slap.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# The game of Slap\n",
    "\n",
    "## [Fiddler, Oct. 13, 2023](https://thefiddler.substack.com/p/can-you-throw-the-card-game)\n",
    "\n",
    "> Every so often, I play the card game Slap with someone who really doesn’t like to lose. (You know who you are.) But before we get into all that, here are the rules of the game:\n",
    ">\n",
    "> Two players are both dealt 26 cards from a standard deck. From there, they take turns putting down one card at a time. Let’s interchangeably designate the players as “A” and “B.”\n",
    ">\n",
    "> - If A puts down a jack, then B puts down one card. If it’s a face card, the game continues with A. Otherwise, A wins the round and adds those cards to the bottom of their pile so that the last card played is at the very bottom of the pile.\n",
    "> - If A puts down a queen, B has two chances to put down a face card, at which point the game would continue with A. Otherwise, A wins the round and collects the cards.\n",
    "> - If A puts down a king, B has three chances to put down a face card, at which point the game would continue with A. Otherwise, A wins the round and collects the cards.\n",
    "> - If A puts down an ace, B has four chances to put down a face card, at which point the game would continue with A. Otherwise, A wins the round and collects the cards.\n",
    "> - If, at any point, two cards have been played in succession (by different players or the same player) that have the same number or face, then both players can slap the pile of played cards to win the round and collect the cards.\n",
    "> - Whoever won the previous round plays the first card in the next round.\n",
    ">\n",
    "> It turns out that rigging the deck while shuffling is very hard to do. Instead, I decide to cheat in my opponent’s favor by ensuring my reaction time is slower than theirs at every single slapping opportunity. In other words, I lose every slap.\n",
    "> Assuming I shuffle and distribute the cards randomly, and that my opponent plays the first card in the game, what is my probability of winning?\n",
    "\n",
    "### Solution by [Laurent Lessard](https://laurentlessard.com)\n",
    "\n",
    "In my code, I assumed there were $N$ players. In this more general version of Slap, there are additional rules:\n",
    "- Play proceeds in a clockwise fashion\n",
    "- When a player runs out of cards, they remain part of the game. They can get back in by winning a \"slap\".\n",
    "- If a player challenges (plays a face card), the next player must meet that challenge. If that player meets the challenge (plays a face card in time), they become the new challenger and now the next player in clockwise order must meet the challenge.\n",
    "- If a player runs out of cards mid-challenge, the next player in order continues with the challenge.\n",
    "- I assumed one player (Player 0) always loses every slap; every other player has an equal chance of winning.\n",
    "- I assumed that a random player is chosen to go first.\n",
    "- I assumed that cards are dealt such that every player has the same number of cards and the rest are discarded. (e.g. in a 5-player game, each player would get 10 cards and the remaining 2 cards would be excluded from the deck).\n",
    "\n",
    "I investigated and found:\n",
    "- The probability of winning for each player. It turns out you are far less likely to win (10-15 times less likely) if you purposefully lose every slap.\n",
    "- The duration of matches. This generally increases as we add more players, but there are some irregularities due to the fact that the number of cards each player starts with changes. e.g. in going from $N=10$ to $N=11$, we go from $5$ cards/player to $4$ cards/player; a dramatic reduction. This causes games to get a lot shorter on average."
