2d6-6 x20

gistfile1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d8bf79e2-5fff-421f-8a00-0e0a0d54db26",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import xarray\n",
    "import pathfinder2e_stats as pf2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9784161-d41b-4169-bc2a-af0d1e87ff15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>variable</th>\n",
       "      <th>(unnamed)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100000.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>31.12391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.76758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>26.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>31.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>36.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>73.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "roll = pf2.roll(\"2d6-6\", dims={\"square\": 20}).sum(\"square\")\n",
    "roll.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6195d52c-febb-42e0-a1ae-55e7561d378d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "roll.to_pandas().hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1889de22-51b8-465e-bfe1-ab0bf2eb0e31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>variable</th>\n",
       "      <th>(unnamed)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>139.999640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>10.777322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>94.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>133.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>140.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>147.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>186.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "roll = pf2.roll(\"2d6\", dims={\"square\": 20}).sum(\"square\")\n",
    "roll.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c990538a-8594-419b-92a7-dd49b16a6ee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "roll.to_pandas().hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4be11f48-8d9b-439a-8abf-5f6e3ef3b198",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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