fiddler_express_dec16_2024.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puzzle [here](https://thefiddler.substack.com/p/can-you-survive-the-floor)\n",
    "\n",
    "\n",
    "Part 1:\n",
    "\n",
    "\n",
    "Each round consists of the following steps:\n",
    "\n",
    "One of the remaining contestants is chosen at random. (Note that each contestant is equally likely to be chosen, regardless of how many squares they currently control.)\n",
    "\n",
    "The set of eligible opponents for this contestant is anyone whose territory shares a common edge with the contestant. One of these eligible opponents is chosen at random.\n",
    "(Again, all eligible opponents are equally likely to be chosen, regardless of how many squares they control or how many edges they have in common with the opponent.)\n",
    "\n",
    "The contestant and their selected opponent have a duel, each with a 50 percent chance of winning. The loser is eliminated, and their territory is added to that of the winner.\n",
    "\n",
    "These rounds repeat until one contestant remains, and that contestant is the overall winner.\n",
    "\n",
    "Which position would you choose? That is, which position or positions give you the best chance of being the overall winner?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting experiments on 8 CPUs...\n",
      "[(0, 0.129037), (2, 0.1289275), (8, 0.128836875), (6, 0.128823), (1, 0.099495875), (5, 0.099428), (3, 0.0993945), (7, 0.09938275), (4, 0.0866745)]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(0, 0.129037),\n",
       " (2, 0.1289275),\n",
       " (8, 0.128836875),\n",
       " (6, 0.128823),\n",
       " (1, 0.099495875),\n",
       " (5, 0.099428),\n",
       " (3, 0.0993945),\n",
       " (7, 0.09938275),\n",
       " (4, 0.0866745)]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "\n",
    "def winner_from_one_game() -> int:\n",
    "    state = dict(enumerate([(i, j)] for i in range(3) for j in range(3)))\n",
    "\n",
    "    while len(state) > 1:\n",
    "        # pick player randomly\n",
    "        p1 = random.choice(list(state.keys()))\n",
    "        have_common_edge = [\n",
    "            player\n",
    "            for player, territory in state.items()\n",
    "            if player != p1 and neighboring(territory, state[p1])\n",
    "        ]\n",
    "        other_player = random.choice(have_common_edge)\n",
    "        p1_wins = random.random() > 0.5\n",
    "        if p1_wins:\n",
    "            state[p1].extend(state[other_player])\n",
    "            state.pop(other_player)\n",
    "        else:\n",
    "            state[other_player].extend(state[p1])\n",
    "            state.pop(p1)\n",
    "        assert sum(map(len, state.values())) == 9, state\n",
    "    return list(state.keys())[0]\n",
    "\n",
    "\n",
    "def neighboring(\n",
    "    territory1: list[tuple[int, int]], territory2: list[tuple[int, int]]\n",
    ") -> bool:\n",
    "    \"\"\"Returns whether `territory1` and `territory2` have at least one neighboring pair of squares\"\"\"\n",
    "    # there's room for optim here eg cache as there are many repeated ops\n",
    "    return any(\n",
    "        neigh in territory2\n",
    "        for (current_r, current_c) in territory1\n",
    "        for neigh in (\n",
    "            (current_r - 1, current_c),\n",
    "            (current_r + 1, current_c),\n",
    "            (current_r, current_c - 1),\n",
    "            (current_r, current_c + 1),\n",
    "        )\n",
    "    )\n",
    "\n",
    "\n",
    "def large_scale_experiment(n_iter: int = 1_000_000) -> dict[int, int]:\n",
    "    stats = dict(enumerate([0] * 9))\n",
    "    for _ in range(n_iter):\n",
    "        stats[winner_from_one_game()] += 1\n",
    "\n",
    "    return stats\n",
    "\n",
    "\n",
    "def large_scale_experiment_multi_cpu(\n",
    "    n_iter_per_cpu: int = 1_000_000, n_cpus: int = 8\n",
    ") -> list[tuple[int, float]]:\n",
    "    # Monte Carlo simulation\n",
    "    from multiprocessing import Pool\n",
    "    import multiprocessing\n",
    "\n",
    "    n_cpus = min(multiprocessing.cpu_count(), n_cpus)\n",
    "    print(f\"Starting experiments on {n_cpus} CPUs...\")\n",
    "    with Pool(n_cpus) as p:\n",
    "        all_simulations = p.map(large_scale_experiment, [n_iter_per_cpu] * n_cpus)\n",
    "    all_results = dict(enumerate([0] * 9))\n",
    "    # add up all the resluts from all experiments\n",
    "    for result_dict in all_simulations:\n",
    "        for k, v in result_dict.items():\n",
    "            all_results[k] += v\n",
    "    stats = sorted(\n",
    "        {k: v / (n_iter_per_cpu * n_cpus) for k, v in all_results.items()}.items(),\n",
    "        key=lambda x: -x[1],\n",
    "    )\n",
    "    print(stats)\n",
    "    return stats\n",
    "\n",
    "\n",
    "stats= large_scale_experiment_multi_cpu()\n",
    "stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x800 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as mcolors\n",
    "\n",
    "percentages = [perc for (_, perc) in sorted(stats)]\n",
    "\n",
    "norm = mcolors.Normalize(vmin=min(percentages), vmax=max(percentages))\n",
    "\n",
    "fig, axes = plt.subplots(3, 3, figsize=(8, 8))\n",
    "fig.suptitle('Approx. winning percentage of each player', fontsize=16)\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    color = plt.cm.viridis(norm(percentages[i]))\n",
    "    ax.set_facecolor(color)\n",
    "    ax.text(0.5, 0.5, f'{round(percentages[i]*100, 2)}%', fontsize=24, ha='center', va='center', color='white')\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "    ax.set_xlim(0, 1)\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.set_aspect('equal')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, opt for a corner square. This will reduce the likelihood of confrontations with other players and thereby help preserve your territory.\n",
    "\n",
    "The theoretical probabilities are equal within the following sets of positions:\n",
    "- the four corners\n",
    "- the center square\n",
    "- the four remaining edge squares\n",
    "\n",
    "The differences shown on the dataviz are due to the randomness of the simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My time is up.\n",
    "\n",
    "Given more time, I'd:\n",
    "\n",
    "- try to compute confidence intervals for the probabilities of winning for each position. That would allow making the above experiment more reliable and also possibly reduce the number of simulations needed.\n",
    "\n",
    "- Work out the underlying distribution (this is best done in part 2 I guess). In these problems, often, `maths > coding`, this would yield the *exact* probabilities of winning for each position without the need for simulations. I would perhaps start defining the sequential relationship between time_t and time_t+1, and then try to find a pattern in the distribution of the number of squares each player has at time_t+1 given the number of squares they had at time_t. This would be a good starting point to understand the problem better."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}