wordle-explore-easyMode.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wordle solver\n",
    "Logic-based solution based on my knowledge of the game from playing it.\n",
    "\n",
    "A better solution may be to use reinforcement learning, so as to avoid making these assumptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in /usr/local/anaconda3/lib/python3.8/site-packages (1.21.2)\n",
      "Requirement already satisfied: pandas in /usr/local/anaconda3/lib/python3.8/site-packages (1.3.2)\n",
      "Requirement already satisfied: multiprocess in /usr/local/anaconda3/lib/python3.8/site-packages (0.70.12.2)\n",
      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/anaconda3/lib/python3.8/site-packages (from pandas) (2.8.1)\n",
      "Requirement already satisfied: pytz>=2017.3 in /usr/local/anaconda3/lib/python3.8/site-packages (from pandas) (2019.1)\n",
      "Requirement already satisfied: dill>=0.3.4 in /usr/local/anaconda3/lib/python3.8/site-packages (from multiprocess) (0.3.5.1)\n",
      "Requirement already satisfied: six>=1.5 in /usr/local/anaconda3/lib/python3.8/site-packages (from python-dateutil>=2.7.3->pandas) (1.15.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install numpy pandas multiprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import string\n",
    "from collections import defaultdict\n",
    "from collections import ChainMap\n",
    "import math\n",
    "from IPython.display import clear_output\n",
    "import warnings\n",
    "import multiprocess as mp\n",
    "from tqdm.notebook import tqdm\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import dill\n",
    "dill.settings['recurse']=True\n",
    "\n",
    "import traceback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "39933 5 letter words in Google trillion words corpus.\n",
      "2309 solution words in Wordle source code.\n",
      "12974 allowed words in Wordle source code.\n",
      "8094 allowed words in both Wordle source code and the Google corpus\n"
     ]
    }
   ],
   "source": [
    "# Alphabet\n",
    "az = string.ascii_lowercase\n",
    "\n",
    "# Word frequency table, from Google trillion words corpus\n",
    "# https://www.kaggle.com/datasets/rtatman/english-word-frequency?resource=download\n",
    "words = pd.read_csv('./data/unigram_freq.csv')\n",
    "# Filter to 5 letter words\n",
    "words = words[words['word'].str.len() == 5]\n",
    "# Scale word count to 0...1\n",
    "words['freq'] = words['count'] / words['count'].max()\n",
    "print(len(words), '5 letter words in Google trillion words corpus.')\n",
    "\n",
    "# Wordle solutions, from Wordle source code\n",
    "# https://www.nytimes.com/games/wordle/main.9622bc55.js\n",
    "solutions = [\"cigar\",\"rebut\",\"sissy\",\"humph\",\"awake\",\"blush\",\"focal\",\"evade\",\"naval\",\"serve\",\"heath\",\"dwarf\",\"model\",\"karma\",\"stink\",\"grade\",\"quiet\",\"bench\",\"abate\",\"feign\",\"major\",\"death\",\"fresh\",\"crust\",\"stool\",\"colon\",\"abase\",\"marry\",\"react\",\"batty\",\"pride\",\"floss\",\"helix\",\"croak\",\"staff\",\"paper\",\"unfed\",\"whelp\",\"trawl\",\"outdo\",\"adobe\",\"crazy\",\"sower\",\"repay\",\"digit\",\"crate\",\"cluck\",\"spike\",\"mimic\",\"pound\",\"maxim\",\"linen\",\"unmet\",\"flesh\",\"booby\",\"forth\",\"first\",\"stand\",\"belly\",\"ivory\",\"seedy\",\"print\",\"yearn\",\"drain\",\"bribe\",\"stout\",\"panel\",\"crass\",\"flume\",\"offal\",\"agree\",\"error\",\"swirl\",\"argue\",\"bleed\",\"delta\",\"flick\",\"totem\",\"wooer\",\"front\",\"shrub\",\"parry\",\"biome\",\"lapel\",\"start\",\"greet\",\"goner\",\"golem\",\"lusty\",\"loopy\",\"round\",\"audit\",\"lying\",\"gamma\",\"labor\",\"islet\",\"civic\",\"forge\",\"corny\",\"moult\",\"basic\",\"salad\",\"agate\",\"spicy\",\"spray\",\"essay\",\"fjord\",\"spend\",\"kebab\",\"guild\",\"aback\",\"motor\",\"alone\",\"hatch\",\"hyper\",\"thumb\",\"dowry\",\"ought\",\"belch\",\"dutch\",\"pilot\",\"tweed\",\"comet\",\"jaunt\",\"enema\",\"steed\",\"abyss\",\"growl\",\"fling\",\"dozen\",\"boozy\",\"erode\",\"world\",\"gouge\",\"click\",\"briar\",\"great\",\"altar\",\"pulpy\",\"blurt\",\"coast\",\"duchy\",\"groin\",\"fixer\",\"group\",\"rogue\",\"badly\",\"smart\",\"pithy\",\"gaudy\",\"chill\",\"heron\",\"vodka\",\"finer\",\"surer\",\"radio\",\"rouge\",\"perch\",\"retch\",\"wrote\",\"clock\",\"tilde\",\"store\",\"prove\",\"bring\",\"solve\",\"cheat\",\"grime\",\"exult\",\"usher\",\"epoch\",\"triad\",\"break\",\"rhino\",\"viral\",\"conic\",\"masse\",\"sonic\",\"vital\",\"trace\",\"using\",\"peach\",\"champ\",\"baton\",\"brake\",\"pluck\",\"craze\",\"gripe\",\"weary\",\"picky\",\"acute\",\"ferry\",\"aside\",\"tapir\",\"troll\",\"unify\",\"rebus\",\"boost\",\"truss\",\"siege\",\"tiger\",\"banal\",\"slump\",\"crank\",\"gorge\",\"query\",\"drink\",\"favor\",\"abbey\",\"tangy\",\"panic\",\"solar\",\"shire\",\"proxy\",\"point\",\"robot\",\"prick\",\"wince\",\"crimp\",\"knoll\",\"sugar\",\"whack\",\"mount\",\"perky\",\"could\",\"wrung\",\"light\",\"those\",\"moist\",\"shard\",\"pleat\",\"aloft\",\"skill\",\"elder\",\"frame\",\"humor\",\"pause\",\"ulcer\",\"ultra\",\"robin\",\"cynic\",\"aroma\",\"caulk\",\"shake\",\"dodge\",\"swill\",\"tacit\",\"other\",\"thorn\",\"trove\",\"bloke\",\"vivid\",\"spill\",\"chant\",\"choke\",\"rupee\",\"nasty\",\"mourn\",\"ahead\",\"brine\",\"cloth\",\"hoard\",\"sweet\",\"month\",\"lapse\",\"watch\",\"today\",\"focus\",\"smelt\",\"tease\",\"cater\",\"movie\",\"saute\",\"allow\",\"renew\",\"their\",\"slosh\",\"purge\",\"chest\",\"depot\",\"epoxy\",\"nymph\",\"found\",\"shall\",\"stove\",\"lowly\",\"snout\",\"trope\",\"fewer\",\"shawl\",\"natal\",\"comma\",\"foray\",\"scare\",\"stair\",\"black\",\"squad\",\"royal\",\"chunk\",\"mince\",\"shame\",\"cheek\",\"ample\",\"flair\",\"foyer\",\"cargo\",\"oxide\",\"plant\",\"olive\",\"inert\",\"askew\",\"heist\",\"shown\",\"zesty\",\"trash\",\"larva\",\"forgo\",\"story\",\"hairy\",\"train\",\"homer\",\"badge\",\"midst\",\"canny\",\"shine\",\"gecko\",\"farce\",\"slung\",\"tipsy\",\"metal\",\"yield\",\"delve\",\"being\",\"scour\",\"glass\",\"gamer\",\"scrap\",\"money\",\"hinge\",\"album\",\"vouch\",\"asset\",\"tiara\",\"crept\",\"bayou\",\"atoll\",\"manor\",\"creak\",\"showy\",\"phase\",\"froth\",\"depth\",\"gloom\",\"flood\",\"trait\",\"girth\",\"piety\",\"goose\",\"float\",\"donor\",\"atone\",\"primo\",\"apron\",\"blown\",\"cacao\",\"loser\",\"input\",\"gloat\",\"awful\",\"brink\",\"smite\",\"beady\",\"rusty\",\"retro\",\"droll\",\"gawky\",\"hutch\",\"pinto\",\"egret\",\"lilac\",\"sever\",\"field\",\"fluff\",\"agape\",\"voice\",\"stead\",\"berth\",\"madam\",\"night\",\"bland\",\"liver\",\"wedge\",\"roomy\",\"wacky\",\"flock\",\"angry\",\"trite\",\"aphid\",\"tryst\",\"midge\",\"power\",\"elope\",\"cinch\",\"motto\",\"stomp\",\"upset\",\"bluff\",\"cramp\",\"quart\",\"coyly\",\"youth\",\"rhyme\",\"buggy\",\"alien\",\"smear\",\"unfit\",\"patty\",\"cling\",\"glean\",\"label\",\"hunky\",\"khaki\",\"poker\",\"gruel\",\"twice\",\"twang\",\"shrug\",\"treat\",\"waste\",\"merit\",\"woven\",\"needy\",\"clown\",\"irony\",\"ruder\",\"gauze\",\"chief\",\"onset\",\"prize\",\"fungi\",\"charm\",\"gully\",\"inter\",\"whoop\",\"taunt\",\"leery\",\"class\",\"theme\",\"lofty\",\"tibia\",\"booze\",\"alpha\",\"thyme\",\"doubt\",\"parer\",\"chute\",\"stick\",\"trice\",\"alike\",\"recap\",\"saint\",\"glory\",\"grate\",\"admit\",\"brisk\",\"soggy\",\"usurp\",\"scald\",\"scorn\",\"leave\",\"twine\",\"sting\",\"bough\",\"marsh\",\"sloth\",\"dandy\",\"vigor\",\"howdy\",\"enjoy\",\"valid\",\"ionic\",\"equal\",\"floor\",\"catch\",\"spade\",\"stein\",\"exist\",\"quirk\",\"denim\",\"grove\",\"spiel\",\"mummy\",\"fault\",\"foggy\",\"flout\",\"carry\",\"sneak\",\"libel\",\"waltz\",\"aptly\"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,\"scaly\",\"scold\",\"hefty\",\"chick\",\"sooty\",\"canal\",\"whiny\",\"slash\",\"quake\",\"joint\",\"swept\",\"prude\",\"heavy\",\"wield\",\"femme\",\"lasso\",\"maize\",\"shale\",\"screw\",\"spree\",\"smoky\",\"whiff\",\"scent\",\"glade\",\"spent\",\"prism\",\"stoke\",\"riper\",\"orbit\",\"cocoa\",\"guilt\",\"humus\",\"shush\",\"table\",\"smirk\",\"wrong\",\"noisy\",\"alert\",\"shiny\",\"elate\",\"resin\",\"whole\",\"hunch\",\"pixel\",\"polar\",\"hotel\",\"sword\",\"cleat\",\"mango\",\"rumba\",\"puffy\",\"filly\",\"billy\",\"leash\",\"clout\",\"dance\",\"ovate\",\"facet\",\"chili\",\"paint\",\"liner\",\"curio\",\"salty\",\"audio\",\"snake\",\"fable\",\"cloak\",\"navel\",\"spurt\",\"pesto\",\"balmy\",\"flash\",\"unwed\",\"early\",\"churn\",\"weedy\",\"stump\",\"lease\",\"witty\",\"wimpy\",\"spoof\",\"saner\",\"blend\",\"salsa\",\"thick\",\"warty\",\"manic\",\"blare\",\"squib\",\"spoon\",\"probe\",\"crepe\",\"knack\",\"force\",\"debut\",\"order\",\"haste\",\"teeth\",\"agent\",\"widen\",\"icily\",\"slice\",\"ingot\",\"clash\",\"juror\",\"blood\",\"abode\",\"throw\",\"unity\",\"pivot\",\"slept\",\"troop\",\"spare\",\"sewer\",\"parse\",\"morph\",\"cacti\",\"tacky\",\"spool\",\"demon\",\"moody\",\"annex\",\"begin\",\"fuzzy\",\"patch\",\"water\",\"lumpy\",\"admin\",\"omega\",\"limit\",\"tabby\",\"macho\",\"aisle\",\"skiff\",\"basis\",\"plank\",\"verge\",\"botch\",\"crawl\",\"lousy\",\"slain\",\"cubic\",\"raise\",\"wrack\",\"guide\",\"foist\",\"cameo\",\"under\",\"actor\",\"revue\",\"fraud\",\"harpy\",\"scoop\",\"climb\",\"refer\",\"olden\",\"clerk\",\"debar\",\"tally\",\"ethic\",\"cairn\",\"tulle\",\"ghoul\",\"hilly\",\"crude\",\"apart\",\"scale\",\"older\",\"plain\",\"sperm\",\"briny\",\"abbot\",\"rerun\",\"quest\",\"crisp\",\"bound\",\"befit\",\"drawn\",\"suite\",\"itchy\",\"cheer\",\"bagel\",\"guess\",\"broad\",\"axiom\",\"chard\",\"caput\",\"leant\",\"harsh\",\"curse\",\"proud\",\"swing\",\"opine\",\"taste\",\"lupus\",\"gumbo\",\"miner\",\"green\",\"chasm\",\"lipid\",\"topic\",\"armor\",\"brush\",\"crane\",\"mural\",\"abled\",\"habit\",\"bossy\",\"maker\",\"dusky\",\"dizzy\",\"lithe\",\"brook\",\"jazzy\",\"fifty\",\"sense\",\"giant\",\"surly\",\"legal\",\"fatal\",\"flunk\",\"began\",\"prune\",\"small\",\"slant\",\"scoff\",\"torus\",\"ninny\",\"covey\",\"viper\",\"taken\",\"moral\",\"vogue\",\"owing\",\"token\",\"entry\",\"booth\",\"voter\",\"chide\",\"elfin\",\"ebony\",\"neigh\",\"minim\",\"melon\",\"kneed\",\"decoy\",\"voila\",\"ankle\",\"arrow\",\"mushy\",\"tribe\",\"cease\",\"eager\",\"birth\",\"graph\",\"odder\",\"terra\",\"weird\",\"tried\",\"clack\",\"color\",\"rough\",\"weigh\",\"uncut\",\"ladle\",\"strip\",\"craft\",\"minus\",\"dicey\",\"titan\",\"lucid\",\"vicar\",\"dress\",\"ditch\",\"gypsy\",\"pasta\",\"taffy\",\"flame\",\"swoop\",\"aloof\",\"sight\",\"broke\",\"teary\",\"chart\",\"sixty\",\"wordy\",\"sheer\",\"leper\",\"nosey\",\"bulge\",\"savor\",\"clamp\",\"funky\",\"foamy\",\"toxic\",\"brand\",\"plumb\",\"dingy\",\"butte\",\"drill\",\"tripe\",\"bicep\",\"tenor\",\"krill\",\"worse\",\"drama\",\"hyena\",\"think\",\"ratio\",\"cobra\",\"basil\",\"scrum\",\"bused\",\"phone\",\"court\",\"camel\",\"proof\",\"heard\",\"angel\",\"petal\",\"pouty\",\"throb\",\"maybe\",\"fetal\",\"sprig\",\"spine\",\"shout\",\"cadet\",\"macro\",\"dodgy\",\"satyr\",\"rarer\",\"binge\",\"trend\",\"nutty\",\"leapt\",\"amiss\",\"split\",\"myrrh\",\"width\",\"sonar\",\"tower\",\"baron\",\"fever\",\"waver\",\"spark\",\"belie\",\"sloop\",\"expel\",\"smote\",\"baler\",\"above\",\"north\",\"wafer\",\"scant\",\"frill\",\"awash\",\"snack\",\"scowl\",\"frail\",\"drift\",\"limbo\",\"fence\",\"motel\",\"ounce\",\"wreak\",\"revel\",\"talon\",\"prior\",\"knelt\",\"cello\",\"flake\",\"debug\",\"anode\",\"crime\",\"salve\",\"scout\",\"imbue\",\"pinky\",\"stave\",\"vague\",\"chock\",\"fight\",\"video\",\"stone\",\"teach\",\"cleft\",\"frost\",\"prawn\",\"booty\",\"twist\",\"apnea\",\"stiff\",\"plaza\",\"ledge\",\"tweak\",\"board\",\"grant\",\"medic\",\"bacon\",\"cable\",\"brawl\",\"slunk\",\"raspy\",\"forum\",\"drone\",\"women\",\"mucus\",\"boast\",\"toddy\",\"coven\",\"tumor\",\"truer\",\"wrath\",\"stall\",\"steam\",\"axial\",\"purer\",\"daily\",\"trail\",\"niche\",\"mealy\",\"juice\",\"nylon\",\"plump\",\"merry\",\"flail\",\"papal\",\"wheat\",\"berry\",\"cower\",\"erect\",\"brute\",\"leggy\",\"snipe\",\"sinew\",\"skier\",\"penny\",\"jumpy\",\"rally\",\"umbra\",\"scary\",\"modem\",\"gross\",\"avian\",\"greed\",\"satin\",\"tonic\",\"parka\",\"sniff\",\"livid\",\"stark\",\"trump\",\"giddy\",\"reuse\",\"taboo\",\"avoid\",\"quote\",\"devil\",\"liken\",\"gloss\",\"gayer\",\"beret\",\"noise\",\"gland\",\"dealt\",\"sling\",\"rumor\",\"opera\",\"thigh\",\"tonga\",\"flare\",\"wound\",\"white\",\"bulky\",\"etude\",\"horse\",\"circa\",\"paddy\",\"inbox\",\"fizzy\",\"grain\",\"exert\",\"surge\",\"gleam\",\"belle\",\"salvo\",\"crush\",\"fruit\",\"sappy\",\"taker\",\"tract\",\"ovine\",\"spiky\",\"frank\",\"reedy\",\"filth\",\"spasm\",\"heave\",\"mambo\",\"right\",\"clank\",\"trust\",\"lumen\",\"borne\",\"spook\",\"sauce\",\"amber\",\"lathe\",\"carat\",\"corer\",\"dirty\",\"slyly\",\"affix\",\"alloy\",\"taint\",\"sheep\",\"kinky\",\"wooly\",\"mauve\",\"flung\",\"yacht\",\"fried\",\"quail\",\"brunt\",\"grimy\",\"curvy\",\"cagey\",\"rinse\",\"deuce\",\"state\",\"grasp\",\"milky\",\"bison\",\"graft\",\"sandy\",\"baste\",\"flask\",\"hedge\",\"girly\",\"swash\",\"boney\",\"coupe\",\"endow\",\"abhor\",\"welch\",\"blade\",\"tight\",\"geese\",\"miser\",\"mirth\",\"cloud\",\"cabal\",\"leech\",\"close\",\"tenth\",\"pecan\",\"droit\",\"grail\",\"clone\",\"guise\",\"ralph\",\"tango\",\"biddy\",\"smith\",\"mower\",\"payee\",\"serif\",\"drape\",\"fifth\",\"spank\",\"glaze\",\"allot\",\"truck\",\"kayak\",\"virus\",\"testy\",\"tepee\",\"fully\",\"zonal\",\"metro\",\"curry\",\"grand\",\"banjo\",\"axion\",\"bezel\",\"occur\",\"chain\",\"nasal\",\"gooey\",\"filer\",\"brace\",\"allay\",\"pubic\",\"raven\",\"plead\",\"gnash\",\"flaky\",\"munch\",\"dully\",\"eking\",\"thing\",\"slink\",\"hurry\",\"theft\",\"shorn\",\"pygmy\",\"ranch\",\"wring\",\"lemon\",\"shore\",\"mamma\",\"froze\",\"newer\",\"style\",\"moose\",\"antic\",\"drown\",\"vegan\",\"chess\",\"guppy\",\"union\",\"lever\",\"lorry\",\"image\",\"cabby\",\"druid\",\"exact\",\"truth\",\"dopey\",\"spear\",\"cried\",\"chime\",\"crony\",\"stunk\",\"timid\",\"batch\",\"gauge\",\"rotor\",\"crack\",\"curve\",\"latte\",\"witch\",\"bunch\",\"repel\",\"anvil\",\"soapy\",\"meter\",\"broth\",\"madly\",\"dried\",\"scene\",\"known\",\"magma\",\"roost\",\"woman\",\"thong\",\"punch\",\"pasty\",\"downy\",\"knead\",\"whirl\",\"rapid\",\"clang\",\"anger\",\"drive\",\"goofy\",\"email\",\"music\",\"stuff\",\"bleep\",\"rider\",\"mecca\",\"folio\",\"setup\",\"verso\",\"quash\",\"fauna\",\"gummy\",\"happy\",\"newly\",\"fussy\",\"relic\",\"guava\",\"ratty\",\"fudge\",\"femur\",\"chirp\",\"forte\",\"alibi\",\"whine\",\"petty\",\"golly\",\"plait\",\"fleck\",\"felon\",\"gourd\",\"brown\",\"thrum\",\"ficus\",\"stash\",\"decry\",\"wiser\",\"junta\",\"visor\",\"daunt\",\"scree\",\"impel\",\"await\",\"press\",\"whose\",\"turbo\",\"stoop\",\"speak\",\"mangy\",\"eying\",\"inlet\",\"crone\",\"pulse\",\"mossy\",\"staid\",\"hence\",\"pinch\",\"teddy\",\"sully\",\"snore\",\"ripen\",\"snowy\",\"attic\",\"going\",\"leach\",\"mouth\",\"hound\",\"clump\",\"tonal\",\"bigot\",\"peril\",\"piece\",\"blame\",\"haute\",\"spied\",\"undid\",\"intro\",\"basal\",\"rodeo\",\"guard\",\"steer\",\"loamy\",\"scamp\",\"scram\",\"manly\",\"hello\",\"vaunt\",\"organ\",\"feral\",\"knock\",\"extra\",\"condo\",\"adapt\",\"willy\",\"polka\",\"rayon\",\"skirt\",\"faith\",\"torso\",\"match\",\"mercy\",\"tepid\",\"sleek\",\"riser\",\"twixt\",\"peace\",\"flush\",\"catty\",\"login\",\"eject\",\"roger\",\"rival\",\"untie\",\"refit\",\"aorta\",\"adult\",\"judge\",\"rower\",\"artsy\",\"rural\",\"shave\",\"bobby\",\"eclat\",\"fella\",\"gaily\",\"harry\",\"hasty\",\"hydro\",\"liege\",\"octal\",\"ombre\",\"payer\",\"sooth\",\"unset\",\"unlit\",\"vomit\",\"fanny\",\"fetus\",\"butch\",\"stalk\",\"flack\",\"widow\",\"augur\"]\n",
