NetHack's functions Rne, Rn2 and Rnz in Python 3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#NetHack's-functions-Rne,-Rn2-and-Rnz-in-Python-3\" data-toc-modified-id=\"NetHack's-functions-Rne,-Rn2-and-Rnz-in-Python-3-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>NetHack's functions Rne, Rn2 and Rnz in Python 3</a></div><div class=\"lev2 toc-item\"><a href=\"#Rn2-distribution\" data-toc-modified-id=\"Rn2-distribution-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span><code>Rn2</code> distribution</a></div><div class=\"lev2 toc-item\"><a href=\"#Rne-distribution\" data-toc-modified-id=\"Rne-distribution-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span><code>Rne</code> distribution</a></div><div class=\"lev2 toc-item\"><a href=\"#Rnz-distribution\" data-toc-modified-id=\"Rnz-distribution-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span><code>Rnz</code> distribution</a></div><div class=\"lev2 toc-item\"><a href=\"#Examples\" data-toc-modified-id=\"Examples-14\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Examples</a></div><div class=\"lev3 toc-item\"><a href=\"#For-x=350\" data-toc-modified-id=\"For-x=350-141\"><span class=\"toc-item-num\">1.4.1&nbsp;&nbsp;</span>For <code>x=350</code></a></div><div class=\"lev2 toc-item\"><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-15\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Conclusion</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NetHack's functions Rne, Rn2 and Rnz in Python 3\n",
    "\n",
    "I liked [this blog post](https://eev.ee/blog/2018/01/02/random-with-care/#beware-gauss) by [Eevee](https://eev.ee/blog/).\n",
    "He wrote about interesting things regarding random distributions, and linked to [this page](https://nethackwiki.com/wiki/Rnz) which describes a weird distribution implemented as `Rnz` in the [NetHack](https://www.nethack.org/) game.\n",
    "\n",
    "> Note: I never heard of any of those before today.\n",
    "\n",
    "I wanted to implement and experiment with the `Rnz` distribution myself.\n",
    "Its code ([see here](https://nethackwiki.com/wiki/Source:NetHack_3.6.0/src/rnd.c#rnz)) uses two other distributions, `Rne` and `Rn2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The watermark extension is already loaded. To reload it, use:\n",
      "  %reload_ext watermark\n",
      "CPython 3.6.3\n",
      "IPython 6.2.1\n",
      "\n",
      "numpy 1.13.3\n",
      "matplotlib 2.1.1\n",
      "\n",
      "compiler   : GCC 7.2.0\n",
      "system     : Linux\n",
      "release    : 4.13.0-21-generic\n",
      "machine    : x86_64\n",
      "processor  : x86_64\n",
      "CPU cores  : 4\n",
      "interpreter: 64bit\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -m -p numpy,matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Rn2` distribution\n",
    "\n",
    "[The `Rn2` distribution](https://nethackwiki.com/wiki/Rn2) is simply an integer uniform distribution, between $0$ and $x-1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rn2(x):\n",
    "    return random.randint(0, x-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 9, 9, 0, 1, 9, 3, 1, 2, 7, 8, 6, 8, 3, 8, 4, 8, 6, 9, 7, 2, 2,\n",
       "       0, 9, 0, 7, 5, 0, 9, 4, 1, 1, 9, 2, 7, 3, 7, 4, 7, 3, 2, 0, 2, 8, 2,\n",
       "       0, 2, 0, 0, 7, 9, 9, 2, 7, 4, 9, 4, 3, 7, 9, 3, 3, 1, 2, 6, 6, 5, 5,\n",
       "       4, 0, 8, 9, 8, 1, 9, 5, 5, 9, 0, 6, 9, 5, 3, 1, 8, 4, 5, 8, 6, 9, 7,\n",
       "       9, 4, 1, 2, 0, 0, 9, 0])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rn2(10) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for `rn2(x) == 0` gives a $1/x$ probability :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({False: 91, True: 9})"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Counter([rn2(10) == 0 for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({False: 894, True: 106})"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Counter([rn2(10) == 0 for _ in range(1000)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({False: 9000, True: 1000})"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Counter([rn2(10) == 0 for _ in range(10000)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Rne` distribution\n",