   ]
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   "cell_type": "markdown",
   "id": "89692cb9-7f25-424c-955e-d2e5b7997490",
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   "source": [
    "## Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "37165e2c-11b6-4a06-8724-6687c21d474b",
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Define the deck of cards\n",
    "ranks = ['2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K', 'A']\n",
    "suits = ['Hearts', 'Diamonds', 'Clubs', 'Spades']\n",
    "attempt_map = {'J':1, 'Q':2, 'K':3, 'A':4}\n",
    "faces = ['J', 'Q', 'K', 'A']\n",
    "deck = [{'rank': rank, 'suit': suit} for rank in ranks for suit in suits]\n",
    "pile = []\n",
    "playing = []\n",
    "hand = []\n",
    "\n",
    "# various counters\n",
    "current_turn = 0\n",
    "challenge = False\n",
    "attempts_remaining = 0\n",
    "winner = None\n",
    "\n",
    "def next(i):\n",
    "    N = len(playing)\n",
    "    for j in range(i+1,i+N):\n",
    "        if playing[j % N]:\n",
    "            return j % N\n",
    "        \n",
    "def prev(i):\n",
    "    N = len(playing)\n",
    "    for j in range(i-1,i-N,-1):\n",
    "        if playing[j % N]:\n",
    "            return j % N\n",
    "\n",
    "# check for doubles (player 0 always loses the slap!)\n",
    "def slap():\n",
    "    global current_turn\n",
    "    global challenge\n",
    "    if len(pile) >= 2 and pile[-1]['rank'] == pile[-2]['rank']:\n",
    "        i = random.randint(1, len(playing) - 1)\n",
    "        # print(f\"SLAP! Player {i} wins the pile!\")\n",
    "        hand[i].extend(pile)\n",
    "        playing[i] = True\n",
    "        pile.clear()\n",
    "        current_turn = i\n",
    "        challenge = False\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "\n",
    "# player i plays a card\n",
    "def play_card(i):\n",
    "    card = hand[i].pop(0)\n",
    "    # print(f\"Player {i} plays: {card['rank']} of {card['suit']}\")\n",
    "    pile.append(card)\n",
    "    return card\n",
    "        \n",
    "# check to see if player i is out of cards, and whether the game is over or not.\n",
    "def check_win(i):\n",
    "    global winner\n",
    "    global current_turn\n",
    "    if not hand[i]:\n",
    "        # print(f\"Player {i} is out of cards, they're out for now\")\n",
    "        playing[i] = False\n",
    "        \n",
    "    # if only one player remaining, they win!\n",
    "    if playing.count(True) == 1:\n",
    "        winner = playing.index(True)\n",
    "        # print(f\"Player {winner} has won the game!\")\n",
    "        # print(playing)\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "\n",
    "def print_status():\n",
    "    print( f\"Currently player turn: {current_turn}\" )\n",
    "    print( f\"Who is playing? {playing}\" )\n",
    "    for i in len(playing):\n",
    "        print( f\"Hand {i}: {[card['rank'] for card in hand[i]]}\" )\n",
    "    print( f\"Pile: {[card['rank'] for card in pile]}\" )\n",
    "    print( f\"Challenge? {challenge}\" )\n",
    "    \n",
    "\n",
    "# Main game loop. Play a game with N players\n",
    "def play_game(N):\n",
    "    \n",
    "    global current_turn \n",
    "    global challenge\n",
    "    global attempts_remaining\n",
    "    global playing\n",
    "    \n",
    "    # deal cards to N players (discard extras)\n",
    "    random.shuffle(deck)\n",
    "    cards_per_player = len(deck) // N\n",
    "    hand.clear()\n",
    "    for i in range(N):\n",
    "        hand.append( deck[i * cards_per_player:(i + 1) * cards_per_player] )\n",
    "\n",
    "    current_turn = random.randint(0,N-1)\n",
    "    playing = [True] * N\n",
    "    challenge = False\n",
    "    attempts_remaining = 0\n",
    "    \n",
    "    for turn in range(100000):\n",
    "                \n",
    "        if not playing[current_turn]:\n",
    "            print_status()\n",
    "            \n",
    "        card = play_card(current_turn)\n",
    "                    \n",
    "        if check_win(current_turn):\n",
    "            break\n",
    "        if slap():\n",
    "            continue\n",
    "            \n",
    "        if challenge:\n",
