War Part II Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just some housekeeping here... pay no mind.\n",
    "from random import seed\n",
    "from random import shuffle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from time import time\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import FuncFormatter\n",
    "%matplotlib inline\n",
    "\n",
    "import WAR\n",
    "\n",
    "# reload if updated script\n",
    "# import importlib\n",
    "# importlib.reload(WAR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reaching a Stable State\n",
    "\n",
    "## Run Simulations\n",
    "\n",
    "Using original rules -- no discard randomness, discard mode is First In First Out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Simulate 1k games\n",
    "results = []\n",
    "seed(0)\n",
    "for i in range(0, 1000):\n",
    "    # Initialize a game\n",
    "    game = WAR.War(max_hands = 20000, discard_recycle_mode = 'fifo', discard_randomness = False)\n",
    "    \n",
    "    # Play each game\n",
    "    _ = game.play_game()\n",
    "    \n",
    "    # Append the game summary dict. (includes number of turns, winner, starting hands, etc.) to the results list\n",
    "    results.append(game.summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent finished: 64%\n"
     ]
    },
    {
     "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>discard_randomness</th>\n",
       "      <th>discard_recycle_mode</th>\n",
       "      <th>finished</th>\n",
       "      <th>hands_played</th>\n",
       "      <th>p1_dealt</th>\n",
       "      <th>p2_dealt</th>\n",
       "      <th>tracks</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>False</td>\n",
       "      <td>fifo</td>\n",
       "      <td>True</td>\n",
       "      <td>781</td>\n",
       "      <td>[4, 14, 8, 4, 14, 9, 7, 12, 3, 12, 9, 2, 6, 11...</td>\n",
       "      <td>[10, 3, 13, 12, 5, 6, 11, 10, 8, 3, 7, 10, 9, ...</td>\n",
       "      <td>0      26\n",
       "1      25\n",
       "2      26\n",
       "3      25\n",
       "4     ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>fifo</td>\n",
       "      <td>True</td>\n",
       "      <td>1170</td>\n",
       "      <td>[2, 12, 3, 13, 10, 2, 13, 3, 5, 11, 7, 2, 14, ...</td>\n",
       "      <td>[14, 11, 6, 5, 2, 10, 9, 7, 8, 8, 7, 8, 13, 3,...</td>\n",
       "      <td>0       26\n",
       "1       25\n",
       "2       26\n",
       "3       25\n",
       "4 ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>False</td>\n",
       "      <td>fifo</td>\n",
       "      <td>True</td>\n",
       "      <td>839</td>\n",
       "      <td>[5, 14, 6, 6, 5, 3, 11, 3, 11, 13, 10, 8, 4, 1...</td>\n",
       "      <td>[8, 3, 12, 14, 7, 12, 9, 9, 7, 11, 7, 4, 10, 4...</td>\n",
       "      <td>0      26\n",
       "1      25\n",
       "2      26\n",
       "3      25\n",
       "4     ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>False</td>\n",
       "      <td>fifo</td>\n",
       "      <td>True</td>\n",
       "      <td>1935</td>\n",
       "      <td>[11, 13, 6, 14, 14, 7, 6, 9, 11, 7, 12, 12, 2,...</td>\n",
       "      <td>[2, 12, 3, 7, 5, 11, 8, 11, 3, 6, 5, 8, 3, 10,...</td>\n",
       "      <td>0       26\n",
       "1       27\n",
       "2       28\n",
       "3       29\n",
       "4 ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>False</td>\n",
       "      <td>fifo</td>\n",
       "      <td>True</td>\n",
       "      <td>152</td>\n",
       "      <td>[12, 3, 14, 8, 8, 12, 11, 9, 3, 9, 14, 13, 6, ...</td>\n",
       "      <td>[9, 10, 13, 7, 7, 4, 10, 6, 10, 4, 10, 7, 5, 2...</td>\n",
       "      <td>0      26\n",
       "1      27\n",
       "2      26\n",
       "3      27\n",
       "4     ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   discard_randomness discard_recycle_mode  finished  hands_played  \\\n",
       "0               False                 fifo      True           781   \n",
       "1               False                 fifo      True          1170   \n",
       "2               False                 fifo      True           839   \n",
       "3               False                 fifo      True          1935   \n",
       "4               False                 fifo      True           152   \n",
       "\n",
       "                                            p1_dealt  \\\n",
       "0  [4, 14, 8, 4, 14, 9, 7, 12, 3, 12, 9, 2, 6, 11...   \n",
       "1  [2, 12, 3, 13, 10, 2, 13, 3, 5, 11, 7, 2, 14, ...   \n",
       "2  [5, 14, 6, 6, 5, 3, 11, 3, 11, 13, 10, 8, 4, 1...   \n",
       "3  [11, 13, 6, 14, 14, 7, 6, 9, 11, 7, 12, 12, 2,...   \n",
       "4  [12, 3, 14, 8, 8, 12, 11, 9, 3, 9, 14, 13, 6, ...   \n",
       "\n",
       "                                            p2_dealt  \\\n",
       "0  [10, 3, 13, 12, 5, 6, 11, 10, 8, 3, 7, 10, 9, ...   \n",
       "1  [14, 11, 6, 5, 2, 10, 9, 7, 8, 8, 7, 8, 13, 3,...   \n",
       "2  [8, 3, 12, 14, 7, 12, 9, 9, 7, 11, 7, 4, 10, 4...   \n",
       "3  [2, 12, 3, 7, 5, 11, 8, 11, 3, 6, 5, 8, 3, 10,...   \n",
       "4  [9, 10, 13, 7, 7, 4, 10, 6, 10, 4, 10, 7, 5, 2...   \n",
       "\n",
       "                                              tracks  \n",
       "0  0      26\n",
       "1      25\n",
       "2      26\n",
       "3      25\n",
       "4     ...  \n",
       "1  0       26\n",
       "1       25\n",
       "2       26\n",
       "3       25\n",
       "4 ...  \n",
       "2  0      26\n",
       "1      25\n",
       "2      26\n",
       "3      25\n",
       "4     ...  \n",
       "3  0       26\n",
       "1       27\n",
       "2       28\n",
       "3       29\n",
       "4 ...  \n",
       "4  0      26\n",
       "1      27\n",
       "2      26\n",
       "3      27\n",
       "4     ...  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Turn results list into a dataframe\n",
    "results_df = pd.DataFrame(results)\n",
    "\n",
    "# Print the percent finished and show head\n",
    "print('Percent finished: {:.0%}'.format(results_df.finished.mean()))\n",
    "results_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Game Tracks\n",
    "\n",
    "Plot tracks for unfinished games -- demonstrate that never-ending games reach a stable state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Loop through the first 10 unfinished games and plot the tracks\n",
    "for a in results_df.loc[~results_df.finished, 'tracks'].iloc[0:10]:\n",
    "    _ = plt.plot(a, linewidth = 0.3, alpha = 0.6)\n",
    "\n",
    "# Format the graphs\n",
    "_ = plt.title('Game Tracks for 10 Unfinished Games')\n",
    "_ = plt.xlabel('Turn Number')\n",
    "_ = plt.xlim(0, 5000)\n",
    "_ = plt.ylabel('Player A Cards')\n",
    "\n",
    "# Save figure\n",
    "_ = plt.savefig('post_2/game_tracks.png', dpi = 300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find Where Stable States Occur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stable_state(game_tracks):\n",
    "    '''\n",
    "    Finds whether the stable state has been reached and, if so, the turn when it was\n",
    "    reached and how many cards player 1 had. If stable state has not been reached, returns\n",
    "    False for stable_reached and np.NaN for stable_cards_p1 and stable_turn.\n",
    "    '''\n",
    "    \n",
    "    # Checks whether stable has been reached by evaluating if there was any shift in the\n",
    "    ## balance of cards in the last 52 recorded turns\n",
    "    last52 = game_tracks.iloc[-52:]\n",
    "    stable_reached = last52.max() - last52.min() == 1\n",
    "    \n",
    "    # Find the stable state turn and card count if stable state has been reached\n",
    "    if stable_reached:\n",
    "        # Find the stable state # of cards (use even number)\n",
    "        last2 = game_tracks.iloc[-2:] # Look at last two card counts\n",
    "        stable_cards_p1 = last2[last2 % 2 == 0].iloc[0] # Choose the one that is even\n",
    "    \n",
    "        # Find the number of turns to get to stable state\n",
    "        game_tracks_rev = game_tracks.sort_index(ascending = False) # Reverse sort the game tracks\n",
    "        outside_stable = abs(game_tracks_rev - stable_cards_p1) > 1\n",
    "        stable_turn = game_tracks_rev[outside_stable].index[0] + 1  # Get index of last time game was\n",
    "                                                                    # outside of the stable state\n",
    "    \n",
    "    # Otherwise, assign NaN\n",
    "    else:\n",
    "        stable_cards_p1, stable_turn = np.NaN, np.NaN\n",
    "        \n",
    "        \n",
    "    \n",
    "    return stable_reached, stable_cards_p1, stable_turn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, 16, 1030)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test function\n",
    "stable_state(results_df.loc[25, 'tracks'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>stable_state_reached</th>\n",
       "      <th>stable_cards_p1</th>\n",
       "      <th>stable_turn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>True</td>\n",
       "      <td>26</td>\n",
