wordle-explore.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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install numpy pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import string\n",
    "from collections import defaultdict\n",
    "import math\n",
    "from IPython.display import clear_output\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
    "\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": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 5 most frequent letters overall:\n",
      "('e', 6693.034610096232)\n",
      "('s', 6686.999311356014)\n",
      "('a', 6011.660721171858)\n",
      "('o', 4458.173086193878)\n",
      "('r', 4179.472228612864)\n",
      "\n",
      "Most frequent letter for positions 1 to 5:\n",
      "('s', 1570.7999064093765)\n",
      "('a', 2269.250225895344)\n",
      "('a', 1242.4464158907488)\n",
      "('e', 2337.3298122673855)\n",
      "('s', 3968.6397843665927)\n"
     ]
    }
   ],
   "source": [
    "# Letter frequency\n",
    "letter_freq = defaultdict(int)\n",
    "for word, word_freq in words[['freq']].itertuples():\n",
    "    for char in word:\n",
    "#         Many ways to weight this:\n",
    "#         letter_freq[char] += w['freq']\n",
    "#         letter_freq[char] += 1\n",
    "        letter_freq[char] += 1 + word_freq\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 words[['freq']].itertuples():\n",
    "    for i, char in enumerate(word):\n",
    "#         Many ways to weight this:\n",
    "#         letter_freq[char] += w['freq']\n",
    "#         letter_freq[char] += 1\n",
    "        letter_pos_freq[i][char] += 1 + word_freq\n",
    "\n",
    "sorted_pos_letters = [sorted(letter_pos_freq[i].items(), key=lambda x: -x[1]) for i in range(5)]\n",
    "print('\\nMost frequent letter for positions 1 to 5:')\n",
    "print(*[s[0] for s in sorted_pos_letters], sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>freq</th>\n",
       "      <th>freq_idx</th>\n",
       "      <th>no_position_score</th>\n",
       "      <th>per_position_score</th>\n",
       "      <th>per_pos_score_repeats</th>\n",
       "      <th>combined_score</th>\n",
       "      <th>anti_pos_score</th>\n",
       "      <th>less_pos_score</th>\n",
       "      <th>more_pos_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>tares</th>\n",
       "      <td>71332</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>5701</td>\n",
       "      <td>26886.231258</td>\n",
       "      <td>10599.749713</td>\n",
       "      <td>10599.749713</td>\n",
       "      <td>0.974690</td>\n",
       "      <td>0.711677</td>\n",
       "      <td>1.454299</td>\n",
       "      <td>2.939544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lares</th>\n",
       "      <td>66326</td>\n",
       "      <td>0.000054</td>\n",
       "      <td>5822</td>\n",
       "      <td>26956.804900</td>\n",
       "      <td>10358.867491</td>\n",
       "      <td>10358.867491</td>\n",
       "      <td>0.964698</td>\n",
       "      <td>0.719820</td>\n",
       "      <td>1.445566</td>\n",
       "      <td>2.897059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cares</th>\n",
       "      <td>4757269</td>\n",
       "      <td>0.003878</td>\n",
       "      <td>1263</td>\n",
       "      <td>25608.583821</td>\n",
       "      <td>10705.050363</td>\n",
       "      <td>10705.050363</td>\n",
       "      <td>0.956817</td>\n",
       "      <td>0.663635</td>\n",
       "      <td>1.413635</td>\n",
       "      <td>2.913635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pares</th>\n",
       "      <td>136717</td>\n",
       "      <td>0.000111</td>\n",
       "      <td>4821</td>\n",
       "      <td>25596.550158</td>\n",
       "      <td>10641.977017</td>\n",
       "      <td>10641.977017</td>\n",
       "      <td>0.953657</td>\n",
       "      <td>0.664679</td>\n",
       "      <td>1.410260</td>\n",
       "      <td>2.901422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dares</th>\n",
       "      <td>526302</td>\n",
       "      <td>0.000429</td>\n",
       "      <td>3107</td>\n",
       "      <td>26033.312191</td>\n",
       "      <td>10465.515922</td>\n",
       "      <td>10465.515922</td>\n",
       "      <td>0.953206</td>\n",
       "      <td>0.684382</td>\n",
       "      <td>1.417600</td>\n",
       "      <td>2.884036</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count      freq  freq_idx  no_position_score  per_position_score  \\\n",
       "tares    71332  0.000058      5701       26886.231258        10599.749713   \n",
       "lares    66326  0.000054      5822       26956.804900        10358.867491   \n",
       "cares  4757269  0.003878      1263       25608.583821        10705.050363   \n",
       "pares   136717  0.000111      4821       25596.550158        10641.977017   \n",
       "dares   526302  0.000429      3107       26033.312191        10465.515922   \n",
       "\n",
       "       per_pos_score_repeats  combined_score  anti_pos_score  less_pos_score  \\\n",
       "tares           10599.749713        0.974690        0.711677        1.454299   \n",
       "lares           10358.867491        0.964698        0.719820        1.445566   \n",
       "cares           10705.050363        0.956817        0.663635        1.413635   \n",
       "pares           10641.977017        0.953657        0.664679        1.410260   \n",
       "dares           10465.515922        0.953206        0.684382        1.417600   \n",
       "\n",
       "       more_pos_score  \n",
       "tares        2.939544  \n",
       "lares        2.897059  \n",
       "cares        2.913635  \n",
       "pares        2.901422  \n",
       "dares        2.884036  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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",
    "# Maximizing letter_pos_freq (most frequent letters, per position)\n",
