Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cc776441",
   "metadata": {
    "tags": []
   },
   "source": [
    "# OMORI One Wing Jash win chance\n",
    "## Summary\n",
    "* Probability of winning against \"One Wing Jash\" is ~13.4%\n",
    "* Num tries to have at least 90% chance of winning is ~16\n",
    "\n",
    "![plot.png](plot.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36396434",
   "metadata": {},
   "source": [
    "## Breakdown\n",
    "Here are the details of the simulations and calculations I did to determine the results above.\n",
    "\n",
    "### Win chance\n",
    "Since I'm a software developer by trade I decided to simulate the game rather than do the proper math out...\n",
    "\n",
    "Doing a random simulation of the game over and over again (counting the wins and losses) will allow us to estimate the chance of winning the game on a single try. The more times we run the simulation (iterations), the more accurate our estimate of the win chance will be.\n",
    "\n",
    "Luckily \"One Wing Jash\" randomly chooses which move to use (rock, paper, scissors) so no matter which move we choose as the player, we always have a 1/3rd chance of hitting, 1/3rd chance of drawing, and 1/3rd chance of being hit.\n",
    "\n",
    "Either us, the player, or the enemy hitting multiple times in a row increases the combo meter and will cause their next uninterrupted hit to do more damage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e5e6ceeb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate(player_health, enemy_health):\n",
    "    combo = 1\n",
    "    hit_last = None\n",
    "\n",
    "    while True:\n",
    "        if player_health <= 0:\n",
    "            return 0\n",
    "        elif enemy_health <= 0:\n",
    "            return 1\n",
    "\n",
    "        result = random.randrange(3)\n",
    "        assert result in [0, 1, 2]\n",
    "\n",
    "        if result == 0:\n",
    "            # Draw\n",
    "            combo = 1\n",
    "            hit_last = None\n",
    "        elif result == 1:\n",
    "            # Player hits\n",
    "            if hit_last == \"enemy\":\n",
    "                combo = 1\n",
    "                \n",
    "            enemy_health -= combo\n",
    "            combo += 1\n",
    "\n",
    "            hit_last = \"player\"\n",
    "        elif result == 2:\n",
    "            # Enemy hits\n",
    "            if hit_last == \"player\":\n",
    "                combo = 1\n",
    "                \n",
    "            player_health -= combo\n",
    "            combo += 1\n",
    "\n",
    "            hit_last = \"enemy\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00d777bf",
   "metadata": {
    "tags": []
   },
   "source": [
    "For now we can run the simulation 10 million times. This should get us pretty close to the exact probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aad4215f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>iterations</th>\n",
       "      <th>win_count</th>\n",
       "      <th>win_percentage</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1000</td>\n",
       "      <td>127</td>\n",
       "      <td>12.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2000</td>\n",
       "      <td>248</td>\n",
       "      <td>12.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3000</td>\n",
       "      <td>383</td>\n",
       "      <td>12.766667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4000</td>\n",
       "      <td>502</td>\n",
       "      <td>12.550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5000</td>\n",
       "      <td>632</td>\n",
       "      <td>12.640000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>9996000</td>\n",
       "      <td>1335522</td>\n",
       "      <td>13.360564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997000</td>\n",
       "      <td>1335651</td>\n",
       "      <td>13.360518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998000</td>\n",
       "      <td>1335798</td>\n",
       "      <td>13.360652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999000</td>\n",
       "      <td>1335918</td>\n",
       "      <td>13.360516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000000</td>\n",
       "      <td>1336040</td>\n",
       "      <td>13.360400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      iterations  win_count  win_percentage\n",
       "0           1000        127       12.700000\n",
       "1           2000        248       12.400000\n",