       "      <td>351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>True</td>\n",
       "      <td>26</td>\n",
       "      <td>2159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>True</td>\n",
       "      <td>26</td>\n",
       "      <td>537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>True</td>\n",
       "      <td>26</td>\n",
       "      <td>715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>True</td>\n",
       "      <td>26</td>\n",
       "      <td>571</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    stable_state_reached  stable_cards_p1  stable_turn\n",
       "5                   True               26          351\n",
       "8                   True               26         2159\n",
       "9                   True               26          537\n",
       "10                  True               26          715\n",
       "16                  True               26          571"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Apply the stable state function on the tracks of never-ending games\n",
    "stable_state_cards = results_df.loc[~results_df['finished']].apply(\n",
    "                                                lambda x: stable_state(x['tracks']), axis = 1, result_type = 'expand')\n",
    "\n",
    "# Rename and show head\n",
    "stable_state_cards.columns = ['stable_state_reached', 'stable_cards_p1', 'stable_turn']\n",
    "stable_state_cards.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8     0.002778\n",
       "12    0.008333\n",
       "16    0.016667\n",
       "20    0.030556\n",
       "24    0.013889\n",
       "26    0.844444\n",
       "28    0.011111\n",
       "32    0.022222\n",
       "36    0.022222\n",
       "40    0.011111\n",
       "44    0.013889\n",
       "48    0.002778\n",
       "Name: stable_cards_p1, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show the percentage of stable state games by p1 cards\n",
    "stable_state_cards.stable_cards_p1.value_counts().sort_index() / len(stable_state_cards)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Investigate a Stable State-26 Case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Find the first never-ending game with a 26-26 stable state\n",
    "game_index = stable_state_cards[stable_state_cards.stable_cards_p1 == 26].index[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the game track\n",
    "_ = plt.plot(results_df.loc[game_index, 'tracks'])\n",
    "_ = plt.title('Game Track')\n",
    "_ = plt.xlabel('Turn Number')\n",
    "_ = plt.xlim(0, 600)\n",
    "_ = plt.ylim(0, 52)\n",
    "_ = plt.ylabel('Player A Cards')\n",
    "\n",
    "_ = plt.savefig('post_2/game_track_26.png', dpi = 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the starting hands for the game and initialize a game with those starting hands\n",
    "\n",
    "starting_hands = [i for i in results_df.loc[game_index, ['p1_dealt', 'p2_dealt']]]\n",
    "game = WAR.War(20000, 'fifo', starting_hands = starting_hands.copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "351"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the stable state turn\n",
    "\n",
    "stable_turn = stable_state_cards.loc[game_index, 'stable_turn']\n",
    "stable_turn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "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>P1</th>\n",
       "      <th>P2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>12</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
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       "      <td>6</td>\n",
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       "      <td>10</td>\n",
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       "      <th>14</th>\n",
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       "      <td>2</td>\n",
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       "      <th>15</th>\n",
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       "      <td>9</td>\n",
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       "      <th>17</th>\n",
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       "      <th>21</th>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>3</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>4</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "    P1  P2\n",
       "0   13   8\n",
       "1    2  14\n",
       "2   11   9\n",
       "3    7  13\n",
       "4   12   3\n",
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       "14  12   2\n",
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       "19   3  14\n",
