lost_game_duration.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import game\n",
    "from math import factorial as fac\n",
    "import seaborn as sns\n",
    "import agent\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['savefig.dpi'] = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Number of cards played in a lost game\n",
    "A game is lost when the sun token has moved 13 spaces.  This can only happen after at least 13 cards have been played.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is the probability that a player starts the game with at least one sun card?\n",
    "Since the turn order is random, this probability is the same for all players.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\n",
    "p\\left(start\\ with\\ at\\ least\\ one\\ sun\\right) &= 1-p\\left(start\\ with\\ zero\\ suns\\right) \\\\\n",
    "\n",
    "&= 1 - \\left( \\frac{36}{50}*\\frac{35}{49}*\\frac{34}{48} \\right) \\\\\n",
    "&\\approx 0.6357\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of the first hand being dealt at leat one sun is 0.6357\n"
     ]
    }
   ],
   "source": [
    "# Probability of the first hand having a sun on the first turn\n",
    "p = 1 - 36/50 * 35/49 * 34/48\n",
    "print(f'The probability of the first hand being dealt at leat one sun is {p:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In 63.55% of the 100,000 games, the first hand started with at least one sun.\n"
     ]
    }
   ],
   "source": [
    "# Deal 100,000 games and count the number of times the first hand contains at least one sun\n",
    "n_games = 100_000\n",
    "count = 0\n",
    "for _ in range(n_games):\n",
    "    g = game.Game()\n",
    "    if game.SUN in g.hands[0]:\n",
    "        count += 1\n",
    "\n",
    "print(f'In {count / n_games:.2%} of the {n_games:,} games, the first hand started with at least one sun.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is the expected position within the deck of the 13th sun card?\n",
    "```\n",
    "<---------------------------------k---------------->\n",
    "       ^                          ^           ^  \n",
    "       12 suns                    13th sun    1 sun\n",
    "```\n",
    "\n",
    "The position of the 13th sun has 12 suns before it and one sun after it.  The number of possible ways to achieve a configuration like this is the number of ways to configure 12 suns within $(k-1)$ positions multiplied by the number of positions that the last sun can be in, which is $(50-k)$.\n",
    "\n",
    "$$ N_{specific\\ permutations} = \\binom{k-1}{12} \\left( 50-k \\right) $$\n",
    "\n",
    "And the total number of ways to distribute 14 sun cards within 50 cards is calculated using a binomial coefficient.\n",
    "\n",
    "$$ N_{total\\ permutations} = \\binom{50}{14} $$\n",
    "\n",
    "So the probability that the 13th sun is in position $k$ is the ratio of the two expressions above.\n",
    "\n",
    "$$ p(k) = \\frac{\\binom{k-1}{12} \\left( 50-k \\right)}{\\binom{50}{14}} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the probability density function\n",
    "def binom(n, k):\n",
    "    return fac(n) / fac(k) / fac(n-k)\n",
    "\n",
    "def p(k):\n",
    "    return binom(k-1, 12) * (50-k) / binom(50, 14)\n",
    "\n",
    "x = []\n",
    "y = []\n",
    "for k in range(13,50):\n",
    "    x.append(k)\n",
    "    y.append(p(k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.stem(x, y)\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Probability density')\n",
    "# plt.grid(True)\n",
    "plt.savefig(fname='pdf_13th_sun_position.png', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "And the expected position of the 13th sun is:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\n",
    "E[k_{13}] &= \\sum_{k=13}^{49}p(k)k \\\\\n",
    "\n",
    "&= \\sum_{k=13}^{49} \\left[ \\frac{\\binom{k-1}{12} \\left( 50-k \\right)}{\\binom{50}{14}} k \\right] \\\\\n",
