": 237,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that blue team does not win but kills dragon and the herald : 0.019\n"
     ]
    }
   ],
   "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": 238,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that blue team wins without killing the dragon and the herald: 0.208\n"
     ]
    }
   ],
   "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)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}