How to Base Dominion Opening.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "swiss-wednesday",
   "metadata": {},
   "source": [
    "# How to Base Dominion Opening"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "instant-minority",
   "metadata": {},
   "source": [
    "Dominion is a game where a small advantage early on can snowball into a decisive advantage later on. As such, your opening buys (i.e., the cards you buy in the first two turns of the game) are very important in laying the foundation for your strategy throughout the rest of the game.\n",
    "\n",
    "Our goal is to rank openings of the second edition of the dominion base set from best to worst. Note the best opening in a game of dominion is very kingdom dependent. This is one reason to focus our analysis on the base set since fewer cards means fewer kingdoms. That said, any such rankings should only be used as a general guide, which hopefully provides insight into the types of openings that generally work best.\n",
    "\n",
    "If you are not familiar with dominion, learn to play for free at [Dominion Online](https://dominion.games/)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "organized-register",
   "metadata": {},
   "source": [
    "## Updates\n",
    "- Burning Skull's games from the 2021 base-space tournament have been added by [jordancurve](https://github.com/jordancurve)! Download and rerun the notebook to see the results!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lined-proportion",
   "metadata": {},
   "source": [
    "## The Data\n",
    "\n",
    "The data for our analysis was manually collected from Burning Skull's phenomenal YouTube series: [How to Base Dominion](https://www.youtube.com/watch?v=JpPtxyGNGcg&list=PLtkTUMIr-WmKZCd4Q_KnrKtNJKR-vpC8a). Burning Skull is one of the best dominion players in the world. At the time of making his series, he was [one of the top 5 players](https://www.reddit.com/r/dominion/comments/6t3d2w/how_to_base_dominion/) on the leaderboard at [Dominion Online](https://dominion.games/). His series consists of him playing through 25 different games of the second edition of the dominion base set and explaining his decisions along the way.\n",
    "\n",
    "Let's begin by taking a look at the file, 'data/openings.csv', which contains the openings made in the series. CSV stands for comma separated values. We can load this data as a DataFrame object using the Pandas Library in Python. For our purposes, the order of the opening buys does not matter, so let's sort them alphabetically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "frozen-punch",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "\n",
    "openings = pd.read_csv('data/openings.csv')\n",
    "openings.opening = openings.opening.apply(lambda x: tuple(sorted(x.split('-'))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "inner-disclosure",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>game_id</th>\n",
       "      <th>hypothetical</th>\n",
       "      <th>player</th>\n",
       "      <th>opening_type</th>\n",
       "      <th>opening</th>\n",
       "      <th>kingdom</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5553096</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>Moat-Harbinger-Vassal-Militia-Poacher-Throne R...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5558534</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>Cellar-Chapel-Moat-Village-Gardens-Smithy-Thro...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5576934</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>Moat-Harbinger-Merchant-Bureaucrat-Poacher-Rem...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5656537</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>Cellar-Chapel-Moat-Harbinger-Vassal-Poacher-Th...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5579553</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>Cellar-Moat-Merchant-Vassal-Workshop-Poacher-F...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5657702</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>Cellar-Harbinger-Gardens-Militia-Poacher-Remod...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5715500</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2-5</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>Chapel-Merchant-Workshop-Bureaucrat-Gardens-Mo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5760302</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>Cellar-Chapel-Harbinger-Vassal-Workshop-Bureau...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5760557</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>Cellar-Merchant-Gardens-Throne Room-Council Ro...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5788864</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(Chapel, Witch)</td>\n",
       "      <td>Chapel-Moat-Vassal-Bandit-Council Room-Festiva...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5844082</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>Merchant-Vassal-Workshop-Moneylender-Remodel-B...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5869577</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Smithy, Workshop)</td>\n",