    "&= \\sum_{k=13}^{49} \\left[ \\frac{k(k-1)!(50-k)} {(k-13)!} \\frac{14!*36!}{12!*50!} \\right] \\\\\n",
    "&= 44.2\n",
    "\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average position of the 13th sun is 44.208\n"
     ]
    }
   ],
   "source": [
    "# Set up 100,000 decks and find the average position of the 13th sun\n",
    "n_games = 100_000\n",
    "sum = 0\n",
    "\n",
    "for _ in range(n_games):\n",
    "    d = game.Deck()\n",
    "    d.shuffle()\n",
    "    sum += d.position_of_nth_card(game.SUN, 13)\n",
    "\n",
    "avg = sum / n_games\n",
    "print(f'The average position of the 13th sun is {avg + 1:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result confirms that a single player game is expected to have 44.2 cards dealt and have 42.2 moves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Average number of cards played\n",
    "Since each player begins the game with an extra two cards in addition to the initial \"draw\", the number of cards that need to be drawn before the 13th sun is reached is two less for each player in the game.\n",
    "\n",
    "$$\n",
    "E[N_{cards\\_played}] = \\sum_{k=13}^{49} \\left[ \\frac{k(k-1)!(50-k)} {(k-13)!} \\frac{14!*36!}{12!*50!} \\right] - 2 N_{players}\n",
    "$$\n",
    "\n",
    "## Average number of cards dealt\n",
    "The number of cards dealt is directly related to the number of cards played and the number of players.  There are two additional cards dealt per player due to the starting hand.  Since the game ends with one player playing one of their three cards, they end with only two cards and a replacement card is not drawn.  Therefore, one less card is dealt.\n",
    "\n",
    "$$\n",
    "N_{cards\\_dealt} = N_{cards\\_played} + 3 N_{players} - 1\n",
    "$$\n",
    "\n",
    "| $N_{players}$ | $E[N_{cards\\_played}]$ | $E[N_{cards\\_dealt}]$ |\n",
    "| --- | --- | --- |\n",
    "| 1 | 42.2 | 44.2 |\n",
    "| 2 | 40.2 | 45.2 |\n",
    "| 3 | 38.2 | 46.2 |\n",
    "| 4 | 36.2 | 47.2 |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average cards played in a 1 player game using random moves is 42.201.\n",
      "The average number of cards dealt in a 1 player game using random moves is 44.201\n",
      "The average cards played in a 2 player game using random moves is 40.167.\n",
      "The average number of cards dealt in a 2 player game using random moves is 45.167\n",
      "The average cards played in a 3 player game using random moves is 38.103.\n",
      "The average number of cards dealt in a 3 player game using random moves is 46.103\n",
      "The average cards played in a 4 player game using random moves is 35.918.\n",
      "The average number of cards dealt in a 4 player game using random moves is 46.918\n"
     ]
    }
   ],
   "source": [
    "# Find the average length of a lost game\n",
    "n_games = 10_000\n",
    "played_cards_counts = {}\n",
    "\n",
    "for N_players in range(1, 5):\n",
    "    sum = 0\n",
    "    played_cards_counts[N_players] = []\n",
    "\n",
    "    for _ in range(n_games):\n",
    "        a = agent.Agent(n_hands=N_players)\n",
    "        a.play_game()\n",
    "\n",
    "        if a.game.state() == game.Game.LOSS:\n",
    "            sum += len(a.game.deck.cards)\n",
    "\n",
    "            n_cards_in_hands = 0\n",
    "            for _p in range(N_players):\n",
    "                n_cards_in_hands += len(a.game.hands[_p])\n",
    "\n",
    "            played_cards_counts[N_players].append(\n",
    "                50 - len(a.game.deck.cards) - n_cards_in_hands\n",
    "            )\n",
    "\n",
    "    avg_cards_remaining = sum / n_games\n",
    "    avg_cards_played = 50 - avg_cards_remaining - 3 * N_players + 1\n",
    "    avg_cards_dealt = 50 - avg_cards_remaining\n",
    "\n",
    "    print(\n",
