#wordle-solver #wordle #puzzle-solver #solver #guess #game #puzzle

rs-wordle-solver

A library for solving Wordle-style puzzles. It provides multiple guessing algorithms, as well as building blocks for implementing your own Wordle solving algorithms.

8 releases (3 stable)

1.2.0 May 1, 2024
1.1.0 Mar 17, 2024
0.3.0 Nov 22, 2023
0.2.0 May 20, 2023
0.1.1 Apr 3, 2022

#114 in Algorithms

MIT/Apache

135KB
2K SLoC

rs-wordle-solver

An automated solving library for the popular game: Wordle

How to use it?

See the docs.

Releases

1.2.0

The main goal of this release is to support changing the GuessFrom value mid-game without creating a whole new Guesser. The GuessFrom value provided in the constructor now acts as the default value when not explicitly specified.

  • Add Guesser::select_next_guess_from to select a guess from a specific GuessFrom list.
  • Add MaxScoreGuesser::select_top_n_guesses_from to select the top guesses from a specific list.
  • Add MaxScoreGuesser::compute_scores_if_needed_from for caching the scores from a specific list.

1.1.0

  • Add MaxScoreGuesser::get_or_compute_scores to extract just the precomputed word scores.
  • Add MaxScoreGuesser::with_scores to use extracted/otherwise precomputed word scores.
  • Change MaxScoreGuesser::with_parallelisation_limit to a builder function that accepts and returns Self, instead of being an alternative constructor.

1.0.0

  • Move score precomputation from MaxEliminationsScorer and MaxComboEliminationsScorer construction into MaxScoreGuesser.
  • Score precomputation is now lazy unless you call MaxScoreGuesser::compute_scores_if_unknown.
  • The parallelisation limit can now be user-modified, and is applied more consistently. The default limit has been lowered.
  • Several constructors take an owned object instead of a reference where they needed to clone that object anyway.
  • MaxScoreGuesser tries to prioritise possible words when breaking ties.
  • Many other breaking changes.

0.3.0

  • Add MaxEliminationsScorer::from_first_guess_eliminations and ::first_guess_eliminations. This is especially useful for efficiently (de)serializing the important bits of this struct.
  • Align WordBank::from_reader and ::from_iterator implementations.

0.2.0

  • Enable parallelization with Rayon

    • Parallelize key parts of MaxEliminationsScorer::new
    • Parallelize key parts of MaxComboEliminationsScorer::new
    • Parallelize MaxScoreGuesser::select_next_guess and ::select_top_n_guesses
  • Make WordScorer::score_word take &self instead of &mut self

  • Fix bugs in MaxComboEliminationsScorer to improve its results

Solve efficiency benchmarks

Different guessing algorithms have been benchmarked against a few word lists:

  • wordle-answers.txt: this list is all the answer words from Wordle before it was purchased by the New York Times.

  • improved-words.txt: this list combines all 5-letter words from the Corncob list of more than 58,000 English words, the MIT 10000 English words list, and any remaining Wordle answer words. This is often used instead of the full wordle word list, as many allowed Wordle words seem to be somewhat nonsensical.

Most algorithms have been benchmarked against the whole improved words list. Some algorithms run in two configurations:

  1. guessing from PossibleWords, i.e. only guessing words that are still possible. This is equivalent to Wordle's "hard" mode.
  2. guessing from AllUnguessedWords, including words that can't be the answer. This is usually better as the algorithms are able to eliminate more words faster.

RandomGuesser

This selects randomly from the words that are still possible. It's a baseline worst-case selection. Any other algorithm should be better than this.

One sample benchmark:

Num guesses Num games
1 1
2 106
3 816
4 1628
5 1248
6 518
7 180
8 67
9 28
10 7
11 2
12 1

Average number of guesses: 4.49 +/- 1.26

MaxUniqueLetterFrequencyScorer

This is a fairly naive selector. It selects the word that maximizes the sum of the frequency of unique letters that have not yet been guessed.

GuessFrom::PossibleWords

Num guesses Num games
1 1
2 137
3 1248
4 1831
5 830
6 321
7 135
8 63
9 26
10 7
11 1
12 1
13 1

Average number of guesses: 4.17 +/- 1.24 Average duration per game: 0.224ms +/- 0.058ms

GuessFrom::AllUnguessedWords

Num guesses Num games
1 1
2 32
3 1045
4 2268
5 1037
6 194
7 23
8 2

Average number of guesses: 4.08 +/- 0.83 Average duration per game: 0.491ms +/- 0.114ms

LocatedLettersScorer

This selects the word that maximizes a score, based on both the presence and the the location of that letter in the possible words. The score is computed for each letter and then summed. Each letter is scored as follows.

For each letter, score:

  • 1 point if the letter must be in this location.

  • 1 point for every word with this letter in this place if the letter's location is not yet known, and this is a new location for the letter.

  • If this letter is completely new:

    • If this letter has not yet been scored in this word:

      • 1 point for every possible word with this letter in the same place.
      • 1 point for every possible word with this letter in another place.
    • Else:

      • 1 point for every possible word with this letter in the same place.