    "solutions = set(solutions)\n",
    "print(len(solutions), 'solution words in Wordle source code.')\n",
    "\n",
    "# Wordle allowable words, from Wordle source code\n",
    "# https://www.nytimes.com/games/wordle/main.9622bc55.jsallowed_words = pd.read_csv('./data/wordle-allowed-words.txt', header=None)\n",
    "allowed_words = [\"aahed\",\"aalii\",\"aargh\",\"aarti\",\"abaca\",\"abaci\",\"abacs\",\"abaft\",\"abaka\",\"abamp\",\"aband\",\"abash\",\"abask\",\"abaya\",\"abbas\",\"abbed\",\"abbes\",\"abcee\",\"abeam\",\"abear\",\"abele\",\"abers\",\"abets\",\"abies\",\"abler\",\"ables\",\"ablet\",\"ablow\",\"abmho\",\"abohm\",\"aboil\",\"aboma\",\"aboon\",\"abord\",\"abore\",\"abram\",\"abray\",\"abrim\",\"abrin\",\"abris\",\"absey\",\"absit\",\"abuna\",\"abune\",\"abuts\",\"abuzz\",\"abyes\",\"abysm\",\"acais\",\"acari\",\"accas\",\"accoy\",\"acerb\",\"acers\",\"aceta\",\"achar\",\"ached\",\"aches\",\"achoo\",\"acids\",\"acidy\",\"acing\",\"acini\",\"ackee\",\"acker\",\"acmes\",\"acmic\",\"acned\",\"acnes\",\"acock\",\"acold\",\"acred\",\"acres\",\"acros\",\"acted\",\"actin\",\"acton\",\"acyls\",\"adaws\",\"adays\",\"adbot\",\"addax\",\"added\",\"adder\",\"addio\",\"addle\",\"adeem\",\"adhan\",\"adieu\",\"adios\",\"adits\",\"adman\",\"admen\",\"admix\",\"adobo\",\"adown\",\"adoze\",\"adrad\",\"adred\",\"adsum\",\"aduki\",\"adunc\",\"adust\",\"advew\",\"adyta\",\"adzed\",\"adzes\",\"aecia\",\"aedes\",\"aegis\",\"aeons\",\"aerie\",\"aeros\",\"aesir\",\"afald\",\"afara\",\"afars\",\"afear\",\"aflaj\",\"afore\",\"afrit\",\"afros\",\"agama\",\"agami\",\"agars\",\"agast\",\"agave\",\"agaze\",\"agene\",\"agers\",\"agger\",\"aggie\",\"aggri\",\"aggro\",\"aggry\",\"aghas\",\"agila\",\"agios\",\"agism\",\"agist\",\"agita\",\"aglee\",\"aglet\",\"agley\",\"agloo\",\"aglus\",\"agmas\",\"agoge\",\"agone\",\"agons\",\"agood\",\"agora\",\"agria\",\"agrin\",\"agros\",\"agued\",\"agues\",\"aguna\",\"aguti\",\"aheap\",\"ahent\",\"ahigh\",\"ahind\",\"ahing\",\"ahint\",\"ahold\",\"ahull\",\"ahuru\",\"aidas\",\"aided\",\"aides\",\"aidoi\",\"aidos\",\"aiery\",\"aigas\",\"aight\",\"ailed\",\"aimed\",\"aimer\",\"ainee\",\"ainga\",\"aioli\",\"aired\",\"airer\",\"airns\",\"airth\",\"airts\",\"aitch\",\"aitus\",\"aiver\",\"aiyee\",\"aizle\",\"ajies\",\"ajiva\",\"ajuga\",\"ajwan\",\"akees\",\"akela\",\"akene\",\"aking\",\"akita\",\"akkas\",\"alaap\",\"alack\",\"alamo\",\"aland\",\"alane\",\"alang\",\"alans\",\"alant\",\"alapa\",\"alaps\",\"alary\",\"alate\",\"alays\",\"albas\",\"albee\",\"alcid\",\"alcos\",\"aldea\",\"alder\",\"aldol\",\"aleck\",\"alecs\",\"alefs\",\"aleft\",\"aleph\",\"alews\",\"aleye\",\"alfas\",\"algal\",\"algas\",\"algid\",\"algin\",\"algor\",\"algum\",\"alias\",\"alifs\",\"aline\",\"alist\",\"aliya\",\"alkie\",\"alkos\",\"alkyd\",\"alkyl\",\"allee\",\"allel\",\"allis\",\"allod\",\"allyl\",\"almah\",\"almas\",\"almeh\",\"almes\",\"almud\",\"almug\",\"alods\",\"aloed\",\"aloes\",\"aloha\",\"aloin\",\"aloos\",\"alowe\",\"altho\",\"altos\",\"alula\",\"alums\",\"alure\",\"alvar\",\"alway\",\"amahs\",\"amain\",\"amate\",\"amaut\",\"amban\",\"ambit\",\"ambos\",\"ambry\",\"ameba\",\"ameer\",\"amene\",\"amens\",\"ament\",\"amias\",\"amice\",\"amici\",\"amide\",\"amido\",\"amids\",\"amies\",\"amiga\",\"amigo\",\"amine\",\"amino\",\"amins\",\"amirs\",\"amlas\",\"amman\",\"ammon\",\"ammos\",\"amnia\",\"amnic\",\"amnio\",\"amoks\",\"amole\",\"amort\",\"amour\",\"amove\",\"amowt\",\"amped\",\"ampul\",\"amrit\",\"amuck\",\"amyls\",\"anana\",\"anata\",\"ancho\",\"ancle\",\"ancon\",\"andro\",\"anear\",\"anele\",\"anent\",\"angas\",\"anglo\",\"anigh\",\"anile\",\"anils\",\"anima\",\"animi\",\"anion\",\"anise\",\"anker\",\"ankhs\",\"ankus\",\"anlas\",\"annal\",\"annas\",\"annat\",\"anoas\",\"anole\",\"anomy\",\"ansae\",\"antae\",\"antar\",\"antas\",\"anted\",\"antes\",\"antis\",\"antra\",\"antre\",\"antsy\",\"anura\",\"anyon\",\"apace\",\"apage\",\"apaid\",\"apayd\",\"apays\",\"apeak\",\"apeek\",\"apers\",\"apert\",\"apery\",\"apgar\",\"aphis\",\"apian\",\"apiol\",\"apish\",\"apism\",\"apode\",\"apods\",\"apoop\",\"aport\",\"appal\",\"appay\",\"appel\",\"appro\",\"appui\",\"appuy\",\"apres\",\"apses\",\"apsis\",\"apsos\",\"apted\",\"apter\",\"aquae\",\"aquas\",\"araba\",\"araks\",\"arame\",\"arars\",\"arbas\",\"arced\",\"archi\",\"arcos\",\"arcus\",\"ardeb\",\"ardri\",\"aread\",\"areae\",\"areal\",\"arear\",\"areas\",\"areca\",\"aredd\",\"arede\",\"arefy\",\"areic\",\"arene\",\"arepa\",\"arere\",\"arete\",\"arets\",\"arett\",\"argal\",\"argan\",\"argil\",\"argle\",\"argol\",\"argon\",\"argot\",\"argus\",\"arhat\",\"arias\",\"ariel\",\"ariki\",\"arils\",\"ariot\",\"arish\",\"arked\",\"arled\",\"arles\",\"armed\",\"armer\",\"armet\",\"armil\",\"arnas\",\"arnut\",\"aroba\",\"aroha\",\"aroid\",\"arpas\",\"arpen\",\"arrah\",\"arras\",\"arret\",\"arris\",\"arroz\",\"arsed\",\"arses\",\"arsey\",\"arsis\",\"artal\",\"artel\",\"artic\",\"artis\",\"aruhe\",\"arums\",\"arval\",\"arvee\",\"arvos\",\"aryls\",\"asana\",\"ascon\",\"ascus\",\"asdic\",\"ashed\",\"ashes\",\"ashet\",\"asked\",\"asker\",\"askoi\",\"askos\",\"aspen\",\"asper\",\"aspic\",\"aspie\",\"aspis\",\"aspro\",\"assai\",\"assam\",\"asses\",\"assez\",\"assot\",\"aster\",\"astir\",\"astun\",\"asura\",\"asway\",\"aswim\",\"asyla\",\"ataps\",\"ataxy\",\"atigi\",\"atilt\",\"atimy\",\"atlas\",\"atman\",\"atmas\"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,\"vodun\",\"voema\",\"vogie\",\"voids\",\"voile\",\"voips\",\"volae\",\"volar\",\"voled\",\"voles\",\"volet\",\"volks\",\"volta\",\"volte\",\"volti\",\"volts\",\"volva\",\"volve\",\"vomer\",\"voted\",\"votes\",\"vouge\",\"voulu\",\"vowed\",\"vower\",\"voxel\",\"vozhd\",\"vraic\",\"vrils\",\"vroom\",\"vrous\",\"vrouw\",\"vrows\",\"vuggs\",\"vuggy\",\"vughs\",\"vughy\",\"vulgo\",\"vulns\",\"vulva\",\"vutty\",\"waacs\",\"wacke\",\"wacko\",\"wacks\",\"wadds\",\"waddy\",\"waded\",\"wader\",\"wades\",\"wadge\",\"wadis\",\"wadts\",\"waffs\",\"wafts\",\"waged\",\"wages\",\"wagga\",\"wagyu\",\"wahoo\",\"waide\",\"waifs\",\"waift\",\"wails\",\"wains\",\"wairs\",\"waite\",\"waits\",\"wakas\",\"waked\",\"waken\",\"waker\",\"wakes\",\"wakfs\",\"waldo\",\"walds\",\"waled\",\"waler\",\"wales\",\"walie\",\"walis\",\"walks\",\"walla\",\"walls\",\"wally\",\"walty\",\"wamed\",\"wames\",\"wamus\",\"wands\",\"waned\",\"wanes\",\"waney\",\"wangs\",\"wanks\",\"wanky\",\"wanle\",\"wanly\",\"wanna\",\"wants\",\"wanty\",\"wanze\",\"waqfs\",\"warbs\",\"warby\",\"wards\",\"wared\",\"wares\",\"warez\",\"warks\",\"warms\",\"warns\",\"warps\",\"warre\",\"warst\",\"warts\",\"wases\",\"washy\",\"wasms\",\"wasps\",\"waspy\",\"wasts\",\"watap\",\"watts\",\"wauff\",\"waugh\",\"wauks\",\"waulk\",\"wauls\",\"waurs\",\"waved\",\"waves\",\"wavey\",\"wawas\",\"wawes\",\"wawls\",\"waxed\",\"waxer\",\"waxes\",\"wayed\",\"wazir\",\"wazoo\",\"weald\",\"weals\",\"weamb\",\"weans\",\"wears\",\"webby\",\"weber\",\"wecht\",\"wedel\",\"wedgy\",\"weeds\",\"weeke\",\"weeks\",\"weels\",\"weems\",\"weens\",\"weeny\",\"weeps\",\"weepy\",\"weest\",\"weete\",\"weets\",\"wefte\",\"wefts\",\"weids\",\"weils\",\"weirs\",\"weise\",\"weize\",\"wekas\",\"welds\",\"welke\",\"welks\",\"welkt\",\"wells\",\"welly\",\"welts\",\"wembs\",\"wench\",\"wends\",\"wenge\",\"wenny\",\"wents\",\"weros\",\"wersh\",\"wests\",\"wetas\",\"wetly\",\"wexed\",\"wexes\",\"whamo\",\"whams\",\"whang\",\"whaps\",\"whare\",\"whata\",\"whats\",\"whaup\",\"whaur\",\"wheal\",\"whear\",\"wheen\",\"wheep\",\"wheft\",\"whelk\",\"whelm\",\"whens\",\"whets\",\"whews\",\"wheys\",\"whids\",\"whift\",\"whigs\",\"whilk\",\"whims\",\"whins\",\"whios\",\"whips\",\"whipt\",\"whirr\",\"whirs\",\"whish\",\"whiss\",\"whist\",\"whits\",\"whity\",\"whizz\",\"whomp\",\"whoof\",\"whoot\",\"whops\",\"whore\",\"whorl\",\"whort\",\"whoso\",\"whows\",\"whump\",\"whups\",\"whyda\",\"wicca\",\"wicks\",\"wicky\",\"widdy\",\"wides\",\"wiels\",\"wifed\",\"wifes\",\"wifey\",\"wifie\",\"wifty\",\"wigan\",\"wigga\",\"wiggy\",\"wikis\",\"wilco\",\"wilds\",\"wiled\",\"wiles\",\"wilga\",\"wilis\",\"wilja\",\"wills\",\"wilts\",\"wimps\",\"winds\",\"wined\",\"wines\",\"winey\",\"winge\",\"wings\",\"wingy\",\"winks\",\"winna\",\"winns\",\"winos\",\"winze\",\"wiped\",\"wiper\",\"wipes\",\"wired\",\"wirer\",\"wires\",\"wirra\",\"wised\",\"wises\",\"wisha\",\"wisht\",\"wisps\",\"wists\",\"witan\",\"wited\",\"wites\",\"withe\",\"withs\",\"withy\",\"wived\",\"wiver\",\"wives\",\"wizen\",\"wizes\",\"woads\",\"woald\",\"wocks\",\"wodge\",\"woful\",\"wojus\",\"woker\",\"wokka\",\"wolds\",\"wolfs\",\"wolly\",\"wolve\",\"wombs\",\"womby\",\"womyn\",\"wonga\",\"wongi\",\"wonks\",\"wonky\",\"wonts\",\"woods\",\"wooed\",\"woofs\",\"woofy\",\"woold\",\"wools\",\"woons\",\"woops\",\"woopy\",\"woose\",\"woosh\",\"wootz\",\"words\",\"works\",\"worms\",\"wormy\",\"worts\",\"wowed\",\"wowee\",\"woxen\",\"wrang\",\"wraps\",\"wrapt\",\"wrast\",\"wrate\",\"wrawl\",\"wrens\",\"wrick\",\"wried\",\"wrier\",\"wries\",\"writs\",\"wroke\",\"wroot\",\"wroth\",\"wryer\",\"wuddy\",\"wudus\",\"wulls\",\"wurst\",\"wuses\",\"wushu\",\"wussy\",\"wuxia\",\"wyled\",\"wyles\",\"wynds\",\"wynns\",\"wyted\",\"wytes\",\"xebec\",\"xenia\",\"xenic\",\"xenon\",\"xeric\",\"xerox\",\"xerus\",\"xoana\",\"xrays\",\"xylan\",\"xylem\",\"xylic\",\"xylol\",\"xylyl\",\"xysti\",\"xysts\",\"yaars\",\"yabas\",\"yabba\",\"yabby\",\"yacca\",\"yacka\",\"yacks\",\"yaffs\",\"yager\",\"yages\",\"yagis\",\"yahoo\",\"yaird\",\"yakka\",\"yakow\",\"yales\",\"yamen\",\"yampy\",\"yamun\",\"yangs\",\"yanks\",\"yapok\",\"yapon\",\"yapps\",\"yappy\",\"yarak\",\"yarco\",\"yards\",\"yarer\",\"yarfa\",\"yarks\",\"yarns\",\"yarrs\",\"yarta\",\"yarto\",\"yates\",\"yauds\",\"yauld\",\"yaups\",\"yawed\",\"yawey\",\"yawls\",\"yawns\",\"yawny\",\"yawps\",\"ybore\",\"yclad\",\"ycled\",\"ycond\",\"ydrad\",\"ydred\",\"yeads\",\"yeahs\",\"yealm\",\"yeans\",\"yeard\",\"years\",\"yecch\",\"yechs\",\"yechy\",\"yedes\",\"yeeds\",\"yeesh\",\"yeggs\",\"yelks\",\"yells\",\"yelms\",\"yelps\",\"yelts\",\"yenta\",\"yente\",\"yerba\",\"yerds\",\"yerks\",\"yeses\",\"yesks\",\"yests\",\"yesty\",\"yetis\",\"yetts\",\"yeuks\",\"yeuky\",\"yeven\",\"yeves\",\"yewen\",\"yexed\",\"yexes\",\"yfere\",\"yiked\",\"yikes\",\"yills\",\"yince\",\"yipes\",\"yippy\",\"yirds\",\"yirks\",\"yirrs\",\"yirth\",\"yites\",\"yitie\",\"ylems\",\"ylike\",\"ylkes\",\"ymolt\",\"ympes\",\"yobbo\",\"yobby\",\"yocks\",\"yodel\",\"yodhs\",\"yodle\",\"yogas\",\"yogee\",\"yoghs\",\"yogic\",\"yogin\",\"yogis\",\"yoick\",\"yojan\",\"yoked\",\"yokel\",\"yoker\",\"yokes\",\"yokul\",\"yolks\",\"yolky\",\"yomim\",\"yomps\",\"yonic\",\"yonis\",\"yonks\",\"yoofs\",\"yoops\",\"yores\",\"yorks\",\"yorps\",\"youks\",\"yourn\",\"yours\",\"yourt\",\"youse\",\"yowed\",\"yowes\",\"yowie\",\"yowls\",\"yowza\",\"yrapt\",\"yrent\",\"yrivd\",\"yrneh\",\"ysame\",\"ytost\",\"yuans\",\"yucas\",\"yucca\",\"yucch\",\"yucko\",\"yucks\",\"yucky\",\"yufts\",\"yugas\",\"yuked\",\"yukes\",\"yukky\",\"yukos\",\"yulan\",\"yules\",\"yummo\",\"yummy\",\"yumps\",\"yupon\",\"yuppy\",\"yurta\",\"yurts\",\"yuzus\",\"zabra\",\"zacks\",\"zaida\",\"zaidy\",\"zaire\",\"zakat\",\"zaman\",\"zambo\",\"zamia\",\"zanja\",\"zante\",\"zanza\",\"zanze\",\"zappy\",\"zarfs\",\"zaris\",\"zatis\",\"zaxes\",\"zayin\",\"zazen\",\"zeals\",\"zebec\",\"zebub\",\"zebus\",\"zedas\",\"zeins\",\"zendo\",\"zerda\",\"zerks\",\"zeros\",\"zests\",\"zetas\",\"zexes\",\"zezes\",\"zhomo\",\"zibet\",\"ziffs\",\"zigan\",\"zilas\",\"zilch\",\"zilla\",\"zills\",\"zimbi\",\"zimbs\",\"zinco\",\"zincs\",\"zincy\",\"zineb\",\"zines\",\"zings\",\"zingy\",\"zinke\",\"zinky\",\"zippo\",\"zippy\",\"ziram\",\"zitis\",\"zizel\",\"zizit\",\"zlote\",\"zloty\",\"zoaea\",\"zobos\",\"zobus\",\"zocco\",\"zoeae\",\"zoeal\",\"zoeas\",\"zoism\",\"zoist\",\"zombi\",\"zonae\",\"zonda\",\"zoned\",\"zoner\",\"zones\",\"zonks\",\"zooea\",\"zooey\",\"zooid\",\"zooks\",\"zooms\",\"zoons\",\"zooty\",\"zoppa\",\"zoppo\",\"zoril\",\"zoris\",\"zorro\",\"zouks\",\"zowee\",\"zowie\",\"zulus\",\"zupan\",\"zupas\",\"zuppa\",\"zurfs\",\"zuzim\",\"zygal\",\"zygon\",\"zymes\",\"zymic\"]\n",
    "allowed_words = set(allowed_words).union(solutions)\n",
    "print(len(allowed_words), 'allowed words in Wordle source code.')\n",
    "\n",
    "# Filter word frequency table to include allowed words only\n",
    "words = words[words['word'].isin(allowed_words)]\n",
    "print(len(words), 'allowed words in both Wordle source code and the Google corpus')\n",
    "\n",
    "# Add the allowed words that weren't in word frequency table\n",
    "missing_allowed_words = allowed_words.difference(set(words['word'].values))\n",
    "words = words.append(pd.DataFrame(\n",
    "    [list(missing_allowed_words),\n",
    "     [0]*len(missing_allowed_words),\n",
    "     [0]*len(missing_allowed_words)],\n",
    "    index=['word', 'count', 'freq']).T)\n",
    "\n",
    "# Create word frequency index\n",
    "words['freq_idx'] = range(len(words))\n",
    "words.index = words['word']\n",
    "words.index.name = None\n",
    "words = words.drop(['word'], axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Find \"best\" words (for information gain)\n",
    "The first choice to make for this model is the **method of calculating letter frequency**, \n",
    "* Do we take word frequency into account when calculating letter frequency?\n",
    "* For our guess words, do we prefer the letters in their correct positions? Don't care? Or prefer not?\n",
    "\n",
    "I've intuited a function for \"letter frequency\" that balances the following:\n",
    "* Number of times the letter appears in the **list** of allowed words (assume solution words are chosen randomly)\n",
    "* Number of times the letter appears in the entire **corpus** (assume solution words chosen proportional to word frequency)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best starting words (sorted by a scoring metric):\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>freq</th>\n",
       "      <th>freq_idx</th>\n",
       "      <th>no_position_score</th>\n",
       "      <th>per_position_score</th>\n",
       "      <th>combined_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>about</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>17937.701035</td>\n",
       "      <td>2956.359911</td>\n",