    "        f'The average cards played in a {N_players} player game using random moves is {avg_cards_played:.3f}.')\n",
    "    print(\n",
    "        f'The average number of cards dealt in a {N_players} player game using random moves is {avg_cards_dealt:.3f}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lost games for 1 player sims = 10000\n",
      "Number of lost games for 2 player sims = 10000\n",
      "Number of lost games for 3 player sims = 10000\n",
      "Number of lost games for 4 player sims = 10000\n"
     ]
    }
   ],
   "source": [
    "for n in range(1, 5):\n",
    "    print(f'Number of lost games for {n} player sims = {len(played_cards_counts[n])}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x=(\n",
    "    played_cards_counts[1],\n",
    "    played_cards_counts[2],\n",
    "    played_cards_counts[3],\n",
    "    played_cards_counts[4]\n",
    "),\n",
    "    bins=range(13, 51),\n",
    "    histtype='step',\n",
    "    stacked=False,\n",
    "    fill=False,\n",
    "    label=['1', '2', '3', '4']\n",
    ")\n",
    "plt.xlabel('Cards Played')\n",
    "plt.ylabel('Frequency')\n",
    "legend = plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulations above do not seem to support the calculated expectations for multiplayer games.  The games seem to be ending sooner than expected.  Since 13 sun cards always need to be played/dealt, I'm not sure why this is the case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ygobprbprygborpygobprgyobprygborpygborpN\n",
      "******                                  | SSg byr Sob pob | Sun: 0 | Cards played: 0\n",
      "******                                  | SgS byr Sob pob | Sun: 1 | Cards played: 1\n",
      " *****  *                               | SgS byS Sob pob | Sun: 1 | Cards played: 2\n",
      " *****  *                               | SgS byS obp pob | Sun: 2 | Cards played: 3\n",
      " * ***  *   *                           | SgS byS obp pbo | Sun: 2 | Cards played: 4\n",
      " * ***  *   *                           | gSg byS obp pbo | Sun: 3 | Cards played: 5\n",
      " * ***  *   *                           | gSg byg obp pbo | Sun: 4 | Cards played: 6\n",
      " * * ** *   *                           | gSg byg opg pbo | Sun: 4 | Cards played: 7\n",
      " * * ** *         *                     | gSg byg opg poy | Sun: 4 | Cards played: 8\n",
      " * * ** *         *                     | ggy byg opg poy | Sun: 5 | Cards played: 9\n",
      "   * ** *  *      *                     | ggy ygo opg poy | Sun: 5 | Cards played: 10\n",
      "   * ** *  *           *                | ggy ygo pgb poy | Sun: 5 | Cards played: 11\n",
      "     ** ** *           *                | ggy ygo pgb pob | Sun: 5 | Cards played: 12\n",
      "     **  ***           *                | gyp ygo pgb pob | Sun: 5 | Cards played: 13\n",
      "     **  * *    *      *                | gyp yoS pgb pob | Sun: 5 | Cards played: 14\n",
      "     **  * *       *   *                | gyp yoS gbr pob | Sun: 5 | Cards played: 15\n",
      "     *   * **      *   *                | gyp yoS gbr pbS | Sun: 5 | Cards played: 16\n",
      "     *   * *   *   *   *                | gpr yoS gbr pbS | Sun: 5 | Cards played: 17\n",
      "     *   * *   *   *   *                | gpr yoS gbr pbS | Sun: 6 | Cards played: 18\n",
      "     *   * *       **  *                | gpr yoS gbS pbS | Sun: 6 | Cards played: 19\n",
      "     *   * *       **  *                | gpr yoS gbS pby | Sun: 7 | Cards played: 20\n",
      "     *   * *       **    *              | grg yoS gbS pby | Sun: 7 | Cards played: 21\n",
      "     *   * *       **    *              | grg yor gbS pby | Sun: 8 | Cards played: 22\n",
      "     *   * *       **    *              | grg yor gbS pby | Sun: 9 | Cards played: 23\n",
      "     *   * *       **      *            | grg yor gbS pbp | Sun: 9 | Cards played: 24\n",