       "2           3000        383       12.766667\n",
       "3           4000        502       12.550000\n",
       "4           5000        632       12.640000\n",
       "...          ...        ...             ...\n",
       "9995     9996000    1335522       13.360564\n",
       "9996     9997000    1335651       13.360518\n",
       "9997     9998000    1335798       13.360652\n",
       "9998     9999000    1335918       13.360516\n",
       "9999    10000000    1336040       13.360400\n",
       "\n",
       "[10000 rows x 3 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "\n",
    "# Make sure our \"random\" results are reproduceable\n",
    "random.seed(42)\n",
    "\n",
    "num_iterations = 10000000 # 10 million iterations\n",
    "\n",
    "data = []\n",
    "win_count = 0\n",
    "for i in range(0, num_iterations):\n",
    "    win_count += simulate(3, 9)\n",
    "\n",
    "    iterations = i + 1\n",
    "\n",
    "    # Record the results after every 1000 iterations so we can make a plot to see how the win\n",
    "    # chance estimate changes as we do more iterations\n",
    "    if iterations % 1000 == 0:\n",
    "        win_percentage = win_count / float(iterations) * 100.0\n",
    "        data.append((iterations, win_count, win_percentage))\n",
    "\n",
    "data = pd.DataFrame(data, columns=[\"iterations\", \"win_count\", \"win_percentage\"])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0db5b0f6",
   "metadata": {},
   "source": [
    "If we do a quick plot of the estimated win chance as we run more iterations of the simulation we can see that we converge to a particular win chance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8bd34663",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8740643343613)>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from plotnine import *\n",
    "\n",
    "ggplot(data, aes(x=\"iterations\", y=\"win_percentage\")) +\\\n",
    "    geom_hline(yintercept=13.36, color=\"blue\") +\\\n",
    "    geom_point(size=0.1) +\\\n",
    "    geom_text(data[data[\"iterations\"] == num_iterations], label=\"13.36 %\", nudge_y=0.05, nudge_x=-300000, color=\"blue\") +\\\n",
    "    xlab(\"Game iterations\") +\\\n",
    "    ylab(\"Win Chance (%)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "24581e47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chance of winning: ~13.3604%\n"
     ]
    }
   ],
   "source": [
    "win_percentage = list(data.iterrows())[-1][1]['win_percentage']\n",
    "\n",
    "print(f\"Chance of winning: ~{win_percentage}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "578cf573-0c27-4c20-8a19-784292093fe0",
   "metadata": {},
   "source": [
    "### How close is our estimate?\n",
    "We calculated the win chance using a lot of simulated matches, so we should be really close to the exact chance, but how close are we?\n",
    "\n",
    "To find this out we can use a Beta distribution. Modelling a Beta distribution will give us a plot where the x-axis represents possible win chances and the y-axis shows how likely that win chance is the true win chance (given the simulation results).\n",
    "\n",
    "For more info on Beta distributions see:\n",
    "* https://vitalflux.com/beta-distribution-explained-with-python-examples/\n",
    "* https://en.wikipedia.org/wiki/Beta_distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "44393a68-3f5f-437e-9d94-f7c39c17ccbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import beta\n",
    "\n",
    "a, b = win_count, num_iterations - win_count\n",
    "\n",
    "# Calculate the distribution (focusing on the 98% most likely values)\n",
    "x = np.linspace(beta.ppf(0.01, a, b),beta.ppf(0.99, a, b), 100)\n",
    "\n",
    "plt.figure(figsize=(7,7))\n",
    "plt.xlim(0.1332, 0.1340)\n",
    "plt.plot(x, beta.pdf(x, a, b), 'r-')\n",
    "plt.title('Beta Distribution', fontsize='15')\n",
    "plt.xlabel('Win chance (0.0 - 1.0)', fontsize='15')\n",
    "plt.ylabel('Probability', fontsize='15')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59ded0bc-c26c-419e-aa6b-bfe9a3a938ab",
   "metadata": {},
   "source": [
    "Looking at this  plot we can see that the true probablility is almost certainly (98% chance) within the following value range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd2052d6-7ecd-42ed-97cd-cce71796d3eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13335 to 0.13385\n"
     ]
    }
   ],
   "source": [
    "print(round(beta.ppf(0.01, a, b), 5), \"to\", round(beta.ppf(0.99, a, b), 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0995ea28",