       "      <td>0.458063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>other</th>\n",
       "      <td>0.797631</td>\n",
       "      <td>1</td>\n",
       "      <td>20417.584474</td>\n",
       "      <td>3641.955278</td>\n",
       "      <td>0.534323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>which</th>\n",
       "      <td>0.660709</td>\n",
       "      <td>2</td>\n",
       "      <td>8628.214586</td>\n",
       "      <td>2440.714024</td>\n",
       "      <td>0.267912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>their</th>\n",
       "      <td>0.638157</td>\n",
       "      <td>3</td>\n",
       "      <td>19734.409007</td>\n",
       "      <td>3821.943879</td>\n",
       "      <td>0.530543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>there</th>\n",
       "      <td>0.571575</td>\n",
       "      <td>4</td>\n",
       "      <td>15959.411388</td>\n",
       "      <td>2983.382129</td>\n",
       "      <td>0.424036</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           freq  freq_idx  no_position_score  per_position_score  \\\n",
       "about       1.0         0       17937.701035         2956.359911   \n",
       "other  0.797631         1       20417.584474         3641.955278   \n",
       "which  0.660709         2        8628.214586         2440.714024   \n",
       "their  0.638157         3       19734.409007         3821.943879   \n",
       "there  0.571575         4       15959.411388         2983.382129   \n",
       "\n",
       "       combined_score  \n",
       "about        0.458063  \n",
       "other        0.534323  \n",
       "which        0.267912  \n",
       "their        0.530543  \n",
       "there        0.424036  "
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Penalties based on my intuition\n",
    "def apply_char_penalty(char, score, a, green_chars, yellow_chars, i=None):\n",
    "    # Incoming chars are filtered to green and yellow only\n",
    "    for j, pos in enumerate(a):\n",
    "        if len(pos) == 1:\n",
    "            # Green characters\n",
    "            # Extract the character from single member set.\n",
    "            green_char, = pos\n",
    "            if char == green_char:\n",
    "                if i is None:\n",
    "#                     print(char, 'is green in any position')\n",
    "                    # 3/4 penalty for green, in general\n",
    "                    return 0\n",
    "                else:\n",
    "                    if i == j:\n",
    "#                         print(char, 'is green in same position')\n",
    "                        # Full penalty for green in same position\n",
    "                        return 0\n",
    "                    else:\n",
    "#                         print(char, 'is green in different position')\n",
    "                        # 90% penalty for green in different position\n",
    "                        return 0.1 * score\n",
    "            # Full penalty for yellow in a green position\n",
    "            elif i == j and char in yellow_chars:\n",
    "#                 print(char, 'is yellow in a green position')\n",
    "                return 0\n",
    "\n",
    "        if char in yellow_chars:\n",
    "            if i is not None:\n",
    "                for j, pos in enumerate(a):\n",
    "                    if i == j and char not in pos:\n",
    "#                         print(char, 'is yellow in same position')\n",
    "                        # Full penalty for yellow in same position\n",
    "                        return 0\n",
    "                    else:\n",
    "#                         print(char, 'is yellow in different position')\n",
    "                        # 80% penalty for yellow in different position\n",
    "                        return 0.2 * score\n",
    "            else:\n",
    "#                 print(char, 'is yellow in any position')\n",
    "                # 1/3 penalty for yellow, in general\n",
    "                return 0\n",
    "            \n",
    "    return score\n",
    "    \n",
    "\n",
    "def score_words(words, ok_words=None, a=None, b=None):\n",
    "    words = words[['freq', 'freq_idx']].copy()\n",
    "    if ok_words is None:\n",
    "        ok_words = words\n",
    "    \n",
    "    if a is not None and b is not None:\n",
    "        # Get green characters\n",
    "        green_chars = set()\n",
    "        for j, pos in enumerate(a):\n",
    "            if len(pos) == 1:\n",
    "                # Green characters\n",
    "                # Extract the character from single member set.\n",
    "                green_char, = pos\n",
    "                green_chars.add(green_char)\n",
    "#         print('Green:', green_chars)\n",
    "        \n",
    "        # Get yellow characters\n",
    "        yellow_chars = b - green_chars\n",
    "#         print('Yellow:', yellow_chars)\n",
    "        \n",
    "    # Letter frequency\n",
    "    letter_freq = defaultdict(int)\n",
    "    for word, word_freq in ok_words[['freq']].itertuples():\n",
    "        for char in word:\n",
    "            letter_freq[char] += 1 + word_freq\n",
    "            \n",
    "    # Apply penalties\n",
    "    if a is not None and b is not None:\n",
    "        for char in list(letter_freq.keys()):\n",
    "            letter_freq[char] = apply_char_penalty(char, letter_freq[char], a, green_chars, yellow_chars)\n",
    "\n",
    "    sorted_letters = sorted(letter_freq.items(), key=lambda x: -x[1])\n",
    "#     print('Top 5 most frequent letters overall:')\n",
    "#     print(*sorted_letters[:5], sep='\\n')\n",
    "\n",
    "    # Letter frequency based on position\n",
    "    letter_pos_freq = [defaultdict(float) for _ in range(5)]\n",
    "    for word, word_freq in ok_words[['freq']].itertuples():\n",
    "        for i, char in enumerate(word):\n",
    "            letter_pos_freq[i][char] += 1 + word_freq\n",
    "            \n",
    "    # Apply penalties\n",
    "    if a is not None:\n",
    "        for i, pos_freq in enumerate(letter_pos_freq):\n",
    "            for char in list(pos_freq.keys()):\n",
    "                pos_freq[char] = apply_char_penalty(char, pos_freq[char], a, green_chars, yellow_chars, i)\n",
    "\n",
    "    sorted_pos_letters = [sorted(letter_pos_freq[i].items(), key=lambda x: -x[1]) for i in range(5)]\n",
    "    \n",
    "#     print('\\nMost frequent letter for positions 1 to 5:')\n",
    "#     print(*[s[0] for s in sorted_pos_letters], sep='\\n')\n",
    "\n",
    "    # Find the best \"starting words\"\n",
    "    # Maximizing total letter_freq (most frequent letters overall)\n",
    "    # No points for a repeated letter\n",
    "    scores = []\n",
    "    for word in words.index:\n",
    "        used_chars = set()\n",
    "        score = 0\n",
    "        for char in word:\n",
    "            if char in used_chars:\n",
    "                continue\n",
    "            score += letter_freq[char]\n",
    "            used_chars.add(char)\n",
    "        scores.append(score)\n",
    "    words['no_position_score'] = scores\n",
    "\n",
    "    # Maximizing letter_pos_freq (most frequent letters, per position)\n",
    "    # No points for a repeated letter\n",
    "    scores = []\n",
    "    for word in words.index:\n",
    "        used_chars = set()\n",
    "        score = 0\n",
    "        for i, char in enumerate(word):\n",
    "            if char in used_chars:\n",