    "\n",
    "[The `Rne` distribution]() is a truncated geometric distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rne(x, truncation=5):\n",
    "    truncation = max(truncation, 1)\n",
    "    tmp = 1\n",
    "    while tmp < truncation and rn2(x) == 0:\n",
    "        tmp += 1\n",
    "    return tmp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> In the NetHack game, the player's experience is used as default value of the `truncation` parameter..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1,\n",
       "       2, 1, 2, 1, 4, 2, 1, 1, 1, 4, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1,\n",
       "       2, 1, 1, 2])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rne(3) for _ in range(50)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6610.,  2268.,   747.,   252.,   123.]),\n",
       " array([ 1. ,  1.8,  2.6,  3.4,  4.2,  5. ]),\n",
       " <a list of 5 Patch objects>)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390a8c3898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.asarray([rne(3) for _ in range(10000)]), bins=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 1, 3, 1, 2, 4, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 6, 1, 2, 1,\n",
       "       1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 4])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rne(4, truncation=10) for _ in range(50)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  7.51300000e+03,   1.88900000e+03,   4.38000000e+02,\n",
       "          0.00000000e+00,   1.12000000e+02,   3.80000000e+01,\n",
       "          0.00000000e+00,   9.00000000e+00,   0.00000000e+00,\n",
       "          1.00000000e+00]),\n",
       " array([ 1. ,  1.7,  2.4,  3.1,  3.8,  4.5,  5.2,  5.9,  6.6,  7.3,  8. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390ad71f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.asarray([rne(4, truncation=10) for _ in range(10000)]), bins=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check what [this page](https://nethackwiki.com/wiki/Rnz#Probability_density_function) says about `rne(4)`:\n",
    "\n",
    "> The rne(4) call returns an integer from 1 to 5, with the following probabilities:\n",
    ">\n",
    "> |Number| Probability |\n",
    "> |:-----|------------:|\n",
    "> | 1 | 3/4 |\n",
    "> | 2 | 3/16 |\n",
    "> | 3 | 3/64 |\n",
    "> | 4 | 3/256 |\n",
    "> | 5 | 1/256 | "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.75, 2: 0.1875, 3: 0.046875, 4: 0.01171875, 5: 0.00390625}"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ref_table = {1: 3/4, 2: 3/16, 3: 3/64, 4: 3/256, 5: 1/256}\n",
    "ref_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.7498, 2: 0.18791, 3: 0.04641, 4: 0.0117, 5: 0.00418}"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 100000\n",
    "table = Counter([rne(4, truncation=5) for _ in range(N)])\n",
    "for k in table:\n",
    "    table[k] /= N\n",
    "table = dict(table)\n",
    "table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For k=1: relative difference is 0.000267 between 0.75 (expectation) and 0.75 (with N=100000 samples).\n",
      "For k=2: relative difference is 0.00219 between 0.188 (expectation) and 0.188 (with N=100000 samples).\n",
      "For k=3: relative difference is 0.00992 between 0.0469 (expectation) and 0.0464 (with N=100000 samples).\n",
      "For k=4: relative difference is 0.0016 between 0.0117 (expectation) and 0.0117 (with N=100000 samples).\n",
      "For k=5: relative difference is 0.0701 between 0.00391 (expectation) and 0.00418 (with N=100000 samples).\n"
     ]
    }
   ],
   "source": [
    "rel_diff = lambda x, y: abs(x - y) / x\n",
    "for k in ref_table:\n",
    "    x, y = ref_table[k], table[k]\n",
    "    r = rel_diff(x, y)\n",
    "    print(f\"For k={k}: relative difference is {r:.3g} between {x:.3g} (expectation) and {y:.3g} (with N={N} samples).\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Seems true !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Rnz` distribution\n",