       "      <td>Cellar-Harbinger-Village-Workshop-Bureaucrat-S...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5903272</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>Harbinger-Workshop-Gardens-Moneylender-Remodel...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5923306</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>Workshop-Militia-Moneylender-Poacher-Remodel-T...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5924162</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>Cellar-Chapel-Village-Bureaucrat-Remodel-Smith...</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5975251</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>Chapel-Harbinger-Village-Workshop-Militia-Mone...</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5982614</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>Cellar-Moat-Gardens-Moneylender-Poacher-Smithy...</td>\n",
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       "      <th>17</th>\n",
       "      <td>6033410</td>\n",
       "      <td>0</td>\n",
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       "      <td>5-2</td>\n",
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       "      <td>Cellar-Village-Bureaucrat-Militia-Poacher-Band...</td>\n",
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       "      <th>18</th>\n",
       "      <td>6065802</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>Chapel-Moat-Village-Workshop-Bureaucrat-Throne...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>6087460</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>Cellar-Moat-Merchant-Village-Remodel-Smithy-Ba...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>6110766</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>Harbinger-Vassal-Village-Remodel-Throne Room-B...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>6138790</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>Cellar-Chapel-Moat-Harbinger-Merchant-Vassal-V...</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>6170038</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>Bureaucrat-Gardens-Poacher-Remodel-Throne Room...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6193342</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>Harbinger-Workshop-Bureaucrat-Militia-Poacher-...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>6227420</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>Merchant-Gardens-Militia-Moneylender-Remodel-T...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5558534</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2-5</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>Cellar-Chapel-Moat-Village-Gardens-Smithy-Thro...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>5656537</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>Cellar-Chapel-Moat-Harbinger-Vassal-Poacher-Th...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>5715500</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3-4</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>Chapel-Merchant-Workshop-Bureaucrat-Gardens-Mo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>5975251</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4-3</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>Chapel-Harbinger-Village-Workshop-Militia-Mone...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>6193342</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>Harbinger-Workshop-Bureaucrat-Militia-Poacher-...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>6227420</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5-2</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>Merchant-Gardens-Militia-Moneylender-Remodel-T...</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "    game_id  hypothetical  player opening_type                opening  \\\n",
       "0   5553096             0       2          4-3      (Militia, Silver)   \n",
       "1   5558534             0       1          4-3       (Chapel, Silver)   \n",
       "2   5576934             0       2          3-4      (Remodel, Silver)   \n",
       "3   5656537             0       1          4-3      (Chapel, Poacher)   \n",
       "4   5579553             0       2          3-4      (Poacher, Silver)   \n",
       "5   5657702             0       1          4-3      (Remodel, Silver)   \n",
       "6   5715500             0       2          2-5   (Chapel, Laboratory)   \n",
       "7   5760302             0       2          4-3      (Chapel, Poacher)   \n",
       "8   5760557             0       1          3-4     (Merchant, Silver)   \n",
       "9   5788864             0       2          5-2        (Chapel, Witch)   \n",
       "10  5844082             0       1          4-3  (Moneylender, Silver)   \n",
       "11  5869577             0       2          4-3     (Smithy, Workshop)   \n",
       "12  5903272             0       2          4-3  (Moneylender, Silver)   \n",
       "13  5923306             0       2          3-4  (Moneylender, Silver)   \n",
       "14  5924162             0       1          5-2       (Chapel, Sentry)   \n",
       "15  5975251             0       1          5-2      (Chapel, Militia)   \n",
       "16  5982614             0       1          3-4  (Moneylender, Silver)   \n",
       "17  6033410             0       1          5-2             (, Sentry)   \n",
       "18  6065802             0       1          4-3       (Chapel, Silver)   \n",
       "19  6087460             0       2          4-3      (Remodel, Silver)   \n",
       "20  6110766             0       1          4-3      (Remodel, Silver)   \n",
       "21  6138790             0       2          4-3      (Chapel, Poacher)   \n",
