notebooks/MaxTwoEnvelopesSimulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d80468e4-d02a-4c6a-858b-8c9c2feb2938",
   "metadata": {},
   "source": [
    "Max Two Envelopes Simulation\n",
    "===\n",
    "\n",
    "Analysis for: https://levon003.github.io/2024/02/26/max-envelope-problem.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1794818a-b294-4cca-b015-554f1dd542c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binomtest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0c07ebfe-44c0-48cc-9c0d-dbe58d42646b",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ad6b8a25-18a2-4511-9e81-83db1bdbea52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000000, 2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10000000\n",
    "envelope_values = rng.normal(size=(n, 2))\n",
    "envelope_values.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0b531f14-122e-4918-b019-214bc6d752bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_B_larger = envelope_values[:,1] > envelope_values[:,0]\n",
    "\n",
    "results = []\n",
    "for name, decision_values in [\n",
    "    (\"Random\", None),\n",
    "    (\"Matching\", rng.normal(size=n)),\n",
    "    (\"Wide\", rng.normal(scale=2.0, size=n)),\n",
    "    (\"Shifted\", rng.normal(loc=2.0, size=n)),\n",
    "]:\n",
    "    # determine if we should swap and choose B instead of A\n",
    "    if decision_values is not None:\n",
    "        will_choose_B = decision_values > envelope_values[:,0]\n",
    "    else:\n",
    "        will_choose_B = False\n",
    "    was_correct = np.logical_not(np.logical_xor(is_B_larger, will_choose_B))\n",
    "    correct_count = was_correct.sum()\n",
    "    results.append((name, correct_count))\n",
    "len(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5394c620-22c2-4d90-b3c7-9fe8a0734489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.4997866524991894, 0.5004065474448806),\n",
       " (0.666634784625184, 0.6672191187253529),\n",
       " (0.6020809894940605, 0.6026877512264531),\n",
       " (0.5551140461285233, 0.555730121782801)]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note: obviously, these CIs are so small it turns out to not be worth showing them\n",
    "cis = []\n",
    "ys_pct = []\n",
    "for name, count in results:\n",
    "    binom = binomtest(k=count, n=n, p=0.5)\n",
    "    cis.append(tuple(binom.proportion_ci()))\n",
    "    ys_pct.append(count / n)\n",
    "cis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "956d03ec-e0a5-4b67-afd3-263f55786ce6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 3))\n",
    "xs = [0, 1, 2, 3]\n",
    "ys_pct = np.array(ys_pct)\n",
    "#cis = np.array(cis).T\n",
    "\n",
    "ax.bar(xs, ys_pct, color=matplotlib.cm.viridis(0.65189), width=1)\n",
    "ax.axhline(0.5, color=\"gray\", alpha=0.9, linestyle=\"--\")\n",
    "for i, pct in enumerate(ys_pct):\n",
    "    ax.text(i, pct, f\"{pct:.1%}\", ha=\"center\", va=\"bottom\")\n",
    "#cis_delta = np.abs(cis - ys_pct)\n",
    "#ax.errorbar(xs, ys_pct, yerr=cis_delta, ecolor=\"black\", capsize=2, elinewidth=1, linewidth=0)\n",
    "\n",
    "margin = 0.0001\n",
    "ax.yaxis.set_major_formatter(matplotlib.ticker.FuncFormatter(lambda y, pos: f\"{y:.0%}\"))\n",
    "#ax.xaxis.set_major_formatter(lambda x, pos: f\"{x:,.0f}g\")\n",
    "ax.set_ylim((0, 0.8))\n",
    "ax.set_xticks(ticks=xs, labels=[name for name, _ in results])\n",
    "ax.set_title(\"Win percentage for varying strategies\")\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"../images/max-envelope-problem-simulation.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47eb01aa-f88a-461d-8398-23bc11fbbecc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6cb4f4ed-779f-4ea5-a215-5fd2126bceb8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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