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       "21   6  10\n",
       "22   9   7\n",
       "23   3  11\n",
       "24   9   4\n",
       "25   4  11"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Move the game ahead to the stable state\n",
    "\n",
    "game.seek(400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "    P1  P2\n",
       "0   13   2\n",
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       "2   11   7\n",
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       "21   5  10\n",
       "22   9   3\n",
       "23   7  11\n",
       "24   9   4\n",
       "25   4  11"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check 26 turns later to see the mirror\n",
    "\n",
    "game.skip(26)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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      "text/plain": [
       "    P1  P2\n",
       "0   13   2\n",
       "1    8  14\n",
       "2   11   7\n",
       "3    9  13\n",
       "4   12   2\n",
       "5    3  13\n",
       "6   10   5\n",
       "7    8  14\n",
       "8    7   4\n",
       "9    5  12\n",
       "10  12   5\n",
       "11   6   7\n",
       "12  13   8\n",
       "13   6  10\n",
       "14  12   6\n",
       "15   2   9\n",
       "16   8   4\n",
       "17   2  14\n",
       "18  11   3\n",
       "19   3  14\n",
       "20  10   6\n",
       "21   5  10\n",
       "22   9   3\n",
       "23   7  11\n",
       "24   9   4\n",
       "25   4  11"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 26 more turns to return to the hands of turn 400\n",
    "\n",
    "x = game.skip(52)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confirm other 26-26 cases follow the stable state structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_diagonals(diagonal_1, diagonal_2):\n",
    "    '''\n",
    "    If passed tuples for diagonals, will confirm that both cards in one tuple\n",
    "    are larger than both tuples in the other (i.e. stable state block)\n",
    "    '''\n",
    "    sorted_tuples = sorted([diagonal_1, diagonal_2], key = sum)\n",
    "    \n",
    "    return max(sorted_tuples[0]) < min(sorted_tuples[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_game_structure(hands_df):\n",
    "    '''\n",
    "    Evaluates a dataframe representing both players hands to see if it follows\n",
    "    the stable state pattern.\n",
    "    '''\n",
    "    hands_df = hands_df.copy()\n",
    "    \n",
    "    # Confirm we have a 26-26 stable state\n",
    "    assert len(hands_df) == 26\n",
    "\n",
    "    #Create tuples with the diagonals (current row and following row)\n",
    "    hands_df['P1_shift'] = hands_df['P1'].shift(-1)\n",
    "    hands_df['P2_shift'] = hands_df['P2'].shift(-1)  \n",
    "    hands_df['diagonal_1'] = hands_df.apply(lambda row: (row['P1'], row['P2_shift']), axis = 1)\n",
    "    hands_df['diagonal_2'] = hands_df.apply(lambda row: (row['P2'], row['P1_shift']), axis = 1)\n",
    "    \n",
    "    #Consider every other row (to deal with 4-card blocks)\n",
    "    hands_df = hands_df.iloc[::2]\n",
    "        \n",
    "    return hands_df.apply(lambda x: check_diagonals(x['diagonal_1'], x['diagonal_2']), axis = 1).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_game_structure(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initiate list to track results\n",
    "structure_validate = []\n",
    "\n",
    "# Loop through every game with a 26-26 stable state\n",
    "for game_index in stable_state_cards[stable_state_cards.stable_cards_p1 == 26].index:\n",
    "    \n",
    "    # Initalize game\n",
    "    starting_hands = [i for i in results_df.loc[game_index, ['p1_dealt', 'p2_dealt']]]\n",
    "    game = WAR.War(20000, 'fifo', starting_hands = starting_hands.copy())\n",
    "    \n",
    "    # Move forward to the stable state\n",
    "    stable_turn = stable_state_cards.loc[game_index, 'stable_turn']\n",
    "    stable_turn = ((stable_turn + 52) // 2)*2\n",
    "    hands = game.seek(stable_turn)\n",
    "    \n",
    "    # Check the game structure and append the result to the trackign list\n",
    "    try:\n",
    "        res = check_game_structure(hands)\n",
    "        structure_validate.append(res)\n",
    "    \n",
    "    # Run one more turn if check game structure didn't work (not at 26-26) and rerun test\n",
    "    except:\n",
    "        hands = game.skip()\n",
    "        res = check_game_structure(hands)\n",