       "22  6170038             0       1          4-3      (Remodel, Silver)   \n",
       "23  6193342             0       2          4-3      (Militia, Silver)   \n",
       "24  6227420             0       2          3-4      (Militia, Silver)   \n",
       "25  5558534             1       1          2-5       (Chapel, Sentry)   \n",
       "26  5656537             1       1          5-2       (Chapel, Market)   \n",
       "27  5715500             1       2          3-4       (Chapel, Silver)   \n",
       "28  5975251             1       1          4-3      (Chapel, Militia)   \n",
       "29  6193342             1       2          5-2             (, Sentry)   \n",
       "30  6227420             1       2          5-2             (, Sentry)   \n",
       "\n",
       "                                              kingdom  \n",
       "0   Moat-Harbinger-Vassal-Militia-Poacher-Throne R...  \n",
       "1   Cellar-Chapel-Moat-Village-Gardens-Smithy-Thro...  \n",
       "2   Moat-Harbinger-Merchant-Bureaucrat-Poacher-Rem...  \n",
       "3   Cellar-Chapel-Moat-Harbinger-Vassal-Poacher-Th...  \n",
       "4   Cellar-Moat-Merchant-Vassal-Workshop-Poacher-F...  \n",
       "5   Cellar-Harbinger-Gardens-Militia-Poacher-Remod...  \n",
       "6   Chapel-Merchant-Workshop-Bureaucrat-Gardens-Mo...  \n",
       "7   Cellar-Chapel-Harbinger-Vassal-Workshop-Bureau...  \n",
       "8   Cellar-Merchant-Gardens-Throne Room-Council Ro...  \n",
       "9   Chapel-Moat-Vassal-Bandit-Council Room-Festiva...  \n",
       "10  Merchant-Vassal-Workshop-Moneylender-Remodel-B...  \n",
       "11  Cellar-Harbinger-Village-Workshop-Bureaucrat-S...  \n",
       "12  Harbinger-Workshop-Gardens-Moneylender-Remodel...  \n",
       "13  Workshop-Militia-Moneylender-Poacher-Remodel-T...  \n",
       "14  Cellar-Chapel-Village-Bureaucrat-Remodel-Smith...  \n",
       "15  Chapel-Harbinger-Village-Workshop-Militia-Mone...  \n",
       "16  Cellar-Moat-Gardens-Moneylender-Poacher-Smithy...  \n",
       "17  Cellar-Village-Bureaucrat-Militia-Poacher-Band...  \n",
       "18  Chapel-Moat-Village-Workshop-Bureaucrat-Throne...  \n",
       "19  Cellar-Moat-Merchant-Village-Remodel-Smithy-Ba...  \n",
       "20  Harbinger-Vassal-Village-Remodel-Throne Room-B...  \n",
       "21  Cellar-Chapel-Moat-Harbinger-Merchant-Vassal-V...  \n",
       "22  Bureaucrat-Gardens-Poacher-Remodel-Throne Room...  \n",
       "23  Harbinger-Workshop-Bureaucrat-Militia-Poacher-...  \n",
       "24  Merchant-Gardens-Militia-Moneylender-Remodel-T...  \n",
       "25  Cellar-Chapel-Moat-Village-Gardens-Smithy-Thro...  \n",
       "26  Cellar-Chapel-Moat-Harbinger-Vassal-Poacher-Th...  \n",
       "27  Chapel-Merchant-Workshop-Bureaucrat-Gardens-Mo...  \n",
       "28  Chapel-Harbinger-Village-Workshop-Militia-Mone...  \n",
       "29  Harbinger-Workshop-Bureaucrat-Militia-Poacher-...  \n",
       "30  Merchant-Gardens-Militia-Moneylender-Remodel-T...  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "openings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "offshore-advocacy",
   "metadata": {},
   "source": [
    "Although there are only 25 games in Burning Skull's series, we have 31 openings since there are some instances in which he gave an indication of the opening he would have made if he had a different 'opening_type'. These instances are marked as 'hypothetical'.\n",
    "\n",
    "To warm up let's rank the openings by popularity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "qualified-maldives",
   "metadata": {},
   "outputs": [],
   "source": [
    "play_counts = openings.opening.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "otherwise-decline",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "play_counts.plot(kind='bar')\n",
    "plt.xlabel('Rank')\n",
    "plt.ylabel('Play Count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "administrative-description",
   "metadata": {},
   "source": [
    "Of course, this plot doesn't tell the whole story. For example, 4-3 openings are 5 times more likely than 5-2 openings to occur in a random dominion game. So let's normalize these openings by the number of times they could have occured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "neutral-geometry",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_possible_openings(kingdom, opening_type):\n",
    "    kingdom = kingdom.split('-')\n",
    "    kingdom += ['Curse', 'Copper', 'Estate', 'Silver', 'Duchy', 'Gold', 'Province']\n",
    "    cards = pd.read_csv('data/base_cards.csv')\n",
    "    cards = cards[cards.card.isin(kingdom)]\n",
    "    first, second = list(map(int, opening_type.split('-')))\n",
    "    first = cards[cards.cost <= first].card.tolist() + ['']\n",
    "    second = cards[cards.cost <= second].card.tolist() + ['']\n",
    "    return set([tuple(sorted([f, s])) for f in first for s in second])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "published-bicycle",
   "metadata": {},
   "outputs": [],
   "source": [
    "availability_counts = {}\n",
    "for i, row in openings.iterrows():\n",
    "    for opening in get_possible_openings(row['kingdom'], row['opening_type']):\n",
    "        availability_counts[opening] = availability_counts.get(opening, 0) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "american-willow",
   "metadata": {},
   "outputs": [],
   "source": [
    "normalized_counts = pd.Series({k: v/availability_counts[k] for k, v in play_counts.iteritems()})\n",