    "# Repeated letters OK\n",
    "scores = []\n",
    "for word in words.index:\n",
    "    score = 0\n",
    "    for i, char in enumerate(word):\n",
    "        score += letter_pos_freq[i][char]\n",
    "    scores.append(score)\n",
    "words['per_pos_score_repeats'] = 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",
    "words = words.sort_values(['combined_score'], ascending=False)\n",
    "\n",
    "# We can try some different combinations\n",
    "words['anti_pos_score'] = (\n",
    "    (words['no_position_score'] / words['no_position_score'].max())\n",
    "    - 0.25 * (words['per_position_score'] / words['per_position_score'].max()))\n",
    "\n",
    "words['less_pos_score'] = (\n",
    "    (words['no_position_score'] / words['no_position_score'].max())\n",
    "    + 0.5 * (words['per_position_score'] / words['per_position_score'].max()))\n",
    "\n",
    "words['more_pos_score'] = (\n",
    "    (words['no_position_score'] / words['no_position_score'].max())\n",
    "    + 2 * (words['per_position_score'] / words['per_position_score'].max()))\n",
    "\n",
    "words = words.sort_values(['combined_score'], ascending=False)\n",
    "print('Best starting words (sorted by a scoring metric):')\n",
    "words.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Solver (hard mode)\n",
    "This 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",
    "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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update constraints based on a new clue\n",
    "def use_clues(word, result):\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",
    "\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):\n",
    "    ok_words = find_ok_words(a, b)\n",
    "    \n",
    "    if not verbose=='quiet':\n",
    "        print()\n",
    "        print(len(ok_words), 'valid words.')\n",
    "    \n",
    "    # Get the most common word in ok_words\n",
    "    ok_words = words[words['word'].isin(ok_words)]\n",
    "\n",
    "    # Balance information gain with how common the word is\n",
    "    # Increasingly favor common words\n",
    "    # The scalar in the next line is important. 0.3 is good.\n",
    "    freq_weight = min(0.3 * guess_num, 1)\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": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=============\n",
      "\n",
      "\n",
      "WORDLE SOLVER\n",
      "\n",
      "12974 valid words.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "tares           0.0         0      5701\n",
      "lares           1.0         1      5822\n",
      "cares           2.0         2      1263\n",
      "pares           3.0         3      4821\n",
      "dares           4.0         4      3107\n",
      "\n",
      "Recommended word:\n",
      "tares\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "verbose = True\n",
    "auto_mode = False\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",
    "    print('\\n=============\\n')\n",
    "    print('\\nWORDLE SOLVER')\n",
    "    word = find_clues_solutions(a, b, 0, verbose=verbose)\n",
    "    print()\n",
    "    for i in range(1, 7):\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",
    "            clear_output(wait=False)\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('Error parsing result. It should be 5 numbers e.g. 20010. Press any key to restart.')\n",
    "            clear_output(wait=False)\n",
    "            break\n",
    "        clear_output(wait=False)\n",
    "        use_clues(word, result)\n",
    "        try:\n",
    "            word = find_clues_solutions(a, b, i, verbose=verbose)\n",
    "        except:\n",
    "            input('Impossible! Press any key to restart.')\n",
    "            clear_output(wait=False)\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": 46,
   "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):\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)\n",
    "        if guess == solution:\n",
    "            print(f'Solved \"{solution}\" in {i} guesses.')\n",
    "            return i\n",
    "        result = test_guess(guess, solution)\n",
    "        use_clues(guess, result)\n",
    "    return 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved \"trade\" in 2 guesses.\n",
      "    (2309 / 2309)\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",
    "solution_test_results = dict()\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')\n",
    "    except:\n",
    "        solution_test_results[solution] = 0\n",
    "    print(f'    ({i+1} / {len(solutions)})')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "97.79% solved in 6 guesses or less.\n",
      "3.94 mean guesses.\n",
      "4.00 median guess.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hkrypqv5j3HMMIsn5AFW1P8kb6H3Pak9V3TXWwY6Q5GLgrcCDVfXwCX/+FuIuSTpcK+fcJUl9jLskNci4S1KDjLskNci4S1KD/h8qPknSSp8MxwAAAABJRU5ErkJggg==\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": 61,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>guesses</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>dolly</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hound</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dopey</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>biddy</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woozy</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>waver</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gusty</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gazer</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>shave</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dilly</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tripe</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ferry</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>viper</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hatch</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