    "        structure_validate.append(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm that each 26-26 game passed the test\n",
    "min(structure_validate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Investigating Other Stable States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11a9bc710>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stable_state_counts = stable_state_cards.stable_cards_p1.apply(lambda x: 26 - abs(x - 26)).value_counts() / \\\n",
    "            len(stable_state_cards)\n",
    "\n",
    "stable_state_counts.sort_index().plot.bar(color = 'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "discard_randomness                                                  False\n",
       "discard_recycle_mode                                                 fifo\n",
       "finished                                                            False\n",
       "hands_played                                                        20000\n",
       "p1_dealt                [3, 12, 10, 10, 9, 11, 7, 6, 5, 9, 6, 2, 5, 8,...\n",
       "p2_dealt                [4, 8, 11, 8, 5, 6, 9, 4, 14, 5, 3, 2, 10, 13,...\n",
       "tracks                  0        26\n",
       "1        25\n",
       "2        26\n",
       "3        2...\n",
       "Name: 991, dtype: object"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_index = stable_state_cards[stable_state_cards.stable_cards_p1.isin([4, 48])].index[0]\n",
    "results_df.loc[game_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1677"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stable_turn = stable_state_cards.loc[game_index, 'stable_turn']\n",
    "stable_turn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(results_df.loc[game_index, 'tracks'])\n",
    "_ = plt.title('Game Track')\n",
    "_ = plt.xlabel('Turn Number')\n",
    "_ = plt.xlim(0, 2000)\n",
    "_ = plt.ylim(0, 52)\n",
    "_ = plt.ylabel('Player A Cards')\n",
    "\n",
    "_ = plt.savefig('post_2/game_track_26.png', dpi = 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "starting_hands = [i for i in results_df.loc[game_index, ['p1_dealt', 'p2_dealt']]]\n",
    "game = WAR.War(20000, 'fifo', starting_hands = starting_hands.copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "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>P1</th>\n",
       "      <th>P2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>14</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>14</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>12</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>12</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>14</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>12</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    P1   P2\n",
       "0   14  6.0\n",
       "1    5  9.0\n",
       "2   12  4.0\n",
       "3    6  8.0\n",
       "4   10  NaN\n",
       "5    2  NaN\n",
       "6   10  NaN\n",
       "7    7  NaN\n",
       "8   14  NaN\n",
       "9    3  NaN\n",
       "10   9  NaN\n",
       "11   5  NaN\n",
       "12  11  NaN\n",
       "13   2  NaN\n",
       "14   9  NaN\n",
       "15   2  NaN\n",
       "16  14  NaN\n",
       "17   8  NaN\n",
       "18  12  NaN\n",
       "19   7  NaN\n",
       "20  12  NaN\n",
       "21   3  NaN\n",
       "22  10  NaN\n",
       "23   4  NaN\n",
       "24  13  NaN\n",
       "25   6  NaN\n",
       "26  11  NaN\n",
       "27   2  NaN\n",
       "28   9  NaN\n",
       "29   8  NaN\n",
       "30   8  NaN\n",
       "31   7  NaN\n",
       "32  11  NaN\n",
       "33   3  NaN\n",
       "34  11  NaN\n",
       "35   4  NaN\n",
       "36  14  NaN\n",
       "37   5  NaN\n",
       "38  12  NaN\n",
       "39   6  NaN\n",
       "40  13  NaN\n",
       "41   3  NaN\n",
       "42  10  NaN\n",
       "43   5  NaN\n",
       "44  13  NaN\n",
       "45   7  NaN\n",
       "46  13  NaN\n",
       "47   4  NaN"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm stable-state like structure\n",
    "\n",
    "x = game.seek(1800)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>P1</th>\n",
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       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>20</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>21</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>22</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>23</th>\n",
       "      <td>2</td>\n",