    "normalized_counts.sort_values(inplace=True, ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "aquatic-palestinian",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "normalized_counts.plot(kind='bar')\n",
    "plt.xlabel('Rank')\n",
    "plt.ylabel('Play Count / Availability Count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "czech-boundary",
   "metadata": {},
   "source": [
    "So (Chapel, Militia) and (Chapel, Witch) were played 100% of the time that they were available to play! So they must be great openings, right? From our previous plot, we know that they were available to play only twice and once, respectively, so we can't be that certain of these rankings either. We're going to need a more sophisticated approach.\n",
    "\n",
    "## The Plan\n",
    "\n",
    "We will consider each opening as a player in the game of \"Which opening does Burning Skull prefer?\". From each dominion game, we can extract a list of matches where the better player is the picked opening and the worse player is an opening that wasn't picked. Then we can use a rating system to rank the openings given the match outcomes.\n",
    "\n",
    "We have many options for ratings systems. One of the most popular is the [Elo rating system](https://en.wikipedia.org/wiki/Elo_rating_system), which was developed by Arpad Elo as a chess-rating system in the 1950s. The Elo system is simple and effective, but with modern computation better rating systems have been developed. The Glicko and Glicko-2 systems developed by [Mark Glickman](http://www.glicko.net/glicko.html) improve over the Elo system. The Glicko system introduces a rating deviation (RD), which captures the uncertainty in a player's rating, and the Glicko-2 system introduces a rating volatility which indicates a degree of expected fluctuation in a player's rating. The Glicko-2 system in particular is [used by Dominion Online](http://forum.shuffleit.nl/index.php?topic=1679.msg5891#msg5891). Finally, there is the [TrueSkill rating system](https://proceedings.neurips.cc/paper/2006/file/f44ee263952e65b3610b8ba51229d1f9-Paper.pdf) developed by Microsoft for XBox Live, which uses sophisticated statistical machinery in the form of approximate message passing on a factor graph representation and can be used on games with more than 2 players.\n",
    "\n",
    "Lucky for us, implementations of all these systems are available in Python. We will use the TrueSkill system as implemented by the [TrueSkill library](https://trueskill.org/) as it has been shown to [better predict match outcomes in practice](https://www.kaggle.com/c/chess/discussion/186), and it converges on skills relatively quickly which is important given our limited data.\n",
    "\n",
    "## The Matches\n",
    "\n",
    "Let's extract the matches from each set of games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "expensive-particle",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_players():\n",
    "    return openings.opening.unique()\n",
    "\n",
    "def get_matches():\n",
    "    matches = {'game_id':[], 'better': [], 'worse': [], 'drawn': []}\n",
    "    for i, row in openings.iterrows():\n",
    "        game_id, better = row['game_id'], row['opening']\n",
    "        for worse in get_possible_openings(row['kingdom'], row['opening_type']) - {better}:\n",
    "            matches['game_id'].append(game_id)\n",
    "            matches['better'].append(better)\n",
    "            matches['worse'].append(worse)\n",
    "            matches['drawn'].append(False)\n",
    "    return pd.DataFrame(matches)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "lucky-jordan",
   "metadata": {},
   "outputs": [],
   "source": [
    "players = get_players()\n",
    "matches = get_matches()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "broadband-assembly",
   "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>game_id</th>\n",
       "      <th>better</th>\n",
       "      <th>worse</th>\n",
       "      <th>drawn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Estate, Militia)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Estate, Estate)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Curse, Curse)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Harbinger, Throne Room)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Copper, Vassal)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(, Duchy)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Estate, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Curse, Merchant)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1994</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Duchy, Estate)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(, Throne Room)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1996 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      game_id             better                     worse  drawn\n",
       "0     5553096  (Militia, Silver)         (Estate, Militia)  False\n",
       "1     5553096  (Militia, Silver)          (Estate, Estate)  False\n",
       "2     5553096  (Militia, Silver)            (Curse, Curse)  False\n",
       "3     5553096  (Militia, Silver)  (Harbinger, Throne Room)  False\n",
       "4     5553096  (Militia, Silver)          (Copper, Vassal)  False\n",
       "...       ...                ...                       ...    ...\n",