    "                continue\n",
    "            score += letter_pos_freq[i][char]\n",
    "            used_chars.add(char)\n",
    "        scores.append(score)\n",
    "    words['per_position_score'] = scores\n",
    "\n",
    "    # Scale each score to 0...1 and take the mean for a combined score\n",
    "    words['combined_score'] = (\n",
    "        (words['no_position_score'] / words['no_position_score'].max())\n",
    "        + (words['per_position_score'] / words['per_position_score'].max())) / 2\n",
    "\n",
    "    words = words.sort_values(['freq'], ascending=False)\n",
    "    words['freq_idx'] = range(len(words))\n",
    "#     words = words.sort_values(['combined_score'], ascending=False)\n",
    "    return words\n",
    "\n",
    "words = score_words(words)\n",
    "print('Best starting words (sorted by a scoring metric):')\n",
    "words.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Solver\n",
    "**Hard mode:** will always use existing clues. Note that this is not an optimal strategy for playing, generally; using a completely different set of letters is preferred for more information gain.\n",
    "\n",
    "**Easy mode:** optimize information gain, not restraining to the existing clues.\n",
    "\n",
    "We define a set of allowable letters for each position, which is initially all letters, then narrows.\n",
    "\n",
    "We also keep a set of letters which *must* occur (ones which have been marked yellow) but whose location may not yet be known.\n",
    "\n",
    "The function to choose which word is another hyperparameter. It balances the word frequency with the information gain. We assume more common words will be solutions. At the first guess, we look solely to information gain (since we would be unlikely to solve on the first guess). At the last guess, we look only for the most common word (since there would be no point gaining more information). In between, the function balances the two, increasingly favoring word frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update constraints based on a new clue\n",
    "def use_clues(word, result, a, b):\n",
    "    for i, r in enumerate(result):\n",
    "        char = word[i]\n",
    "        if r == 'green':\n",
    "            a[i] = set([char])\n",
    "        elif r == 'yellow':\n",
    "            try:\n",
    "                a[i].remove(char)\n",
    "            except:\n",
    "                continue\n",
    "            b.add(char)\n",
    "        elif r == 'grey':\n",
    "            # Remove from all positions except green ones\n",
    "            for pos in a:\n",
    "                if len(pos) == 1:\n",
    "                    continue\n",
    "                try:\n",
    "                    pos.remove(char)\n",
    "                except:\n",
    "                    continue\n",
    "    return a, b\n",
    "\n",
    "# Find all allowable words matching the constraints\n",
    "def find_ok_words(a, b):\n",
    "    a_met = (\n",
    "        np.in1d(words_array[:,0], list(a[0]))\n",
    "        & np.in1d(words_array[:,1], list(a[1]))\n",
    "        & np.in1d(words_array[:,2], list(a[2]))\n",
    "        & np.in1d(words_array[:,3], list(a[3]))\n",
    "        & np.in1d(words_array[:,4], list(a[4]))\n",
    "    )\n",
    "    if len(b) > 0:\n",
    "        b_met_each = []\n",
    "        for char in b:\n",
    "            b_met_each.append(np.array([char in word for word in words.index]))\n",
    "        b_met_all = np.array([True] * len(words.index))\n",
    "        for b_met in b_met_each:\n",
    "            b_met_all = b_met_all & b_met\n",
    "    else:\n",
    "        b_met_all = np.array([True] * len(words.index))\n",
    "    ok_words = words_array[a_met & b_met_all]\n",
    "    return [''.join(w) for w in ok_words]\n",
    "\n",
    "# Recommend guess words based on the constraints\n",
    "def find_clues_solutions(a, b, guess_num, verbose=False, mode='hard'):\n",
    "    ok_words = find_ok_words(a, b)\n",
    "    \n",
    "    # Filter the words table to ok_words\n",
    "    ok_words = words[words['word'].isin(ok_words)]\n",
    "    \n",
    "    if not verbose=='quiet':\n",
    "        print()\n",
    "        print(len(ok_words), 'valid words.')\n",
    "    \n",
    "    # How likely is it that the top potential solution word is correct?\n",
    "    # (Much more frequent than other solution words)\n",
    "    try:\n",
    "        p_correct = ok_words['freq'].max() / ok_words['freq'].sum()\n",
    "    except:\n",
    "        # Division by zero happens when words weren't in the frequency corpus\n",
    "        p_correct = 1\n",
    "    if not verbose == 'quiet':\n",
    "        print(f'Top solution word {ok_words[\"freq\"].astype(float).idxmax()} has p_correct = {p_correct:.4f}')\n",
    "    \n",
    "    # Switch to hard mode (solve) if we have a good chance of success\n",
    "    if p_correct >= 0.5:\n",
    "        mode = 'hard'\n",
    "        \n",
    "#     ok_solutions = ok_words[ok_words.index.isin(solutions)]\n",
    "\n",
    "    if mode == 'easy':\n",
    "        if not verbose == 'quiet':\n",
    "            print('Pursuing info gain rather than solution.')\n",
    "        # Select from *all* words for best info gain\n",
    "        ok_words = score_words(words, ok_words, a, b)\n",
    "        ok_words = ok_words.sort_values(['no_position_score'], ascending=False)\n",
    "        ok_words['info_idx'] = range(len(ok_words))\n",
    "    else:\n",
    "        ok_words = score_words(ok_words, ok_words, a, b)\n",
    "        ok_words = ok_words.sort_values(['combined_score'], ascending=False)\n",
    "        ok_words['info_idx'] = range(len(ok_words))\n",
    "        if not verbose == 'quiet':\n",
    "            print('Pursuing solution.')\n",
    "            \n",
    "#     ok_words['freq_idx'] = ok_words.index.isin(solutions).astype(int)*-len(ok_words)\n",
    "\n",
    "\n",
    "    if mode == 'easy':\n",
    "        # Prefer information gain only\n",
    "        info_weight = 1\n",
    "        freq_weight = 0\n",
    "    else:\n",
    "        # Balance information gain with how common the word is\n",
    "        # Increasingly favor common words\n",
    "        # The formula in the next line is a hyperparameter\n",
    "        freq_weight = min(1, max(p_correct, 0.3 * guess_num))\n",
    "        info_weight = 1 - freq_weight\n",
    "\n",
    "    ok_words['weighted_idx'] = (ok_words['info_idx'] * info_weight\n",
    "                                  + ok_words['freq_idx'] * freq_weight)\n",
    "    ok_words = ok_words.sort_values(['weighted_idx'], ascending=True)\n",
    "    \n",
    "    if verbose == True:\n",
    "        print(f'\\nWeighted combination (w_info={info_weight:.1f}, w_freq={freq_weight:.1f}):')\n",
    "        print(ok_words[['weighted_idx', 'info_idx', 'freq_idx']].head(5))\n",
    "    \n",
    "    if not verbose == 'quiet':\n",
    "        print('\\nRecommended word:')\n",
    "        print(ok_words.index[0])\n",
    "        print()\n",
    "    return ok_words.index[0]\n",
    "    \n",
    "# Shorthands to make entering results easier\n",
    "sh = ['grey', 'yellow', 'green']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Game loop\n",
    "Use the solver manually with Wordle in another browser window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "3 valid words.\n",
      "Top solution word peter has p_correct = 0.7063\n",
      "Pursuing solution.\n",
      "\n",