   "metadata": {},
   "source": [
    "### Number of tries to get at least 90 percent chance to win"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8beb139c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n",
      "0.75\n",
      "0.875\n",
      "0.9375\n"
     ]
    }
   ],
   "source": [
    "win_probability = win_percentage / 100.0\n",
    "\n",
    "def chance_of_at_least_one_success(p, num_tries):\n",
    "    return 1.0 - ((1.0 - p) ** num_tries)\n",
    "\n",
    "print(chance_of_at_least_one_success(0.5, 1))\n",
    "print(chance_of_at_least_one_success(0.5, 2))\n",
    "print(chance_of_at_least_one_success(0.5, 3))\n",
    "print(chance_of_at_least_one_success(0.5, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89326f10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_tries</th>\n",
       "      <th>at_least_one_win_percentage</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.360400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>24.935797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>34.964675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>43.653654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>51.181752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>57.704065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>63.354971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>68.250893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>72.492701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>76.167786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>79.351865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>82.110539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>84.500642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>86.571418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15</td>\n",
       "      <td>88.365531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>16</td>\n",
       "      <td>89.919942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17</td>\n",
       "      <td>91.266678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>18</td>\n",
       "      <td>92.433485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>19</td>\n",
       "      <td>93.444402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>20</td>\n",
       "      <td>94.320256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>21</td>\n",
       "      <td>95.079092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>22</td>\n",
       "      <td>95.736545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>23</td>\n",
       "      <td>96.306160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>24</td>\n",
       "      <td>96.799672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>25</td>\n",
       "      <td>97.227248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>26</td>\n",
       "      <td>97.597699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>27</td>\n",
       "      <td>97.918656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>28</td>\n",
       "      <td>98.196732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>29</td>\n",
       "      <td>98.437656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>30</td>\n",
       "      <td>98.646391</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    num_tries  at_least_one_win_percentage\n",
       "0           0                     0.000000\n",
       "1           1                    13.360400\n",
       "2           2                    24.935797\n",
       "3           3                    34.964675\n",
       "4           4                    43.653654\n",
       "5           5                    51.181752\n",
       "6           6                    57.704065\n",
       "7           7                    63.354971\n",
       "8           8                    68.250893\n",
       "9           9                    72.492701\n",
       "10         10                    76.167786\n",
       "11         11                    79.351865\n",
       "12         12                    82.110539\n",
       "13         13                    84.500642\n",
       "14         14                    86.571418\n",
       "15         15                    88.365531\n",
       "16         16                    89.919942\n",
       "17         17                    91.266678\n",
       "18         18                    92.433485\n",
       "19         19                    93.444402\n",
       "20         20                    94.320256\n",
       "21         21                    95.079092\n",
       "22         22                    95.736545\n",