       "1991  6227420         (, Sentry)                 (, Duchy)  False\n",
       "1992  6227420         (, Sentry)          (Estate, Silver)  False\n",
       "1993  6227420         (, Sentry)         (Curse, Merchant)  False\n",
       "1994  6227420         (, Sentry)           (Duchy, Estate)  False\n",
       "1995  6227420         (, Sentry)           (, Throne Room)  False\n",
       "\n",
       "[1996 rows x 4 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matches"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exclusive-liberal",
   "metadata": {},
   "source": [
    "Hidden within the original 25 games were nearly 2000 comparisons between openings! Unfortunately, not all comparisons are equal. Note most of the opening comparisons are to openings Burning Skull never even played. Perhaps he didn't play them because he would never play such an opening (Curse, Curse), or perhaps he would play them if only he had played more than 25 games (Festival, Chapel). Either way, to the rating system (Curse, Curse) and (Festival, Chapel) would look pretty much the same – like really bad openings since they have both lost all their matches. In light of this, let's keep only comparisons between openings that were played."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "greenhouse-seeker",
   "metadata": {},
   "outputs": [],
   "source": [
    "matches = matches[matches.worse.isin(players)].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "elementary-settle",
   "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>game_id</th>\n",
       "      <th>better</th>\n",
       "      <th>worse</th>\n",
       "      <th>drawn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5576934</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5576934</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5656537</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5656537</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5579553</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5657702</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5657702</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5760302</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5760302</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5788864</td>\n",
       "      <td>(Chapel, Witch)</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5788864</td>\n",
       "      <td>(Chapel, Witch)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5844082</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5844082</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5903272</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5903272</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Smithy, Workshop)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5923306</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5923306</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5923306</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5924162</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>5924162</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>5982614</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>6087460</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>6138790</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>6138790</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>6138790</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>6170038</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>6193342</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>5558534</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>5558534</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>5656537</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>5656537</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>5715500</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>(Merchant, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>5975251</td>\n",
       "      <td>(Chapel, Militia)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    game_id                 better                  worse  drawn\n",
       "0   5553096      (Militia, Silver)      (Poacher, Silver)  False\n",
       "1   5576934      (Remodel, Silver)      (Poacher, Silver)  False\n",
       "2   5576934      (Remodel, Silver)     (Merchant, Silver)  False\n",
       "3   5656537      (Chapel, Poacher)      (Poacher, Silver)  False\n",
       "4   5656537      (Chapel, Poacher)       (Chapel, Silver)  False\n",
       "5   5579553      (Poacher, Silver)     (Merchant, Silver)  False\n",
       "6   5657702      (Remodel, Silver)      (Militia, Silver)  False\n",
       "7   5657702      (Remodel, Silver)      (Poacher, Silver)  False\n",
       "8   5715500   (Chapel, Laboratory)       (Chapel, Market)  False\n",
       "9   5715500   (Chapel, Laboratory)       (Chapel, Sentry)  False\n",
       "10  5715500   (Chapel, Laboratory)             (, Sentry)  False\n",
       "11  5715500   (Chapel, Laboratory)       (Chapel, Silver)  False\n",
       "12  5760302      (Chapel, Poacher)      (Poacher, Silver)  False\n",
       "13  5760302      (Chapel, Poacher)       (Chapel, Silver)  False\n",
       "14  5788864        (Chapel, Witch)   (Chapel, Laboratory)  False\n",
       "15  5788864        (Chapel, Witch)       (Chapel, Silver)  False\n",
       "16  5844082  (Moneylender, Silver)      (Remodel, Silver)  False\n",
       "17  5844082  (Moneylender, Silver)     (Merchant, Silver)  False\n",
