cjb230/Riddler Classic 20200515.ipynb

## Riddler Classic 20200515.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "160000\n",
      "160000\n"
     ]
    }
   ],
   "source": [
    "dis_of_ad_freq = {a:0 for a in range(1, 21)}\n",
    "ad_of_dis_freq = {a:0 for a in range(1, 21)}\n",
    "\n",
    "# Four loops, nested, to enumerate every possibility\n",
    "for w in range(1, 21):\n",
    "    for x in range(1, 21):\n",
    "        disadvantage_1 = min(w, x)\n",
    "        advantage_1 = max(w, x)\n",
    "\n",
    "        for y in range(1, 21):\n",
    "            for z in range(1, 21):\n",
    "                disadvantage_2 = min(y, z)\n",
    "                advantage_2 = max(y, z)\n",
    "                advantage_of_disadvantage = max(disadvantage_1, disadvantage_2)\n",
    "                disadvantage_of_advantage = min(advantage_1, advantage_2)\n",
    "                ad_of_dis_freq[advantage_of_disadvantage] = ad_of_dis_freq[advantage_of_disadvantage] + 1\n",
    "                dis_of_ad_freq[disadvantage_of_advantage] = dis_of_ad_freq[disadvantage_of_advantage] + 1\n",
    "\n",
    "# Got all the values we expected?\n",
    "print(sum(dis_of_ad_freq.values()))\n",
    "print(sum(ad_of_dis_freq.values()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of 'advantage of disadvantage' = 9.8333375\n",
      "Expected value of 'disadvantage of advantage' = 11.1666625\n"
     ]
    }
   ],
   "source": [
    "# What are the expected values?\n",
    "ev_adv_of_dis = sum([key * value for (key, value) in ad_of_dis_freq.items()]) / 160000\n",
    "ev_dis_of_adv = sum([key * value for (key, value) in dis_of_ad_freq.items()]) / 160000\n",
    "\n",
    "print(\"Expected value of 'advantage of disadvantage' = \" + str(ev_adv_of_dis))\n",
    "print(\"Expected value of 'disadvantage of advantage' = \" + str(ev_dis_of_adv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of a single die = 10.5\n"
     ]
    }
   ],
   "source": [
    "# What about a single d20?\n",
    "ev_single_die = sum(range(1, 21)) / 20\n",
    "print(\"Expected value of a single die = \" + str(ev_single_die))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a score of 2 or better:\n",
      "    Single die = 152000\n",
      "    Disadvantage of advantage = 159201\n",
      "    Advantage of disadvantage = 158479\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 3 or better:\n",
      "    Single die = 144000\n",
      "    Disadvantage of advantage = 156816\n",
      "    Advantage of disadvantage = 154224\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 4 or better:\n",
      "    Single die = 136000\n",
      "    Disadvantage of advantage = 152881\n",
      "    Advantage of disadvantage = 147679\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 5 or better:\n",
      "    Single die = 128000\n",
      "    Disadvantage of advantage = 147456\n",
      "    Advantage of disadvantage = 139264\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 6 or better:\n",
      "    Single die = 120000\n",
      "    Disadvantage of advantage = 140625\n",
      "    Advantage of disadvantage = 129375\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 7 or better:\n",
      "    Single die = 112000\n",
      "    Disadvantage of advantage = 132496\n",
      "    Advantage of disadvantage = 118384\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 8 or better:\n",
      "    Single die = 104000\n",
      "    Disadvantage of advantage = 123201\n",
      "    Advantage of disadvantage = 106639\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 9 or better:\n",
      "    Single die = 96000\n",
      "    Disadvantage of advantage = 112896\n",
      "    Advantage of disadvantage = 94464\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 10 or better:\n",
      "    Single die = 88000\n",
      "    Disadvantage of advantage = 101761\n",
      "    Advantage of disadvantage = 82159\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 11 or better:\n",
      "    Single die = 80000\n",
      "    Disadvantage of advantage = 90000\n",
      "    Advantage of disadvantage = 70000\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 12 or better:\n",
      "    Single die = 72000\n",
      "    Disadvantage of advantage = 77841\n",
      "    Advantage of disadvantage = 58239\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 13 or better:\n",
      "    Single die = 64000\n",
      "    Disadvantage of advantage = 65536\n",
      "    Advantage of disadvantage = 47104\n",
      "    Best option = disadvantage of advantage\n",
      "\n",
      "For a score of 14 or better:\n",
      "    Single die = 56000\n",
      "    Disadvantage of advantage = 53361\n",