      "Weighted combination (w_info=0.2, w_freq=0.8):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "meter          -2.4         0        -3\n",
      "deter          -2.2         1        -3\n",
      "peter           0.4         2         0\n",
      "\n",
      "Recommended word:\n",
      "meter\n",
      "\n",
      "\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "Interrupted by user",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-71-7a924b79e2e5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     29\u001b[0m \u001b[0;31m#         print(b)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     30\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mauto_mode\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m             \u001b[0mword\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'Guess {i} (or type \"exit\", \"restart\"): '\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     32\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     33\u001b[0m             \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"Enter the word ({word}) in Wordle now.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/anaconda3/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    858\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    859\u001b[0m             )\n\u001b[0;32m--> 860\u001b[0;31m         return self._input_request(str(prompt),\n\u001b[0m\u001b[1;32m    861\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent_ident\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    862\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent_header\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/anaconda3/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36m_input_request\u001b[0;34m(self, prompt, ident, parent, password)\u001b[0m\n\u001b[1;32m    902\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    903\u001b[0m                 \u001b[0;31m# re-raise KeyboardInterrupt, to truncate traceback\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 904\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Interrupted by user\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    905\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    906\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Invalid Message:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexc_info\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: Interrupted by user"
     ]
    }
   ],
   "source": [
    "verbose = True\n",
    "auto_mode = False\n",
    "mode = 'hard'\n",
    "\n",
    "# How we sort the \"words\" dataframe determines which word is considered the \"best\" guess\n",
    "words = words.sort_values(['combined_score'], ascending=False)\n",
    "# Now that we've chosen the metric, a bit of prep for the solver\n",
    "words['info_idx'] = range(len(words))\n",
    "words['word'] = words.index\n",
    "words_array = np.array([np.array([c for c in w]) for w in words.index])\n",
    "\n",
    "while True:\n",
    "    # Reset allowed (yellow, green, or untried) letters\n",
    "    # Initially, set of all letters in the alphabet at each position\n",
    "    a = [set(az) for _ in range(5)]\n",
    "    # Reset necessary (green) letters\n",
    "    # Initially, empty set\n",
    "    b = set()\n",
    "    \n",
    "    quit = False\n",
    "    \n",
    "    clear_output(wait=True)\n",
    "    print('\\n=============\\n')\n",
    "    print('\\nWORDLE SOLVER')\n",
    "    word = find_clues_solutions(a, b, 0, verbose=verbose, mode=mode)\n",
    "    print()\n",
    "    for i in range(1, 7):\n",
    "#         print(a)\n",
    "#         print(b)\n",
    "        if not auto_mode:\n",
    "            word = input(f'Guess {i} (or type \"exit\", \"restart\"): ').lower()\n",
    "        else:\n",
    "            print(f\"Enter the word ({word}) in Wordle now.\")\n",
    "        if word == 'restart':\n",
    "            break\n",
    "        elif word == 'exit':\n",
    "            quit = True\n",
    "            break\n",
    "        elif not word in words.index:\n",
    "            input('Word not allowed. Press any key to restart.')\n",
    "            break\n",
    "        result = input('Result? (0=grey, 1=yellow, 2=green): ')\n",
    "        try:\n",
    "            result = [sh[int(s)] for s in result]\n",
    "        except:\n",
    "            input('Needs to be 5 digits e.g. 20021. Press any key to restart.')\n",
    "            break\n",
    "        a, b = use_clues(word, result, a, b)\n",
    "        clear_output(wait=True)\n",
    "        try:\n",
    "            word = find_clues_solutions(a, b, i, verbose=verbose, mode=mode)\n",
    "        except:\n",
    "            input('Impossible! Press any key to restart.')\n",
    "            break\n",
    "        print('')\n",
    "    \n",
    "    if quit:\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate the solver against all Wordle solution words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_guess(guess, solution):\n",
    "    assert len(solution) == 5\n",
    "    assert len(guess) == 5\n",
    "    response = ''\n",
    "    for i in range(5):\n",
    "        # Green\n",
    "        if guess[i] == solution[i]:\n",
    "            response += '2'\n",
    "        elif guess[i] in solution:\n",
    "            response += '1'\n",
    "        else:\n",
    "            response += '0'\n",
    "#     print(response)\n",
    "    return [sh[int(s)] for s in response]\n",
    "    \n",
    "def test_solver(solution, a, b, verbose=False, mode='hard'):\n",
    "    assert len(solution) == 5\n",
    "    guess = None\n",
    "    i = 0\n",
    "    while i < 20:\n",
    "        i += 1\n",
    "        guess = find_clues_solutions(a, b, i-1, verbose=verbose, mode=mode)\n",
    "        if guess == solution:\n",
    "#             print(f'Solved \"{solution}\" in {i} guesses.')\n",
    "            return i\n",
    "        result = test_guess(guess, solution)\n",
    "        a, b = use_clues(guess, result, a, b)\n",
    "    return 20"
   ]
  },
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      "Number of CPU cores: 16\n",
      "              "
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     "text": [
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "All task is done!\n"
     ]
    }
   ],
   "source": [
    "# How we sort the \"words\" dataframe determines which word is considered the \"best\" guess\n",
    "words = words.sort_values(['combined_score'], ascending=False)\n",
    "words['info_idx'] = range(len(words))\n",
    "words['word'] = words.index\n",
    "words_array = np.array([np.array([c for c in w]) for w in words.index])\n",
    "\n",
    "solutions = list(solutions)\n",
    "\n",
    "nprocs = mp.cpu_count()\n",
    "print(f\"Number of CPU cores: {nprocs}\")\n",
    "\n",
    "# Store solution test results here\n",
    "q_out = mp.Queue()\n",
    "\n",
    "# split a list into evenly sized chunks\n",
    "def chunks(l, n):\n",
    "    return [l[i:i+n] for i in range(0, len(l), n)]\n",
    "\n",
    "def do_job(job_id, data_slice, q):\n",
    "    print(' ', end='')\n",
    "    solution_test_results = dict()\n",
    "    for solution in tqdm(data_slice):\n",
    "#         clear_output(wait=True)\n",
    "        a = [set(az) for _ in range(5)]\n",
    "        b = set()\n",
    "        try:\n",
    "            result = test_solver(\n",
    "                solution, a, b, verbose='quiet', mode='hard')\n",