       "18  5903272  (Moneylender, Silver)      (Remodel, Silver)  False\n",
       "19  5903272  (Moneylender, Silver)     (Smithy, Workshop)  False\n",
       "20  5923306  (Moneylender, Silver)      (Remodel, Silver)  False\n",
       "21  5923306  (Moneylender, Silver)      (Poacher, Silver)  False\n",
       "22  5923306  (Moneylender, Silver)      (Militia, Silver)  False\n",
       "23  5924162       (Chapel, Sentry)             (, Sentry)  False\n",
       "24  5924162       (Chapel, Sentry)       (Chapel, Silver)  False\n",
       "25  5975251      (Chapel, Militia)      (Chapel, Poacher)  False\n",
       "26  5975251      (Chapel, Militia)       (Chapel, Market)  False\n",
       "27  5975251      (Chapel, Militia)       (Chapel, Silver)  False\n",
       "28  5982614  (Moneylender, Silver)      (Poacher, Silver)  False\n",
       "29  6087460      (Remodel, Silver)     (Merchant, Silver)  False\n",
       "30  6138790      (Chapel, Poacher)     (Merchant, Silver)  False\n",
       "31  6138790      (Chapel, Poacher)      (Poacher, Silver)  False\n",
       "32  6138790      (Chapel, Poacher)       (Chapel, Silver)  False\n",
       "33  6170038      (Remodel, Silver)      (Poacher, Silver)  False\n",
       "34  6193342      (Militia, Silver)      (Poacher, Silver)  False\n",
       "35  6227420      (Militia, Silver)      (Remodel, Silver)  False\n",
       "36  6227420      (Militia, Silver)  (Moneylender, Silver)  False\n",
       "37  6227420      (Militia, Silver)     (Merchant, Silver)  False\n",
       "38  5558534       (Chapel, Sentry)             (, Sentry)  False\n",
       "39  5558534       (Chapel, Sentry)       (Chapel, Silver)  False\n",
       "40  5656537       (Chapel, Market)      (Chapel, Poacher)  False\n",
       "41  5656537       (Chapel, Market)       (Chapel, Silver)  False\n",
       "42  5715500       (Chapel, Silver)  (Moneylender, Silver)  False\n",
       "43  5715500       (Chapel, Silver)     (Merchant, Silver)  False\n",
       "44  5975251      (Chapel, Militia)      (Chapel, Poacher)  False\n",
       "45  5975251      (Chapel, Militia)  (Moneylender, Silver)  False\n",
       "46  5975251      (Chapel, Militia)      (Militia, Silver)  False\n",
       "47  5975251      (Chapel, Militia)      (Poacher, Silver)  False\n",
       "48  5975251      (Chapel, Militia)       (Chapel, Silver)  False"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matches"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "flying-legislation",
   "metadata": {},
   "source": [
    "## The Ratings\n",
    "\n",
    "Great! We were able to extract 49 informative matches from our 31 games. Now we need some code to compute the ratings and plot the results. Updating the ratings is easy using trueskill.rate_1vs1 for each match. After we compute the ratings, we can plot the skill (mu) and the uncertainty (95% confidence interval) for each opening. Instead of ranking the openings by skill though, we will rank them using the lower bound of the uncertainty, which is a more conservative estimate of skill that takes into account the uncertainty. This is similar to what is done for the [Dominion Online leaderboard](http://forum.shuffleit.nl/index.php?topic=1679.msg5891#msg5891)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "black-earthquake",
   "metadata": {},
   "outputs": [],
   "source": [
    "import trueskill\n",
    "\n",
    "\n",
    "def update_ratings(ratings, matches):\n",
    "    for i, row in matches.iterrows():\n",
    "        b, w, d = row['better'], row['worse'], row['drawn']\n",
    "        ratings[b], ratings[w] = trueskill.rate_1vs1(ratings[b], ratings[w], d)\n",
    "\n",
    "def plot_ratings(ratings):\n",
    "    ratings = ratings.to_frame('rating')\n",
    "    ratings['mu'] = ratings.rating.apply(lambda x: x.mu)\n",
    "    ratings['lo'] = ratings.rating.apply(lambda x: x.mu - 2*x.sigma)\n",
    "    ratings['hi'] = ratings.rating.apply(lambda x: x.mu + 2*x.sigma)\n",
    "    ratings.sort_values('lo', inplace=True, ascending=False)\n",
    "    confidence_interval = [ratings.mu - ratings.lo, ratings.hi - ratings.mu]\n",
    "    ratings.plot(kind='bar', y='mu', yerr=confidence_interval, legend=False)\n",
    "    plt.xlabel('Rank')\n",
    "    plt.ylabel('Skill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "joint-forum",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratings = pd.Series({p: trueskill.Rating() for p in players})\n",
    "update_ratings(ratings, matches)\n",
    "plot_ratings(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "specialized-error",
   "metadata": {},
   "source": [
    "All right, let's unpack this plot. The blue bar shows the estimated skill (i.e., mu), and the black line shows the 95% confidence interval of our estimate (i.e., \\[mu - 2\\*sigma, mu + 2\\*sigma\\]). There is clearly a lot of uncertainty in our rankings, but that makes sense because of our limited data. However, these rankings are also highly dependent on the order in which we do our updates. Observe what happens if we randomly shuffle the matches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "experimental-spokesman",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratings = pd.Series({p: trueskill.Rating() for p in players})\n",
    "update_ratings(ratings, matches.sample(frac=1))\n",
    "plot_ratings(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "detailed-tulsa",