GuessFrom::PossibleWords

Num guesses Num games
1 1
2 180
3 1448
4 1836
5 720
6 255
7 100
8 44
9 12
10 4
11 1
12 1

Average number of guesses: 4.00 +/- 1.15 Average duration per game: 0.211ms +/- 0.040ms

GuessFrom::AllUnguessedWords

Num guesses Num games
1 1
2 128
3 1599
4 1924
5 638
6 199
7 75
8 25
9 9
10 2
11 1
12 1

Average number of guesses: 3.91 +/- 1.04 Average duration per game: 0.491ms +/- 0.117ms

MaxApproximateEliminationsScorer

This selects the word that is expected to eliminate approximately the most other words. For each letter, the expected number of eliminations is computed for each possible state:

  • {expected number of eliminated words if in state} * {fraction of possible words matching this state}

So for example, with the words ["could", "match", "coast"], these would be computed as follows for the letter c in could:

  • if correct: match is removed, so: 1 * (2/3)
  • if present not here: could and coast are removed, so: 2 * (1/3)
  • if not present: all are removed, so: 3 _ (0/3) _(note: this expectation is skipped if this letter* has already been checked at another location).

These per-letter expectations are then summed together to get the expectation value for the word. Approximating the expected eliminations in this way is cheap to compute, but slightly less accurate, and therefore less effective, than using the precise counts computed by MaxEliminationsScorer.

GuessFrom::PossibleWords

Num guesses Num games
1 1
2 180
3 1430
4 1846
5 721
6 258
7 105
8 41
9 13
10 5
11 1
12 1

Average number of guesses: 4.01 +/- 1.15 Average duration per game: 0.210ms +/- 0.041ms

GuessFrom::AllUnguessedWords

Num guesses Num games
1 1
2 73
3 1331
4 2486
5 655
6 53
7 3

Average number of guesses: 3.85 +/- 0.72 Average duration per game: 0.503ms +/- 0.106ms

MaxEliminationsScorer

This probabilistically calculates the expectation value for how many words will be eliminated by each guess, and chooses the word that eliminates the most other guesses. This is relatively expensive to compute, so it precomputes as much as possible when the scorer is first created. On my machine, constructing the scorer with the improved-words list takes about 120ms, but this enables each subsequent game to be played in about 4ms.

GuessFrom::PossibleWords

Num guesses Num games
1 1
2 180
3 1476
4 1928
5 653
6 223
7 93
8 33
9 10
10 4
11 1

Average number of guesses: 3.95 +/- 1.10 Average duration per game: 0.342ms +/- 0.190ms

GuessFrom::AllUnguessedWords

Num guesses Num games
1 1
2 73
3 1616
4 2474
5 419
6 19

Average number of guesses: 3.72 +/- 0.67 Average duration per game: 3.578ms +/- 2.608ms

MaxComboEliminationsScorer

This extends the MaxEliminationsScorer to choose the word that should maximize the number of eliminated words across the next two guesses, as long as there are more than a specifiable limit of possible words. We'll call this the combo limit. Once there are fewer than the combo limit possible words left, this falls back to the MaxEliminationsScorer behavior.

The theory behind this scorer is that, since most words take at least 3 guesses, the scorer should try to eliminate the most possible words collectively in the first two guesses. This could perform differently from choosing the best individual word per round, as is done in MaxEliminationsScorer.

This is extremely expensive to compute, as it scales in approximately O(n3) where n is the number of words in the word bank. Computing the scores for the first guess with 4600 words takes about 2.5 minutes using PossibleWords, and 14 minutes using AllPossibleWords.

Combo limit: 256 and GuessFrom::PossibleWords:

Num guesses Num games
1 1
2 148
3 1508
4 2034
5 617
6 179
7 75
8 27
9 9
10 2
11 2

Average number of guesses: 3.91 +/- 1.03 Average duration per game: 40.549ms +/- 84.745ms

Combo limit: 256 and GuessFrom::AllUnguessedWords:

Num guesses Num games
1 1
2 83
3 1587
4 2556
5 353
6 22

Average number of guesses: 3.70 +/- 0.65 Average duration per game: 6111.912ms +/- 23946.495ms

Speed benchmarks

RandomGuesser

test bench_guess_random_improved_words                             ... bench:     134,544 ns/iter (+/- 13,317)
test bench_guess_random_wordle_words                               ... bench:     360,913 ns/iter (+/- 48,680)

MaxUniqueLetterFrequencyScorer

test bench_unique_letters_improved_words                           ... bench:   1,572,994 ns/iter (+/- 516,087)

LocatedLettersScorer

test bench_located_letters_improved_words                          ... bench:   1,575,697 ns/iter (+/- 512,853)

MaxApproximateEliminationsScorer

test bench_max_approximate_eliminations_improved_words             ... bench:   1,595,036 ns/iter (+/- 839,135)

MaxEliminationsScorer

test bench_max_eliminations_scorer_precompute_improved_words       ... bench: 404,998,819 ns/iter (+/- 7,069,306)
test bench_max_eliminations_scorer_with_precomputed_improved_words ... bench:  10,699,991 ns/iter (+/- 10,244,686)

MaxComboEliminationsScorer

Precompute on improved words takes roughly: 41 minutes (guess from all words) or 3.5 minutes (guess from possible words) Solving a single word takes roughly: 10 seconds (guess from all words) or 0.16 seconds (guess from possible words)

Dependencies

~2MB
~34K SLoC