       "23         23                    96.306160\n",
       "24         24                    96.799672\n",
       "25         25                    97.227248\n",
       "26         26                    97.597699\n",
       "27         27                    97.918656\n",
       "28         28                    98.196732\n",
       "29         29                    98.437656\n",
       "30         30                    98.646391"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = [\n",
    "    (num_tries, chance_of_at_least_one_success(win_probability, num_tries) * 100.0)\n",
    "    for num_tries in range(0, 31)\n",
    "]\n",
    "\n",
    "data2 = pd.DataFrame(data2, columns=[\"num_tries\", \"at_least_one_win_percentage\"])\n",
    "data2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "58ab9756",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/chris/anaconda3/envs/omori_pet_rocks/lib/python3.10/site-packages/plotnine/ggplot.py:718: PlotnineWarning: Saving 6.4 x 4.8 in image.\n",
      "/home/chris/anaconda3/envs/omori_pet_rocks/lib/python3.10/site-packages/plotnine/ggplot.py:719: PlotnineWarning: Filename: plot.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8740640860743)>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = ggplot(data, aes(x=\"num_tries\", y=\"at_least_one_win_percentage\")) +\\\n",
    "    geom_point(data2[data2[\"num_tries\"] != 16]) +\\\n",
    "    geom_hline(yintercept=90) +\\\n",
    "    geom_text(data2[data2[\"num_tries\"] == 16], aes(label=\"num_tries\"), nudge_y=3, color=\"red\") +\\\n",
    "    geom_text(data2[data2[\"num_tries\"] == 0], label=\"90%\", nudge_y=92) +\\\n",
    "    geom_point(data2[data2[\"num_tries\"] == 16], color=\"red\") +\\\n",
    "    ylim(0.0, 100.0) +\\\n",
    "    xlab(\"Number of tries\") +\\\n",
    "    ylab(\"Chance of winning at least once (%)\")\n",
    "\n",
    "ggsave(plot=p, filename='plot.png', dpi=100)\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84009dc1-3c94-47cf-b3df-de37b4b6953b",
   "metadata": {},
   "source": [
    "## Prior works\n",
    "* [Hhhhhhhhhh7 on the OMORI Wiki](https://omori.fandom.com/wiki/Talk:PET_ROCKS) (December 2021)\n",
    "    * The code for their calculation is available [here](https://pastebin.com/TZm3PW48)\n",
    "    * They calculated a win chance of ~13.4% (agrees with my findings).\n",
    "        * The exact value calculated by their code is 13.35463730995656%\n",
    "* [u/vu47 on r/omori](https://www.reddit.com/r/OMORI/comments/ncfb1k/comment/idjj24m/?utm_source=reddit&utm_medium=web2x&context=3) (June 2022)\n",
    "    * Simulated 1 million matches using a few different settings for player and enemy choice randomization and health values.\n",
    "    * For their \"constant3 vs. uniform9\" case (comparable to the one I analyzed) they calculated a win chance of 13.37337% (agrees with my findings)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cab675a7-2a58-4cf6-8531-e42c13a35b17",
   "metadata": {},
   "source": [
    "### Hhhhhhhhhh7's algorithm\n",
    "Hhhhhhhhhh7 took a different approach to calculating the win chance by using a dynamic programming solution that simulates each path through the game states that a match could take, tracking the probability of each state.\n",
    "\n",
    "This results in a win chance that is incredibly close to the actual value and does not take as much runtime as simulating randomized matches.\n",
    "\n",
    "Below is a Python adaptation of their algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c9c27662-331f-446e-95cf-d0188c391622",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Draw fraction: 1185476006914719301616125/4977414122938492192881464029729961679802517669640314331069754317413863193300588672960378941038799444233797200629740876278809425638436874294137213623651683084623545115805694417048191856898335577690331770093271154442020977681305435856437590481321498962517248672813060123683011804992094505499691756946329466238029256908317387659245893361869285485179777099016847012698558309358412176001 ~= 0.0\n",
      "\n",
      "Win chance: 13.35463730995656%\n"
     ]
    }
   ],
   "source": [
    "from dataclasses import dataclass\n",
    "from typing import DefaultDict, Optional\n",
    "\n",
    "import collections\n",
    "import enum\n",
    "import fractions\n",
    "\n",
    "class Fighter(enum.Enum):\n",
    "    Player = enum.auto()\n",
    "    Enemy = enum.auto()\n",
    "    \n",
    "class RoundResult(enum.Enum):\n",
    "    PlayerHits = enum.auto()\n",
    "    EnemyHits = enum.auto()\n",