   "metadata": {},
   "source": [
    "This happens because the first couple updates are relatively uninformed. For example, if you beat a strong player before the rating system knows that player is strong, then the rating system may underestimate your skill. We can solve this problem by updating the ratings with the same set of matches several times until the rankings stabilize. This will give us a more accurate estimate of skill, but this solution isn't perfect. It will artificially reduce our estimate of the uncertainty. This is somewhat compensated by the fact that Burning Skull picking one opening over another is a strong indication of that opening being better. That said, we can certainly get more accurate estimates of uncertainty through a method known as the [empirical bootstrap](https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf), which involves repeating our procedure several times with random samples of our dataset. However, it is more computationally expensive, so let's get to that later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "stunning-aquarium",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_ratings(players, matches, repeat=10):\n",
    "    ratings = pd.Series({p: trueskill.Rating() for p in players})\n",
    "    for i in range(1 + repeat):\n",
    "        update_ratings(ratings, matches.sample(frac=1))\n",
    "    return ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "interesting-split",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratings = get_ratings(players, matches)\n",
    "plot_ratings(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seven-finish",
   "metadata": {},
   "source": [
    "These rankings are starting to look quite reasonable! A strong trasher, Chapel, as well as attacks, like Witch and Militia, are prioritized. Openings with Silver are less effective which is reasonable since Silver is available in every kingdom, and thus serves as a good default option, but not necessarily the best option.\n",
    "\n",
    "That said, one opening in particular seems out of place: (, Sentry). Burning Skull frequently commented on 5-2 type openings being good when Sentry is around. While Chapel is more effective at trashing, Sentry is a strong trasher, and it remains a good card in the late game because it can also discard bad cards before they are drawn.\n",
    "\n",
    "Our current approach is good at comparing openings of the same opening type, since it compares the actual opening against the openings that could have been made with that opening type, but it is less effective at comparing openings with different opening types. On a given board, is it better to have a 5-2 opening or a 4-3 opening?\n",
    "\n",
    "Lucky for us, Burning Skull occasionally sheds light on this question in his explanations. The file 'data/opening_comparisons.csv' contains comparisons between openings with different opening types, as well as some openings that he says are similar in strength (which are marked as 'drawn'), extracted from specific games in his videos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "infinite-trial",
   "metadata": {},
   "outputs": [],
   "source": [
    "additional_matches = pd.read_csv('data/opening_comparisons.csv')\n",
    "additional_matches.better = additional_matches.better.apply(lambda x: tuple(sorted(x.split('-'))))\n",
    "additional_matches.worse = additional_matches.worse.apply(lambda x: tuple(sorted(x.split('-'))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "gentle-bones",
   "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>game_id</th>\n",
       "      <th>better</th>\n",
       "      <th>worse</th>\n",
       "      <th>drawn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5553096</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5558534</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5656537</td>\n",
       "      <td>(Chapel, Market)</td>\n",
       "      <td>(Chapel, Poacher)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5579553</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5788864</td>\n",
       "      <td>(Chapel, Laboratory)</td>\n",
       "      <td>(Chapel, Witch)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5844082</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5924162</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5982614</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Moneylender, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6033410</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6033410</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6065802</td>\n",
       "      <td>(Chapel, Sentry)</td>\n",
       "      <td>(Chapel, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6087460</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6170038</td>\n",
       "      <td>(Poacher, Silver)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6170038</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Remodel, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6193342</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6227420</td>\n",
       "      <td>(, Sentry)</td>\n",
       "      <td>(Militia, Silver)</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    game_id                better                  worse  drawn\n",
       "0   5553096            (, Sentry)      (Militia, Silver)      0\n",
       "1   5558534      (Chapel, Sentry)       (Chapel, Silver)      0\n",