    "\n",
    "It's not too hard to write."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rnz(i, truncation=10):\n",
    "    x = i\n",
    "    tmp = 1000\n",
    "    tmp += rn2(1000)\n",
    "    tmp *= rne(4, truncation=truncation)\n",
    "    flip = rn2(2)\n",
    "    if flip:\n",
    "        x *= tmp\n",
    "        x /= 1000\n",
    "    else:\n",
    "        x *= 1000\n",
    "        x /= tmp\n",
    "    return int(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5,  2,  1,  1,  2,  5,  3,  0,  3,  2,  2,  5,  5,  3,  0,  1,  3,\n",
       "        4,  4,  1,  4,  2,  6,  4,  3,  3,  8,  2,  3,  5,  2,  4,  1,  4,\n",
       "        4,  2,  4,  1,  1,  3,  1,  2,  0,  5,  1,  2,  5, 14,  2,  1,  0,\n",
       "        1,  5, 17,  2,  3,  1,  1,  1,  4, 13,  1,  4,  4,  2,  5,  5,  1,\n",
       "        2,  0,  4,  4,  0,  5, 20,  6,  2,  3,  5,  2,  1,  3,  2,  5,  0,\n",
       "        2,  5,  1,  4,  2,  1,  1,  2,  2, 11,  2,  1,  5,  5,  1])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rnz(3) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  5,  5,  5,  2, 16,  2,  1,  3,  2,  5,  3,  2,  5,  0,  4,  2,\n",
       "        2,  4,  3, 10,  4,  5,  1,  1,  2,  5, 10,  1,  1,  0,  5,  4,  5,\n",
       "        1,  7, 16,  1,  3,  5,  3,  1, 11,  2, 10,  9,  4,  1,  8,  4,  1,\n",
       "        1,  4,  0,  2,  5,  2,  2,  7,  2, 10,  2,  7,  5,  1, 10,  2,  4,\n",
       "        3,  1,  1,  6, 10,  2,  2,  0,  4,  1,  4,  3,  1,  4,  3,  2,  3,\n",
       "        5,  1,  5,  0,  1,  2, 10,  5,  1,  3,  2,  1,  2,  1,  1])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rnz(3, truncation=10) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For `x=350`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 668,  511,  360, 1548,  211,  495,  321,  180,  667, 1339,  179,\n",
       "        257,  696,  192,  211,  134,  312,  164,  202,  206,  299,  316,\n",
       "        182,  566,  445,  392,  363,  592,  656,  605,  676,  287,  704,\n",
       "       1190,  253,  118,  359,  142,  331,  586,  597,  204,  196,   60,\n",
       "        178, 1605,  606,  692,  187,  486,  696,  624,  182,  322,  260,\n",
       "        580, 1283,  100,  663,   89,  465,  305,  420,  436,  500,   93,\n",
       "        178,  348,  489,  499,  227, 1143,  187,  220,  513,  193, 1270,\n",
       "        461,  299,  323,  679,  729, 1301,  910,  509, 1006, 2071, 1575,\n",
       "        183,   44,  229,  119,  515,  327,   87,  281,  638,  177,  208,\n",
       "        114])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rnz(350) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f39087c5908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(np.asarray([rnz(350) for _ in range(100000)]), bins=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1288,   58,   27, 2349, 4723, 2011, 1767, 2200, 1685,   19, 2873,\n",
       "         66,  884, 1517,  159, 2758, 4657,  957,  225,   32, 2626,  176,\n",
       "       1000,  737, 2353,   50,  928,   67,   52, 1543,  229,   34, 3725,\n",
       "         75,  163, 2431, 3307,  460, 2144, 1411,  108,  131, 2447, 1170,\n",
       "       2024,   32,  431,   98,  489, 2417,  210, 5569,  963,  132,  479,\n",
       "        195, 3752,  257, 4429, 1219,  446,  153,  619,   18,  105,  144,\n",
       "       1520,   40, 2608,  260,  412, 1755, 1057,   99,   64,  322, 1981,\n",
       "        112,  146,   53,   56, 1270, 1808, 4517, 1598,   79, 1355, 6954,\n",
       "       2075, 3458,   64, 1061,  176,  474, 1309, 3260, 4118,   19,  260,\n",
       "        872])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([rnz(350, truncation=10) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390945ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(np.asarray([rnz(350, truncation=10) for _ in range(10000)]), bins=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "That's it, not so interesting but I wanted to write this."
   ]
  }
 ],
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