      "     *    **       **      *            | rgg yor gbS pbp | Sun: 9 | Cards played: 25\n",
      "     *    **       *      **            | rgg yop gbS pbp | Sun: 9 | Cards played: 26\n",
      "     *    **       *      **            | rgg yop gbS pbp | Sun: 10 | Cards played: 27\n",
      "     *    **            * **            | rgg yop gbS ppr | Sun: 10 | Cards played: 28\n",
      "     *    **            * * *           | rgp yop gbS ppr | Sun: 10 | Cards played: 29\n",
      "     *     **           * * *           | rgp ypS gbS ppr | Sun: 10 | Cards played: 30\n",
      "     *     **           * * *           | rgp ypS gby ppr | Sun: 11 | Cards played: 31\n",
      "     *     **           * *     *       | rgp ypS gby prS | Sun: 11 | Cards played: 32\n",
      "     *      *   *       * *     *       | rpo ypS gby prS | Sun: 11 | Cards played: 33\n",
      "     *      *   *       * *     *       | rpo ypr gby prS | Sun: 12 | Cards played: 34\n",
      "     *      *   *       *    *  *       | rpo ypr gyS prS | Sun: 12 | Cards played: 35\n",
      "     *      *   *       *    *  *       | rpo ypr gyS pr | Sun: 13 | Cards played: 36\n",
      "Game result: Loss\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = agent.Agent(n_hands=4)\n",
    "a.play_game(show_game=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Probability that the 13th sun is played and the game ends when k cards have been removed from the deck\n",
    "def p_end(k, n_players):\n",
    "    return (\n",
    "        fac(k-num_players) * (49-k+num_players) * fac(14) * fac(36)\n",
    "        / fac(k-12-num_players) / fac(50) / fac(12)\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k=15, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=16, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=17, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=18, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=19, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=20, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=21, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=22, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=23, p=0.000, sum_cards=0.001, sum_p=0.000\n",
      "k=24, p=0.000, sum_cards=0.002, sum_p=0.000\n",
      "k=25, p=0.000, sum_cards=0.003, sum_p=0.000\n",
      "k=26, p=0.000, sum_cards=0.007, sum_p=0.000\n",
      "k=27, p=0.000, sum_cards=0.013, sum_p=0.001\n",
      "k=28, p=0.000, sum_cards=0.025, sum_p=0.001\n",
      "k=29, p=0.001, sum_cards=0.044, sum_p=0.002\n",
      "k=30, p=0.001, sum_cards=0.078, sum_p=0.003\n",
      "k=31, p=0.002, sum_cards=0.132, sum_p=0.004\n",
      "k=32, p=0.003, sum_cards=0.219, sum_p=0.007\n",
      "k=33, p=0.004, sum_cards=0.354, sum_p=0.011\n",
      "k=34, p=0.006, sum_cards=0.560, sum_p=0.017\n",
      "k=35, p=0.009, sum_cards=0.867, sum_p=0.026\n",
      "k=36, p=0.012, sum_cards=1.315, sum_p=0.039\n",
      "k=37, p=0.017, sum_cards=1.957, sum_p=0.056\n",
      "k=38, p=0.024, sum_cards=2.858, sum_p=0.080\n",
      "k=39, p=0.032, sum_cards=4.096, sum_p=0.111\n",
      "k=40, p=0.042, sum_cards=5.764, sum_p=0.153\n",
      "k=41, p=0.054, sum_cards=7.962, sum_p=0.207\n",
      "k=42, p=0.067, sum_cards=10.792, sum_p=0.274\n",
      "k=43, p=0.083, sum_cards=14.341, sum_p=0.357\n",
      "k=44, p=0.098, sum_cards=18.659, sum_p=0.455\n",
      "k=45, p=0.112, sum_cards=23.719, sum_p=0.567\n",
      "k=46, p=0.123, sum_cards=29.361, sum_p=0.690\n",
      "k=47, p=0.124, sum_cards=35.211, sum_p=0.814\n",
      "k=48, p=0.111, sum_cards=40.560, sum_p=0.926\n",
      "k=49, p=0.074, sum_cards=44.200, sum_p=1.000\n",
      "k=50, p=0.000, sum_cards=44.200, sum_p=1.000\n",
      "k=51, p=-0.129, sum_cards=37.598, sum_p=0.871\n",
      "k=52, p=-0.339, sum_cards=19.994, sum_p=0.532\n",
      "The expected number of cards dealt for a 1 player game is 19.994.\n",
