Wordle Solver

The most comprehensive, exhaustive, parameterized command-line wordle (https://www.powerlanguage.co.uk/wordle/) solver. Wordle is a really popular game made viral by it's inscrutable and quirky emoticon-based game description.

The solver boasts a 99.35%+ accuracy on the 8636 valid 5-letter words. Features:

• Supports 4 modes: play, show (to show a solution for a specific word), solve (to solve a puzzle online) and eval (evaluate the performance)
• Deterministic
• Highest accuracy of all solutions evaluated
• Fully tested
• Latency ~0.26s per run Current dictionary used is the valid Scrabble dictionary.

Solver’s attempt to solve the Jan 10, 2022 wordle for the word query:

⬛🟨⬛⬛🟨 AROSE
⬛🟩⬛⬛⬛ TUMID
⬛⬛🟨⬛⬛ GLYPH
🟩🟩🟩🟩🟩 QUERY

Algorithm

With the settings for non-strict play, using positional

• Find all candidates that fit the criteria
• Amongst the valid candidates, compute a distribution of letters at each position
• Find a word from all valid guesses which optimizes sum(P(letter at pos i)) + 0.5 * sum(P letter not at pos i)
• Repeat

The 56 failure cases are sakes, mooed, jived, wanes, jocks, minks, wades, jaded, zoner, joker, wived, jakes, mozos, goxes, vills, rover, zooks, cozes, jibes, wakes, hajes, joked, sinhs, zaxes, yaffs, hiker, bases, moved, bises, zills, hided, eaved, vined, surfs, jiber, gibed, dozer, fuzed, mixed, boxed, waxes, waves, vomer, egged, mazed, pests, hived, socks, fazes, vests, jibed, mewed, hazes, sooks, woods, sinks For all these words, there are 2-5 candidate words left at the last guess, and with a random last guess, there is a probability of guessing these too.

Usage

Play it yourself

python main.py -m play

Guess? tares
TARES
⬛🟩🟨⬛⬛
Guess? unlit
UNLIT
⬛⬛⬛⬛⬛
Guess? raver
RAVER
🟨🟩🟩⬛🟩
Guess? favor
FAVOR
🟩🟩🟩🟩🟩
Solved! - favor

Solve for an unknown word

python main.py -m solve

Try the word [TARES]. There are 8636 possible words: ['aahed', 'aalii', 'aargh', 'abaca', 'abaci']...
How did it do (0=⬛, 1=🟨, 2=🟩) e.g. 00000? 00000
Try the word [NOILY]. There are 575 possible words: ['biddy', 'biffy', 'bifid', 'bigly', 'bijou']...
How did it do (0=⬛, 1=🟨, 2=🟩) e.g. 00000? 02002
Try the word [DHOBI]. There are 39 possible words: ['bobby', 'boggy', 'booby', 'boogy', 'boomy']...
How did it do (0=⬛, 1=🟨, 2=🟩) e.g. 00000? 20100
Try the word [DODGY]. There are 3 possible words: ['dodgy', 'doggy', 'dowdy']...
How did it do (0=⬛, 1=🟨, 2=🟩) e.g. 00000? 22122
Try the word [DOGGY]. There are 1 possible words: ['doggy']...
How did it do (0=⬛, 1=🟨, 2=🟩) e.g. 00000? 22222
Solved! = doggy

Show a solution for a specific word

python main.py -m show -w oozed

Word [OOZED]
Choosing [tares]. Total 8636 candidates: ['aahed', 'aalii', 'aargh', 'abaca', 'abaci']...
TARES
⬛⬛⬛🟩⬛
Choosing [coled]. Total 288 candidates: ['bedel', 'bedew', 'bevel', 'bezel', 'bided']...
COLED
⬛🟩⬛🟩🟩
Choosing [howdy]. Total 31 candidates: ['boded', 'boned', 'booed', 'bowed', 'boxed']...
HOWDY
⬛🟩⬛🟨⬛
Choosing [bipod]. Total 16 candidates: ['boded', 'boned', 'booed', 'boxed', 'domed']...
BIPOD
⬛⬛⬛🟨🟩
Choosing [dozen]. Total 8 candidates: ['domed', 'dozed', 'foxed', 'joked', 'mooed']...
DOZEN
🟨🟩🟩🟩⬛
Choosing [oozed]. Total 1 candidates: ['oozed']...
OOZED
🟩🟩🟩🟩🟩
Solved! - oozed
Woohoo! Solver solved it in 6 guesses!

Evaluate its performance

python main.py -m eval -k 1000

Evaluating on 1000 words
k=10:	Failed: 1	Accuracy:90.00%	Avg Time: 0.258s
k=20:	Failed: 1	Accuracy:95.00%	Avg Time: 0.250s
k=30:	Failed: 1	Accuracy:96.67%	Avg Time: 0.249s
k=40:	Failed: 1	Accuracy:97.50%	Avg Time: 0.244s
k=50:	Failed: 1	Accuracy:98.00%	Avg Time: 0.239s
...
k=970:	Failed: 10	Accuracy:98.97%	Avg Time: 0.236s
k=980:	Failed: 10	Accuracy:98.98%	Avg Time: 0.236s
k=990:	Failed: 10	Accuracy:98.99%	Avg Time: 0.236s
Failed on: ['jived', 'hides', 'razer', 'zooks', 'jills', 'gibed', 'wises', 'yipes', 'wipes', 'sises']
Distribution of remaining candidates: [(4, 5), (3, 3), (2, 1), (5, 1)]
K=999:	Failed: 10	Accuracy:99.00%

Run Tests

python -m unittest runs the entire test suite.

Evaluation

Using a dictionary of scrabble words, there are 172,819 total words and around 5% of them are exactly 5 letters long (8,636). The algorithm devised achieves a 99.28% success rate at guessing the right word, failing to get the correct the answer for 62 words.

Other settings achieved:

• Global character frequency heuristic: Couldn't solve for 133 out of 1000 random samples (86.7% Success rate)
• Conditional character frequency heuristic, on candidates left: Couldn't solve for 100 out of 1000 random samples (90.0% Success rate)
• Non-strict solution: Couldn't solve for 46 out of 1000 random samples (95.4% Success rate)
• Position-aware frequency heuristic + bug fixes: Couldn't solve for 9 out of 1000 random samples (99.1% Success rate)

Future Work

• Support passing in solver settings through command line, including the weight of NON_POS_WEIGHT
• Support passing in a custom dictionary through settings
• Expose customizable number of letters in the word (N) and MAX_GUESSES.