    "    Draw = enum.auto()\n",
    "\n",
    "@dataclass(eq=True, frozen=True)\n",
    "class GameState:\n",
    "    player_health: int\n",
    "    enemy_health: int\n",
    "    combo: int\n",
    "    hit_last: Optional[Fighter]\n",
    "    \n",
    "    def get_winner(self) -> Optional[Fighter]:\n",
    "        if self.player_health == 0:\n",
    "            return Fighter.Enemy\n",
    "        if self.enemy_health == 0:\n",
    "            return Fighter.Player\n",
    "        \n",
    "        return None\n",
    "    \n",
    "    def is_done(self) -> bool:\n",
    "        return self.get_winner() is not None\n",
    "    \n",
    "    def advance(self, result: RoundResult) -> \"GameState\":\n",
    "        # Make sure we're not trying to advance an end state\n",
    "        assert self.player_health > 0\n",
    "        assert self.enemy_health > 0\n",
    "        \n",
    "        player_health = self.player_health\n",
    "        enemy_health = self.enemy_health\n",
    "        combo = self.combo\n",
    "        hit_last = self.hit_last\n",
    "        \n",
    "        if result == RoundResult.Draw:\n",
    "            combo = 1\n",
    "            hit_last = None\n",
    "        elif result == RoundResult.PlayerHits:\n",
    "            if hit_last == \"enemy\":\n",
    "                combo = 1\n",
    "                \n",
    "            enemy_health -= combo\n",
    "            combo += 1\n",
    "\n",
    "            hit_last = \"player\"\n",
    "        elif result == RoundResult.EnemyHits:\n",
    "            if hit_last == \"player\":\n",
    "                combo = 1\n",
    "                \n",
    "            player_health -= combo\n",
    "            combo += 1\n",
    "\n",
    "            hit_last = \"enemy\"\n",
    "        else:\n",
    "            assert False\n",
    "            \n",
    "        player_health = max(player_health, 0)\n",
    "        enemy_health = max(enemy_health, 0)\n",
    "            \n",
    "        return GameState(player_health, enemy_health, combo, hit_last)\n",
    "\n",
    "# Start with just the initial state, at the beginning the initial state is always the case (1.0 = 1/1)\n",
    "# Note that we're using fraction.Fraction to avoid floating point rounding errors\n",
    "states: DefaultDict[GameState, fractions.Fraction] = collections.defaultdict(fractions.Fraction)\n",
    "states[GameState(3, 9, 1, None)] = fractions.Fraction(1, 1)\n",
    "\n",
    "# Simulate games of up to 800 rounds\n",
    "for _ in range(0, 800):\n",
    "    new_states: DefaultDict[GameState, fractions.Fraction] = collections.defaultdict(fractions.Fraction)\n",
    "\n",
    "    # For each game, it is either already done or can be simulated further\n",
    "    for state, probability in states.items():\n",
    "        if state.is_done():\n",
    "            new_states[state] += probability\n",
    "        else:\n",
    "            # Branch off into a separate simulation for each possible round result\n",
    "            for result in list(RoundResult):\n",
    "                next_state = state.advance(result)\n",
    "                next_probability = probability / 3\n",
    "\n",
    "                # Track this new simulation and combine the probability with that of any other\n",
    "                # simulations that resulted in the same game state (since all those games are\n",
    "                # equivalent)\n",
    "                new_states[next_state] += next_probability\n",
    "                \n",
    "    states = new_states\n",
    "\n",
    "# Double check that all the game state probabilities add up \n",
    "assert sum(states.values()) == 1\n",
    "\n",
    "# Because we are only simulating games up to a fixed number of rounds we will always end up with\n",
    "# some games that don't end (ex. infinitely repeated draws), let's caclulate the total probability\n",
    "# of those cases. Since we are simulating a lot of rounds this value should be negligible.\n",
    "draw_probability = sum([\n",
    "    p\n",
    "    for state, p in states.items()\n",
    "    if not state.is_done()\n",
    "])\n",
    "print(\"Draw fraction:\", draw_probability, \"~=\", float(draw_probability))\n",
    "print()\n",
    "\n",
    "# Sum up the probability of all the game states where the player wins. This should be the exact\n",
    "# win chance, since the draw probability is negligible in our case.\n",
    "win_probability = float(sum([\n",
    "    p\n",
    "    for state, p in states.items()\n",
