{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solution to a problem posted at\n",
    "\n",
    "https://www.reddit.com/r/statistics/comments/4csjee/finding_pab_given_two_sets_of_data/\n",
    "\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: http://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "from numpy.random import choice\n",
    "from collections import Counter\n",
    "from collections import defaultdict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Roll six 6-sided dice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 2, 1, 1, 1])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "def roll(die):\n",
    "    return choice(die, 6)\n",
    "\n",
    "die = [1,2,3,4,5,6]\n",
    "roll(die)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Count how many times each outcome occurs and score accordingly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def compute_score(outcome):\n",
    "    counts = Counter(outcome)\n",
    "    dd = defaultdict(list)\n",
    "    [dd[v].append(k) for k, v in counts.items()]\n",
    "    return len(dd[max(dd)])\n",
    "\n",
    "compute_score([1,1,1,1,1,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run many times and accumulate scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 100000\n",
    "scores = [compute_score(roll(die)) for _ in range(n)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the percentages of each score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 59.178\n",
      "2 35.384\n",
      "3 3.867\n",
      "6 1.571\n"
     ]
    }
   ],
   "source": [
    "for score, freq in sorted(Counter(scores).items()):\n",
    "    print(score, 100*freq/n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or even better, just enumerate the possibilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "die = [1,2,3,4,5,6]\n",
    "counts = Counter(compute_score(list(outcome)) for outcome in product(*[die]*6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 59.2335390947\n",
      "2 35.3652263374\n",
      "3 3.85802469136\n",
      "6 1.54320987654\n"
     ]
    }
   ],
   "source": [
    "n = sum(counts.values())\n",
    "for score, freq in sorted(counts.items()):\n",
    "    print(score, 100*freq/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
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  "language_info": {
   "codemirror_mode": {
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