{
 "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": null,
   "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": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins is:  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": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins and kills the dragon is:  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": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that Blue Team wins and kills the herald is:  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": null,
   "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, 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",
    "    else if(Dat['blueDragons'][game] == 1):\n",
    "        game_blue_dragon.add(game)\n",
    "    else 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": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 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",
    "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilty that Blue Team loses, doesn't kill dragons and heralds:  0.3138981678307521\n"
     ]
    }
   ],
   "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": [
    {
     "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": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that blue team kills dragon and the herald but does not win:  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": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability that blue team wins without killing the graon 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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