      "k=18, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=19, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=20, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=21, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=22, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=23, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=24, p=0.000, sum_cards=0.001, sum_p=0.000\n",
      "k=25, p=0.000, sum_cards=0.002, sum_p=0.000\n",
      "k=26, p=0.000, sum_cards=0.004, sum_p=0.000\n",
      "k=27, p=0.000, sum_cards=0.007, sum_p=0.000\n",
      "k=28, p=0.000, sum_cards=0.014, sum_p=0.001\n",
      "k=29, p=0.000, sum_cards=0.026, sum_p=0.001\n",
      "k=30, p=0.001, sum_cards=0.046, sum_p=0.002\n",
      "k=31, p=0.001, sum_cards=0.080, sum_p=0.003\n",
      "k=32, p=0.002, sum_cards=0.136, sum_p=0.004\n",
      "k=33, p=0.003, sum_cards=0.226, sum_p=0.007\n",
      "k=34, p=0.004, sum_cards=0.365, sum_p=0.011\n",
      "k=35, p=0.006, sum_cards=0.577, sum_p=0.017\n",
      "k=36, p=0.009, sum_cards=0.893, sum_p=0.026\n",
      "k=37, p=0.012, sum_cards=1.353, sum_p=0.039\n",
      "k=38, p=0.017, sum_cards=2.013, sum_p=0.056\n",
      "k=39, p=0.024, sum_cards=2.937, sum_p=0.080\n",
      "k=40, p=0.032, sum_cards=4.207, sum_p=0.111\n",
      "k=41, p=0.042, sum_cards=5.917, sum_p=0.153\n",
      "k=42, p=0.054, sum_cards=8.169, sum_p=0.207\n",
      "k=43, p=0.067, sum_cards=11.066, sum_p=0.274\n",
      "k=44, p=0.083, sum_cards=14.698, sum_p=0.357\n",
      "k=45, p=0.098, sum_cards=19.114, sum_p=0.455\n",
      "k=46, p=0.112, sum_cards=24.286, sum_p=0.567\n",
      "k=47, p=0.123, sum_cards=30.051, sum_p=0.690\n",
      "k=48, p=0.124, sum_cards=36.026, sum_p=0.814\n",
      "k=49, p=0.111, sum_cards=41.486, sum_p=0.926\n",
      "k=50, p=0.074, sum_cards=45.200, sum_p=1.000\n",
      "k=51, p=0.000, sum_cards=45.200, sum_p=1.000\n",
      "k=52, p=-0.129, sum_cards=38.469, sum_p=0.871\n",
      "The expected number of cards dealt for a 2 player game is 38.469.\n",
      "k=21, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=22, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=23, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=24, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=25, p=0.000, sum_cards=0.001, sum_p=0.000\n",
      "k=26, p=0.000, sum_cards=0.002, sum_p=0.000\n",
      "k=27, p=0.000, sum_cards=0.004, sum_p=0.000\n",
      "k=28, p=0.000, sum_cards=0.007, sum_p=0.000\n",
      "k=29, p=0.000, sum_cards=0.014, sum_p=0.001\n",
      "k=30, p=0.000, sum_cards=0.027, sum_p=0.001\n",
      "k=31, p=0.001, sum_cards=0.048, sum_p=0.002\n",
      "k=32, p=0.001, sum_cards=0.083, sum_p=0.003\n",
      "k=33, p=0.002, sum_cards=0.141, sum_p=0.004\n",
      "k=34, p=0.003, sum_cards=0.233, sum_p=0.007\n",
      "k=35, p=0.004, sum_cards=0.376, sum_p=0.011\n",
      "k=36, p=0.006, sum_cards=0.594, sum_p=0.017\n",
      "k=37, p=0.009, sum_cards=0.919, sum_p=0.026\n",
      "k=38, p=0.012, sum_cards=1.392, sum_p=0.039\n",
      "k=39, p=0.017, sum_cards=2.069, sum_p=0.056\n",
      "k=40, p=0.024, sum_cards=3.017, sum_p=0.080\n",
      "k=41, p=0.032, sum_cards=4.319, sum_p=0.111\n",
      "k=42, p=0.042, sum_cards=6.070, sum_p=0.153\n",
      "k=43, p=0.054, sum_cards=8.376, sum_p=0.207\n",
      "k=44, p=0.067, sum_cards=11.340, sum_p=0.274\n",
      "k=45, p=0.083, sum_cards=15.054, sum_p=0.357\n",
      "k=46, p=0.098, sum_cards=19.568, sum_p=0.455\n",
      "k=47, p=0.112, sum_cards=24.853, sum_p=0.567\n",
      "k=48, p=0.123, sum_cards=30.741, sum_p=0.690\n",
      "k=49, p=0.124, sum_cards=36.840, sum_p=0.814\n",
      "k=50, p=0.111, sum_cards=42.411, sum_p=0.926\n",
      "k=51, p=0.074, sum_cards=46.200, sum_p=1.000\n",
      "k=52, p=0.000, sum_cards=46.200, sum_p=1.000\n",
      "The expected number of cards dealt for a 3 player game is 46.200.\n",
      "k=24, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=25, p=0.000, sum_cards=0.000, sum_p=0.000\n",