    "        except Exception as e:\n",
    "            print(e)\n",
    "            traceback.print_exc()\n",
    "            result = 0\n",
    "        solution_test_results[solution] = result\n",
    "#         print(f'    ({i+1} / {len(solutions)})')\n",
    "    q.put(solution_test_results)\n",
    "\n",
    "def dispatch_jobs(data, job_number):\n",
    "    total = len(data)\n",
    "    chunk_size = math.ceil(total / job_number)\n",
    "    slice = chunks(data, chunk_size)\n",
    "    jobs = []\n",
    "    for i, s in enumerate(slice):\n",
    "        j = mp.Process(target=do_job, args=(i, s, q_out))\n",
    "        jobs.append(j)\n",
    "    for j in jobs:\n",
    "        j.daemon = True\n",
    "        j.start()\n",
    "    \n",
    "    unsorted_result = [q_out.get() for j in jobs]\n",
    "    # we can concatenate and sort result by using the index\n",
    "    for j in jobs:\n",
    "       # p.join tells the process to wait until all jobs finished then exit, effectively cleaning up the process.\n",
    "       j.join()\n",
    "    # p.close terminate the process and tells the process not to accept any new job. \n",
    "       j.close()\n",
    "    print('All task is done!')\n",
    "    return unsorted_result\n",
    "\n",
    "test_results_list = dispatch_jobs(solutions, nprocs)\n",
    "solution_test_results = dict(ChainMap(*test_results_list))\n",
    "\n",
    "# solution_test_results = dict()\n",
    "\n",
    "# for i, solution in enumerate(solutions):\n",
    "#     clear_output(wait=True)\n",
    "#     a = [set(az) for _ in range(5)]\n",
    "#     b = set()\n",
    "#     try:\n",
    "#         solution_test_results[solution] = test_solver(\n",
    "#             solution, a, b, verbose='quiet', mode='easy')\n",
    "#     except:\n",
    "#         solution_test_results[solution] = 0\n",
    "#     print(f'    ({i+1} / {len(solutions)})')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "98.01% solved in 6 guesses or less.\n",
      "3.90 mean guesses.\n",
      "4.00 median guess.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
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    },
    {
     "data": {
      "image/png": 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jEEnOBKiqZ5K8k95rVtur6t6xDraPJOcC7wMeqarHDvvjtxB3SdLeWjnnLknqY9wlqUHGXZIaZNwlqUHGXZIa9P/6yEnQ8AJbnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame(solution_test_results, index=['guesses']).T\n",
    "\n",
    "p_solved = 1 - len(df.query('(guesses > 6) | (guesses == 0)')) / len(df)\n",
    "print(f'{100*p_solved:.2f}% solved in 6 guesses or less.')\n",
    "print(f'{df.guesses.mean():.2f} mean guesses.')\n",
    "print(f'{df.guesses.median():.2f} median guess.')\n",
    "\n",
    "df['guesses'].value_counts().sort_index().plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['wooer'], dtype=object)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What words did the model *not* guess within 6?\n",
    "df.query('guesses > 6').index.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inspect a specific word solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "12974 valid words.\n",
      "Top solution word about has p_correct = 0.0194\n",
      "Pursuing info gain rather than solution.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "tares             0         0      5701\n",
      "lares             1         1      5822\n",
      "cares             2         2      1263\n",
      "pares             3         3      4821\n",
      "dares             4         4      3107\n",
      "\n",
      "Recommended word:\n",
      "tares\n",
      "\n",
      "\n",
      "282 valid words.\n",
      "Top solution word order has p_correct = 0.1477\n",
      "Pursuing info gain rather than solution.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "diner             0         0      1781\n",
      "cider             1         1      1979\n",
      "oiler             2         2      4668\n",
      "doper             3         3      8032\n",
      "doner             4         4      5951\n",
      "\n",
      "Recommended word:\n",
      "diner\n",
      "\n",
      "\n",
      "94 valid words.\n",
      "Top solution word power has p_correct = 0.2606\n",
      "Pursuing info gain rather than solution.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "coyer             0         0      7880\n",
      "foyer             1         1      2420\n",
      "loper             2         2      5445\n",
      "coper             3         3      7423\n",
      "power             4         4        48\n",
      "\n",
      "Recommended word:\n",
      "coyer\n",
      "\n",
      "\n",
      "28 valid words.\n",
      "Top solution word power has p_correct = 0.4734\n",
      "Pursuing info gain rather than solution.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "powre             0         0     11210\n",
      "power             1         1        48\n",
      "mower             2         2      2052\n",
      "lower             3         3       208\n",
      "rowme             4         4     11136\n",
      "\n",
      "Recommended word:\n",
      "powre\n",
      "\n",
      "\n",
      "2 valid words.\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-46-8053e7abf71d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maz\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mtest_solver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'wooer'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'easy'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-41-06b659b51dfc>\u001b[0m in \u001b[0;36mtest_solver\u001b[0;34m(solution, a, b, verbose, mode)\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0mi\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m         \u001b[0mguess\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfind_clues_solutions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mverbose\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mguess\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0msolution\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0;31m#             print(f'Solved \"{solution}\" in {i} guesses.')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-38-1fb81ab45c5e>\u001b[0m in \u001b[0;36mfind_clues_solutions\u001b[0;34m(a, b, guess_num, verbose, mode)\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;31m# How likely is it that the top potential solution word is correct?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m     \u001b[0;31m# (Much more frequent than other solution words)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m     \u001b[0mp_correct\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mok_words\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'freq'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mok_words\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'freq'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     59\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mverbose\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'quiet'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'Top solution word {ok_words[\"freq\"].astype(float).idxmax()} has p_correct = {p_correct:.4f}'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "a = [set(az) for _ in range(5)]\n",
    "b = set()\n",
    "test_solver('wooer', a, b, verbose=True, mode='easy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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