    "    if state.get_winner() == Fighter.Player\n",
    "]))\n",
    "print(f\"Win chance: {win_probability * 100.0}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5790ee0b-4a5e-4e22-ac1b-d11ad0c76258",
   "metadata": {},
   "source": [
    "Since this algorithm results in an exact value for the win chance, I like it better than the random simulation approach I used above.\n",
    "\n",
    "#### Close wins and losses\n",
    "For fun let's also use this as an opportunity to see how close some of the losing and winning cases are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ea208f71-db00-43a1-ba82-aa2bcbc41c65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>player_health</th>\n",
       "      <th>enemy_health</th>\n",
       "      <th>combo</th>\n",
       "      <th>hit_last</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>player</td>\n",
       "      <td>0.022119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>player</td>\n",
       "      <td>0.014301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>player</td>\n",
       "      <td>0.016735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>enemy</td>\n",
       "      <td>0.021609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>player</td>\n",
       "      <td>0.012985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>player</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>player</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123</th>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>player</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>enemy</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>None</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>126 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     player_health  enemy_health  combo hit_last  probability\n",
       "0                3             0      5   player     0.022119\n",
       "1                2             0      3   player     0.014301\n",
       "2                1             0      3   player     0.016735\n",
       "3                0             1      2    enemy     0.021609\n",
       "4                1             0      2   player     0.012985\n",
       "..             ...           ...    ...      ...          ...\n",
       "121              3             3      4   player     0.000000\n",
       "122              3             6      3   player     0.000000\n",
       "123              3             8      2   player     0.000000\n",
       "124              2             9      2    enemy     0.000000\n",
       "125              3             9      1     None     0.000000\n",
       "\n",
       "[126 rows x 5 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = [\n",
    "    (state.player_health, state.enemy_health, state.combo, state.hit_last, float(probability))\n",
    "    for state, probability in states.items()\n",
    "]\n",
    "\n",
    "results = pd.DataFrame(results, columns=[\"player_health\", \"enemy_health\", \"combo\", \"hit_last\", \"probability\"])\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c35e5b8e-ce05-442b-a4fa-f2ce36a9c9d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8740641010007)>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wins = results[results[\"enemy_health\"] == 0].copy()\n",
    "wins[\"probability\"] = wins[\"probability\"] / sum(wins[\"probability\"])\n",
    "\n",
    "assert abs(sum(wins[\"probability\"]) - 1.0) < 0.0000001\n",
    "\n",
    "ggplot(wins, aes(\"player_health\", \"probability\")) +\\\n",
    "    geom_col() +\\\n",
    "    ggtitle(\"Closeness of Wins\") +\\\n",
    "    xlab(\"Player health at end of match\") +\\\n",
    "    ylab(\"Probability (assuming win)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "abb48729-07d8-424c-80e8-a74f6233212b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8740640874947)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "losses = results[results[\"player_health\"] == 0].copy()\n",
    "losses[\"probability\"] = losses[\"probability\"] / sum(losses[\"probability\"])\n",
    "\n",
    "assert abs(sum(losses[\"probability\"]) - 1.0) < 0.0000001\n",
    "\n",
    "ggplot(losses, aes(\"enemy_health\", \"probability\")) +\\\n",
    "    geom_col() +\\\n",
    "    ggtitle(\"Closeness of Losses\") +\\\n",
    "    xlab(\"Enemy health at end of match\") +\\\n",
    "    ylab(\"Probability (assuming loss)\") +\\\n",
    "    scale_x_discrete(breaks=list(range(1, 10)), labels=[str(n) for n in range(1, 10)], limits=list(range(1, 10)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}