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": 281,
   "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": 282,
   "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": 283,
   "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": 284,
   "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": 285,
   "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": 286,
   "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.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": 287,
   "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(0.5, -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": 288,
   "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": 289,
   "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": 290,
   "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)"
   ]
  }
 ],
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