    "            if card['rank'] in faces:\n",
    "                # challenger beat the challenge, passes on to next player\n",
    "                attempts_remaining = attempt_map[card['rank']]\n",
    "                # print(f\"Player {current_turn} is challenging with a {card['rank']}, {attempts_remaining} attempts remaining.\")\n",
    "                current_turn = next(current_turn)\n",
    "                continue\n",
    "            else:\n",
    "                attempts_remaining -= 1\n",
    "                if attempts_remaining == 0:\n",
    "                    # they did not beat the challenge, challenger takes the pile\n",
    "                    i = prev(current_turn)\n",
    "                    # print(f\"Challenger (Player {i}) wins the challenge.\")\n",
    "                    hand[i].extend(pile)\n",
    "                    playing[i] = True\n",
    "                    pile.clear()\n",
    "                    current_turn = i\n",
    "                    challenge = False\n",
    "                else:\n",
    "                    # they just keep going. But if they're out of cards, the next person takes their place\n",
    "                    if not playing[current_turn]:\n",
    "                        current_turn = next(current_turn)\n",
    "        else:\n",
    "            if card['rank'] in faces:\n",
    "                challenge = True\n",
    "                attempts_remaining = attempt_map[card['rank']]\n",
    "                # print(f\"Player {current_turn} is challenging with a {card['rank']}, {attempts_remaining} attempts remaining.\")\n",
    "            \n",
    "            current_turn = next(current_turn)\n",
    "            continue\n",
    "    return (winner, turn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "684487aa-57c4-4dc3-b54c-8ea0d7f459b7",
   "metadata": {},
   "source": [
    "## Monte Carlo simulation (time-consuming)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5180475f-2f84-496e-b1ea-25701c8e016c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Currently on Experiment 2\n",
      "Currently on Experiment 3\n",
      "Currently on Experiment 4\n",
      "Currently on Experiment 5\n",
      "Currently on Experiment 6\n",
      "Currently on Experiment 7\n",
      "Currently on Experiment 8\n",
      "Currently on Experiment 9\n",
      "Currently on Experiment 10\n",
      "Currently on Experiment 11\n",
      "Currently on Experiment 12\n",
      "Currently on Experiment 13\n",
      "CPU times: total: 1h 11min 9s\n",
      "Wall time: 4h 40min 51s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "random.seed(1)\n",
    "\n",
    "M = 100000 # 1000 = 0:45, 10000 = 7:41\n",
    "\n",
    "expt = []\n",
    "for N in range(2,14):    \n",
    "    print(f\"Currently on Experiment {N}\")\n",
    "    counts = [0] * N\n",
    "    turns = []\n",
    "    for _ in range(M):\n",
    "        i,t = play_game(N)\n",
    "        counts[i] += 1\n",
    "        turns.append(t)\n",
    "    expt.append( (N,M,counts,turns) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d9e3539-f346-4f08-85cc-bdcc798e8bd9",
   "metadata": {},
   "source": [
    "## Show empirical probability distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "1d7ee02e-e949-4a4d-9eb5-342293c6f39b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities: [0.0119 0.2489 0.2478 0.2461 0.2454]\n",
      "       Errors: [0.0007 0.0027 0.0027 0.0027 0.0027]\n",
      "   Mean turns: 965.16\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_results(N,M,counts,turns):\n",
    "    probs = np.array(counts) / M\n",
    "    z = 1.96 # z-score for 95% confidence\n",
    "    errors = [ z * np.sqrt(p * (1 - p) / M + z**2 / (4 * M**2)) for p in probs ]\n",
    "    m = np.mean(turns)\n",
    "    print(f\"Probabilities: {np.round(probs,4)}\")\n",
    "    print(f\"       Errors: {np.round(errors,4)}\")\n",
    "    print(f\"   Mean turns: {round(m,2)}\")\n",
    "\n",
    "    \n",
    "    fig,axs = plt.subplots(1,2, figsize=(10,5))\n",
    "    \n",
    "    plt.sca(axs[0])\n",
    "    plt.bar(range(N), probs, yerr=errors, capsize=5, zorder=2)\n",
    "    plt.xticks(range(N))\n",