      "k=26, p=0.000, sum_cards=0.001, sum_p=0.000\n",
      "k=27, p=0.000, sum_cards=0.002, sum_p=0.000\n",
      "k=28, p=0.000, sum_cards=0.004, sum_p=0.000\n",
      "k=29, p=0.000, sum_cards=0.008, sum_p=0.000\n",
      "k=30, p=0.000, sum_cards=0.015, sum_p=0.001\n",
      "k=31, p=0.000, sum_cards=0.027, sum_p=0.001\n",
      "k=32, p=0.001, sum_cards=0.049, sum_p=0.002\n",
      "k=33, p=0.001, sum_cards=0.086, sum_p=0.003\n",
      "k=34, p=0.002, sum_cards=0.145, sum_p=0.004\n",
      "k=35, p=0.003, sum_cards=0.240, sum_p=0.007\n",
      "k=36, p=0.004, sum_cards=0.387, sum_p=0.011\n",
      "k=37, p=0.006, sum_cards=0.611, sum_p=0.017\n",
      "k=38, p=0.009, sum_cards=0.945, sum_p=0.026\n",
      "k=39, p=0.012, sum_cards=1.431, sum_p=0.039\n",
      "k=40, p=0.017, sum_cards=2.125, sum_p=0.056\n",
      "k=41, p=0.024, sum_cards=3.096, sum_p=0.080\n",
      "k=42, p=0.032, sum_cards=4.430, sum_p=0.111\n",
      "k=43, p=0.042, sum_cards=6.223, sum_p=0.153\n",
      "k=44, p=0.054, sum_cards=8.582, sum_p=0.207\n",
      "k=45, p=0.067, sum_cards=11.614, sum_p=0.274\n",
      "k=46, p=0.083, sum_cards=15.411, sum_p=0.357\n",
      "k=47, p=0.098, sum_cards=20.023, sum_p=0.455\n",
      "k=48, p=0.112, sum_cards=25.420, sum_p=0.567\n",
      "k=49, p=0.123, sum_cards=31.431, sum_p=0.690\n",
      "k=50, p=0.124, sum_cards=37.654, sum_p=0.814\n",
      "k=51, p=0.111, sum_cards=43.337, sum_p=0.926\n",
      "k=52, p=0.074, sum_cards=47.200, sum_p=1.000\n",
      "The expected number of cards dealt for a 4 player game is 47.200.\n"
     ]
    }
   ],
   "source": [
    "for num_players in range(1, 5):\n",
    "    avg_cards_dealt = 0\n",
    "    p_sum = 0\n",
    "    for k in range(3*num_players+12, 53):\n",
    "        p = p_end(k, num_players)\n",
    "        p_sum += p\n",
    "        avg_cards_dealt += k * p\n",
    "        print(f'k={k}, p={p:.3f}, sum_cards={avg_cards_dealt:.3f}, sum_p={p_sum:.3f}')\n",
    "    print(f'The expected number of cards dealt for a {num_players} player game is {avg_cards_dealt:.3f}.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for num_players in range(1, 5):\n",
    "    k = list(range(3*num_players+12, 51))\n",
    "    p = []\n",
    "    for i in k:\n",
    "        p.append(p_end(i, num_players))\n",
    "    plt.plot(k, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sum of this probability distribution over all values of k:\n",
    "\n",
    "| $N_{players}$ | $p(k_{13})$ |\n",
    "| --- | --- |\n",
    "| 1 | 1.000 |\n",
    "| 2 | 1.000 |\n",
    "| 3 | 0.926 |\n",
    "| 4 | 0.814 |\n",
    "\n",
    "What are the unaccounted for possibilities for 3 and 4 player games?\n",
    "\n",
    "It seems like 3 players is missing the last $p(k_{13})$ that 1 and 2 player games have.  i.e.\n",
    "\n",
    "$$1 - 0.926 = 0.074$$\n",
    "\n",
    "It seems like 3 players is missing that and also the second to last value.  i.e.\n",
    "\n",
    "$$1 - 0.814 = 0.186 = 0.074 + 0.111$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot n_cards_dealt vs. n_cards_played\n",
    "for n_hands in range(1, 5):\n",
    "    n_cards_played = list(range(13, 51))\n",
    "    n_cards_dealt = []\n",
    "    for n in n_cards_played:\n",
    "        n_cards_dealt.append(n + 3*n_hands - 1)\n",
    "        if n_cards_dealt[-1] > 50:\n",
    "            n_cards_dealt[-1] = 50\n",
    "    plt.plot(n_cards_played, n_cards_dealt, label=str(n_hands))\n",
    "plt.legend()\n",
    "plt.xlabel('Cards Played')\n",
    "plt.ylabel('Cards Dealt')\n",
    "# plt.savefig('cards_dealt.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "df4e6b70a5fe3c12393ad7d487e5616e7544ce8f37b0ece5df19391db8b0b32b"
  },
  "kernelspec": {
   "display_name": "Python 3.8.10 ('env': venv)",
   "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": "3.8.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}