>golly</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>crave</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>parer</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ember</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wooer</th>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wafer</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>brace</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>waxen</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stoop</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>craze</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>swill</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>expel</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gawky</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>frown</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>saner</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gummy</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>goner</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ninny</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>giver</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stung</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>surer</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mound</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hater</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sappy</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cramp</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mammy</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>folly</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tatty</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hover</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>graze</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cower</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stump</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vaunt</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>latch</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stalk</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ladle</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freed</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       guesses\n",
       "dolly        7\n",
       "hound        8\n",
       "dopey        7\n",
       "biddy        7\n",
       "woozy        8\n",
       "waver        8\n",
       "gusty        7\n",
       "gazer        7\n",
       "shave        7\n",
       "dilly        8\n",
       "tripe        7\n",
       "ferry        7\n",
       "viper        7\n",
       "hatch        7\n",
       "golly        9\n",
       "crave        7\n",
       "parer        7\n",
       "ember        7\n",
       "wooer        9\n",
       "wafer        7\n",
       "brace        7\n",
       "waxen        7\n",
       "stoop        7\n",
       "craze        8\n",
       "swill        7\n",
       "expel        7\n",
       "gawky        8\n",
       "frown        7\n",
       "saner        8\n",
       "gummy        8\n",
       "goner        8\n",
       "ninny        7\n",
       "giver        7\n",
       "stung        7\n",
       "surer        7\n",
       "mound        7\n",
       "hater        7\n",
       "sappy        8\n",
       "cramp        7\n",
       "mammy        7\n",
       "folly        8\n",
       "tatty        7\n",
       "hover        7\n",
       "graze        7\n",
       "cower        7\n",
       "stump        7\n",
       "vaunt        7\n",
       "latch        8\n",
       "stalk        7\n",
       "ladle        7\n",
       "freed        7"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What words did the model not guess within 6?\n",
    "df.query('guesses > 6')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inspect a specific word solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "12974 valid words.\n",
      "\n",
      "Weighted combination (w_info=1.0, w_freq=0.0):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "tares           0.0         0      5701\n",
      "lares           1.0         1      5822\n",
      "cares           2.0         2      1263\n",
      "pares           3.0         3      4821\n",
      "dares           4.0         4      3107\n",
      "\n",
      "Recommended word:\n",
      "tares\n",
      "\n",
      "\n",
      "814 valid words.\n",
      "\n",
      "Weighted combination (w_info=0.7, w_freq=0.3):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "coins         763.4       833       601\n",
      "louis         803.6      1001       343\n",
      "lions        1142.2      1189      1033\n",
      "coils        1157.0       755      2095\n",
      "bonus        1236.8      1577       443\n",
      "\n",
      "Recommended word:\n",
      "coins\n",
      "\n",
      "\n",
      "17 valid words.\n",
      "\n",
      "Weighted combination (w_info=0.4, w_freq=0.6):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "bucks        2700.8      5108      1096\n",
      "ducks        2857.6      4975      1446\n",
      "fucks        3295.2      5889      1566\n",
      "mucus        4556.4      6918      2982\n",
      "pucks        4571.0      4958      4313\n",
      "\n",
      "Recommended word:\n",
      "bucks\n",
      "\n",
      "\n",
      "2 valid words.\n",
      "\n",
      "Weighted combination (w_info=0.1, w_freq=0.9):\n",
      "       weighted_idx  info_idx  freq_idx\n",
      "mucus        3375.6      6918      2982\n",
      "fucus        6256.3      7618      6105\n",
      "\n",
      "Recommended word:\n",
      "mucus\n",
      "\n",
      "Solved \"mucus\" in 4 guesses.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [set(az) for _ in range(5)]\n",
    "b = set()\n",
    "test_solver('mucus', a, b, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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