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       "      <th>24</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>14</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>12</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>13</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>14</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>12</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    P1   P2\n",
       "0   10  5.0\n",
       "1    2  9.0\n",
       "2   10  6.0\n",
       "3    7  8.0\n",
       "4   14  NaN\n",
       "5    3  NaN\n",
       "6    9  NaN\n",
       "7    5  NaN\n",
       "8   11  NaN\n",
       "9    2  NaN\n",
       "10   9  NaN\n",
       "11   2  NaN\n",
       "12  14  NaN\n",
       "13   8  NaN\n",
       "14  12  NaN\n",
       "15   7  NaN\n",
       "16  12  NaN\n",
       "17   3  NaN\n",
       "18  10  NaN\n",
       "19   4  NaN\n",
       "20  13  NaN\n",
       "21   6  NaN\n",
       "22  11  NaN\n",
       "23   2  NaN\n",
       "24   9  NaN\n",
       "25   8  NaN\n",
       "26   8  NaN\n",
       "27   7  NaN\n",
       "28  11  NaN\n",
       "29   3  NaN\n",
       "30  11  NaN\n",
       "31   4  NaN\n",
       "32  14  NaN\n",
       "33   5  NaN\n",
       "34  12  NaN\n",
       "35   6  NaN\n",
       "36  13  NaN\n",
       "37   3  NaN\n",
       "38  10  NaN\n",
       "39   5  NaN\n",
       "40  13  NaN\n",
       "41   7  NaN\n",
       "42  13  NaN\n",
       "43   4  NaN\n",
       "44  14  NaN\n",
       "45   6  NaN\n",
       "46  12  NaN\n",
       "47   4  NaN"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Similar structure maintained four turns later\n",
    "\n",
    "game.skip(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Breaking the Stable State\n",
    "\n",
    "Simulate games with discard randomness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "seed(0)\n",
    "for i in range(0, 1000):\n",
    "    game = WAR.War(20000, 'fifo', True)\n",
    "    _ = game.play_game()\n",
    "    results.append(game.summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "discard_randomness\n",
       "False    0.64\n",
       "True     1.00\n",
       "Name: finished, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dataframe out of results and check the percentage of games finished\n",
    "# by discard randomness\n",
    "\n",
    "results_df = pd.DataFrame(results)\n",
    "results_df.groupby('discard_randomness').finished.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a running percent distribution of finished games by turn count, grouped by randomness\n",
    "\n",
    "running_dist = results_df.groupby('discard_randomness').hands_played.apply(\n",
    "    lambda x: x.value_counts().sort_index().cumsum() / len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot result comparison between original and random discard\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize = (12, 4))\n",
    "\n",
    "_ = results_df.groupby('discard_randomness').finished.mean().plot.bar(ax = ax[0])\n",
    "_ = ax[0].set_ylabel('Pct of Games Finished')\n",
    "_ = ax[0].set_title('Game Completion After 20k Turns')\n",
    "_ = ax[0].yaxis.set_major_formatter(FuncFormatter(lambda y, _: '{:.0%}'.format(y)))\n",
    "\n",
    "_ = running_dist.unstack(level = 0).fillna(method = 'backfill').plot(ax = ax[1])\n",
    "_ = ax[1].set_xlim(0, 2000)\n",
    "_ = ax[1].set_xlabel('Turn Number')\n",
    "_ = ax[1].set_ylabel('Pct of Games Finished')\n",
    "_ = ax[1].set_title('Game Completion Rate by Turn')\n",
    "_ = ax[1].yaxis.set_major_formatter(FuncFormatter(lambda y, _: '{:.0%}'.format(y)))\n",
    "\n",
    "plt.savefig('post_2/discard_randomness_comp.png', bbox_inches = 'tight', dpi = 300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Thoughts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "john = [13, 11, 9, 12, 3, 8, 6, 5, 6, 5, 13, 6, 13, 4, 4, 6, 10, 4, 3, 2, 7, 10, 9, 3, 14, 2, 10, 2, 3, 12, 5, 2]\n",
    "kelly = [8, 4, 9, 12, 7, 14, 8, 14, 8, 7, 5, 11, 10, 12, 7, 9, 13, 11, 14, 11]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "turns_to_res = []\n",
    "for i in range(0, 100):\n",
    "    seed(i)\n",
    "    game = WAR.War(20000, discard_recycle_mode = 'filo', discard_randomness = True,\n",
    "                    starting_hands = [john.copy(), kelly.copy()])\n",
    "    \n",
    "    summary = game.play_game()\n",
    "    \n",
    "    turns_to_res.append(summary['hands_played'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 297.5 ,  535.5 ,  844.3 , 1159.27])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(turns_to_res, [50, 75, 90, 99])"
   ]
  }
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