    "    plt.title(f\"Probability of winning ({M} trials)\")\n",
    "    plt.xlabel(\"Player\")\n",
    "    plt.grid(zorder = 1)\n",
    "    \n",
    "    plt.sca(axs[1])\n",
    "    plt.hist(turns,range(0,np.max(turns),50),density=False)\n",
    "    plt.axvline(x=m, color='red', linestyle='--', label=f'mean = {m:.0f}')\n",
    "    plt.grid()\n",
    "    plt.title(f\"Distribution of game duration for {N} players\")\n",
    "    plt.xlabel(\"number of turns\")\n",
    "    plt.legend()\n",
    "    \n",
    "    fig.tight_layout()\n",
    "    return fig\n",
    "    \n",
    "fig = plot_results(*expt[5 - 2])\n",
    "# fig.savefig('slap13.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b131de5-f36a-4e96-ba2b-90c93ad0621a",
   "metadata": {},
   "source": [
    "## Compare statistics as we change number of players"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4e2768f5-d856-4469-9aeb-89104e62dbbe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx = [] # number of players\n",
    "px = [] # empirical probability of winning for player 0\n",
    "ex = [] # confidence interval for px\n",
    "dx = [] # mean number of turns in a game\n",
    "sx1 = [] # lower error for dx (bootstrap)\n",
    "sx2 = [] # upper error for dx (bootstrap)\n",
    "\n",
    "q = 0\n",
    "for (N,M,counts,turns) in expt:\n",
    "    q += 1\n",
    "    print(q)\n",
    "    nx.append( N )\n",
    "    p = counts[0] / M\n",
    "    z = 1.96\n",
    "    px.append( np.maximum(p,1e-2) )\n",
    "    ex.append( z * np.sqrt(p * (1 - p) / M + z**2 / (4 * M**2)) )\n",
    "    dx.append( np.mean(turns) )\n",
    "    \n",
    "    \n",
    "    # Number of bootstrap samples\n",
    "    num_bootstraps = 1000\n",
    "\n",
    "    # Create an array to store sample means\n",
    "    bootstrap_means = np.zeros(num_bootstraps)\n",
    "\n",
    "    # Perform bootstrapping\n",
    "    for i in range(num_bootstraps):\n",
    "        # Resample with replacement\n",
    "        bootstrap_sample = np.random.choice(turns, size=M, replace=True)\n",
    "\n",
    "        # Calculate the mean for the bootstrap sample\n",
    "        bootstrap_means[i] = np.mean(bootstrap_sample)\n",
    "\n",
    "    # Calculate the confidence interval\n",
    "    confidence_interval = np.percentile(bootstrap_means, [2.5, 97.5])\n",
    "    \n",
    "    sx1.append( np.mean(turns) - confidence_interval[0] )\n",
    "    sx2.append( confidence_interval[1] - np.mean(turns) )\n",
    "    \n",
    "    \n",
    "    \n",
    "rx = [1/nx[i]/px[i] for i in range(len(nx))]\n",
    "erlo = [1/nx[i]/px[i] - 1/nx[i]/(px[i]+ex[i]) for i in range(len(nx))]\n",
    "erhi = [1/nx[i]/(px[i]-ex[i]) - 1/nx[i]/px[i] for i in range(len(nx))]\n",
    "\n",
    "fig,axs = plt.subplots(1,2, figsize=(10,5))\n",
    "\n",
    "plt.sca(axs[0])\n",
    "plt.bar(nx, rx, yerr=[erlo,erhi], capsize=5, zorder=2)\n",
    "plt.xticks(nx)\n",
    "plt.grid(zorder=1)\n",
    "plt.xlabel(\"number of players\")\n",
    "plt.title(\"times less likely to win if never slapping\")\n",
    "\n",
    "plt.sca(axs[1])\n",
    "plt.bar(nx, dx, yerr=[sx1,sx2], capsize=5, zorder=2)\n",
    "plt.xticks(nx)\n",
    "plt.grid(zorder=1)\n",
    "plt.xlabel(\"number of players\")\n",
    "plt.title(\"average game duration (cards played)\")\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "fig.savefig(\"slapx.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1a94642-2307-4fa5-8ea0-e245bac972c5",
   "metadata": {},
   "source": [
    "### How many cards per hand as a function of number of players?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "80c9bd28-4ed1-4b7b-87e1-639f8fc0871e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2, 26),\n",
       " (3, 17),\n",
       " (4, 13),\n",
       " (5, 10),\n",
       " (6, 8),\n",
       " (7, 7),\n",
       " (8, 6),\n",
       " (9, 5),\n",
       " (10, 5),\n",
       " (11, 4),\n",
       " (12, 4),\n",
       " (13, 4)]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(N, 52//N) for N in range(2,14)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "546b0a46-1eb8-478c-b178-ad206da63b2e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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