      "    Advantage of disadvantage = 36799\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 15 or better:\n",
      "    Single die = 48000\n",
      "    Disadvantage of advantage = 41616\n",
      "    Advantage of disadvantage = 27504\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 16 or better:\n",
      "    Single die = 40000\n",
      "    Disadvantage of advantage = 30625\n",
      "    Advantage of disadvantage = 19375\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 17 or better:\n",
      "    Single die = 32000\n",
      "    Disadvantage of advantage = 20736\n",
      "    Advantage of disadvantage = 12544\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 18 or better:\n",
      "    Single die = 24000\n",
      "    Disadvantage of advantage = 12321\n",
      "    Advantage of disadvantage = 7119\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 19 or better:\n",
      "    Single die = 16000\n",
      "    Disadvantage of advantage = 5776\n",
      "    Advantage of disadvantage = 3184\n",
      "    Best option = single die\n",
      "\n",
      "For a score of 20 or better:\n",
      "    Single die = 8000\n",
      "    Disadvantage of advantage = 1521\n",
      "    Advantage of disadvantage = 799\n",
      "    Best option = single die\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Extra Credit\n",
    "# how many successes in 160 000 attempts?\n",
    "\n",
    "for a in range(2, 21):\n",
    "    print(\"For a score of \" + str(a) + \" or better:\")\n",
    "    single_die_success = (21 - a) * 8000  # gives accurate result, unlike \"1 - ((a - 1) / 20)\"\n",
    "    disadvantage_of_advantage_success = sum([value for (key, value) in dis_of_ad_freq.items() if key >= a])\n",
    "    advantage_of_disadvantage_success = sum([value for (key, value) in ad_of_dis_freq.items() if key >= a])\n",
    "    if single_die_success > max(disadvantage_of_advantage_success, advantage_of_disadvantage_success):\n",
    "        best_option = \"single die\"\n",
    "    elif disadvantage_of_advantage_success > max(single_die_success, advantage_of_disadvantage_success):\n",
    "        best_option = \"disadvantage of advantage\"\n",
    "    elif advantage_of_disadvantage_success > max(single_die_success, disadvantage_of_advantage_success):\n",
    "        best_option = \"advantage of disadvantage\"\n",
    "    \n",
    "    print(\"    Single die = \" + str(single_die_success))\n",
    "    print(\"    Disadvantage of advantage = \" + str(disadvantage_of_advantage_success))\n",
    "    print(\"    Advantage of disadvantage = \" + str(advantage_of_disadvantage_success))\n",
    "    print(\"    Best option = \" + best_option)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Create list of probabilities from dictionary of frequencies\n",
    "disadvantage_of_advantage_probs = ((x, y/160000) for x, y in dis_of_ad_freq.items())\n",
    "advantage_of_disadvantage_probs = ((x, y/160000) for x, y in ad_of_dis_freq.items())\n",
    "da_x, da_y = zip(*disadvantage_of_advantage_probs)\n",
    "ad_x, ad_y = zip(*advantage_of_disadvantage_probs)\n",
    "\n",
    "single_die_probs = ((x, 0.05) for x in range(1, 21))\n",
    "sd_x, sd_y = zip(*single_die_probs)\n",
    "\n",
    "\n",
    "plt.plot(da_x, da_y, label='Disadvantage of Advantage')\n",
    "plt.plot(ad_x, ad_y, label='Advantage of Disadvantage')\n",
    "plt.plot(sd_x, sd_y, label='Single Die')\n",
    "plt.ylabel('Probability of Score')\n",
    "plt.xlabel('Score')\n",
    "plt.title('Probability')\n",
    "plt.xticks(np.arange(1, 21))\n",
    "plt.legend()\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now the cumulative probabilities (\"score x or higher\")\n",
    "\n",
    "disadvantage_of_advantage_cum_probs = ((x, sum([value for (key, value) in dis_of_ad_freq.items() if key >= x]) / 160000) for x in range(1, 21))\n",
    "advantage_of_disadvantage_cum_probs = ((x, sum([value for (key, value) in ad_of_dis_freq.items() if key >= x]) / 160000) for x in range(1, 21))\n",
    "da_x, da_y = zip(*disadvantage_of_advantage_cum_probs)\n",
    "ad_x, ad_y = zip(*advantage_of_disadvantage_cum_probs)\n",
    "\n",
    "single_die_cum_probs = ((x, ((21 - x) / 20)) for x in range(1, 21))\n",
    "sd_x, sd_y = zip(*single_die_cum_probs)\n",
    "\n",
    "plt.plot(da_x, da_y, label='Disadvantage of Advantage')\n",
    "plt.plot(ad_x, ad_y, label='Advantage of Disadvantage')\n",
    "plt.plot(sd_x, sd_y, label='Single Die')\n",
    "plt.ylabel('Probability of Score or Higher')\n",
    "plt.xlabel('Score')\n",
    "plt.title('Cumulative Probability')\n",
    "plt.xticks(np.arange(1, 21))\n",
    "plt.legend()\n",
    "plt.show"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}