       "2   5656537      (Chapel, Market)      (Chapel, Poacher)      0\n",
       "3   5579553            (, Sentry)      (Poacher, Silver)      0\n",
       "4   5788864  (Chapel, Laboratory)        (Chapel, Witch)      1\n",
       "5   5844082            (, Sentry)  (Moneylender, Silver)      0\n",
       "6   5924162      (Chapel, Silver)      (Remodel, Silver)      0\n",
       "7   5982614            (, Sentry)  (Moneylender, Silver)      0\n",
       "8   6033410            (, Sentry)      (Militia, Silver)      0\n",
       "9   6033410            (, Sentry)      (Poacher, Silver)      0\n",
       "10  6065802      (Chapel, Sentry)       (Chapel, Silver)      0\n",
       "11  6087460            (, Sentry)      (Remodel, Silver)      0\n",
       "12  6170038     (Poacher, Silver)      (Remodel, Silver)      1\n",
       "13  6170038            (, Sentry)      (Remodel, Silver)      0\n",
       "14  6193342            (, Sentry)      (Militia, Silver)      0\n",
       "15  6227420            (, Sentry)      (Militia, Silver)      0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "additional_matches"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "substantial-belle",
   "metadata": {},
   "source": [
    "We have 16 additional matches, which brings our total to 65. Let's see how they affect the rankings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "entire-stability",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_matches = pd.concat([matches, additional_matches])\n",
    "ratings = get_ratings(players, total_matches)\n",
    "plot_ratings(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "refined-journalism",
   "metadata": {},
   "source": [
    "Looks good! As a final sanity check, let's compare these rankings to those available at [Council Room](http://councilroom.com/openings). It's a bit outdated, so it doesn't have all the openings from the second edition of the base set. Also, how base dominion openings compare in the context of base set is different than how base dominion openings compare in the context of the expansions. That said, it should be helpful, so let's take a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dietary-modification",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ranks = pd.read_html('http://councilroom.com/openings')[0]\n",
    "ranks.cards = ranks.cards.apply(lambda x: tuple(sorted(x.split(' / '))))\n",
    "ranks.cards = ranks.cards.apply(lambda x: ('', x[0]) if len(x) < 2 else x)\n",
    "ranks = ranks[ranks.cards.isin(players)]\n",
    "ranks[['level', 'uncertainty']] = ranks['skill range'].str.split(' ± ', expand=True).astype(float)\n",
    "ranks.plot(kind='bar', x='cards', y='level', yerr='uncertainty', legend=False)\n",
    "plt.xlabel('Rank')\n",
    "plt.ylabel('Level')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incorrect-steal",
   "metadata": {},
   "source": [
    "Pretty consistent with our results! The only opening with a much different rank is (Chapel, Militia). Is it a better opening in the context of the base set or does Burning Skull just love Militia? Who's to say? We would need more data to answer that question.\n",
    "\n",
    "\n",
    "## The Finale\n",
    "\n",
    "We've made it this far. Only one loose end left to tie up: the uncertainties. Uncertainty is something we can't ignore with a dataset of this size. Our skill estimates will remain unchanged — we're just calculating the uncertainties — but it could change the rankings a little."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "intense-denmark",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "\n",
    "def get_bootstrapped_ratings(players, matches, samples=1000, alpha=0.05):\n",
    "    ratings = get_ratings(players, matches).apply(lambda x: x.mu).to_frame('mu')\n",
    "    for i in tqdm(range(samples)):\n",
    "        ratings[i] = get_ratings(players, matches.sample(frac=1, replace=True)).apply(lambda x: x.mu)\n",
    "    # reverse percentile interval\n",
    "    ratings['lo'] = 2*ratings.mu - ratings[list(range(samples))].quantile(1 - alpha/2, axis=1)\n",
    "    ratings['hi'] = 2*ratings.mu - ratings[list(range(samples))].quantile(alpha/2, axis=1)\n",
    "    return ratings[['mu', 'lo', 'hi']]\n",
    "\n",
    "def plot_bootstrapped_ratings(ratings):\n",
    "    ratings.sort_values('lo', inplace=True, ascending=False)\n",
    "    confidence_interval = [ratings.mu - ratings.lo, ratings.hi - ratings.mu]\n",
    "    ratings.plot(kind='bar', y='mu', yerr=confidence_interval, legend=False)\n",
    "    plt.xlabel('Rank')\n",
    "    plt.ylabel('Skill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "animal-plymouth",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [08:58<00:00,  1.86it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratings = get_bootstrapped_ratings(players, total_matches)\n",
    "plot_bootstrapped_ratings(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "liberal-government",
   "metadata": {},
   "source": [
    "And there we have it. The best base dominion openings ;) Enjoy!\n",
    "\n",
    "For a different, more ambitious (and more suspicious lol) approach, check out [Part 2](https://github.com/zuirod/tensor-skill/blob/main/How%20to%20Base%20Dominion%20Opening%2C%20Part%202.ipynb)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "charged-ordering",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}