Wordle

Pyrdle (pronounced purr-dul) is Wordle implemented in Python.

Contributions welcome, but I don't have a ton of interest in providing support on this code, so use at your own risk.

Install and Play

$ pip install pyrdle
$ wordle

Use --help to see how to set the game to have a different number of letters, different number of guesses, or to use a different language.

Notes, See Also, and Acknowledgements

• The english word list is from https://pypi.org/project/english-words/. This has some weird stuff missing from it.
• The german word list comes from the Leibniz-Institute für Deutsche Sprache
• An implementation of Wordle in R: https://github.com/coolbutuseless/wordle
• A tiny Wordle guessing companion in Python https://pypi.org/project/pywordle/

Why We're Really Here: to Ruin Wordle

I originally wrote this after talking to @scolby33 and @deoxys314 because I wanted to write an algorithm to play Wordle for me. I started by creating a way of simulating a game, then realized there were lots of ways to play, so naturally I wanted to be able to figure which was best.

This repository assesses two metrics about each algorithm:

1. Success: how many of the words of the given length and number of guesses can it successfully solve?
2. Efficiency: what's the average number of guesses needed over all successful words?

Later, this repository will run multiple trials in order to assign confidence intervals for success and quality for randomized algorithms.

Strategies

This repository is a playground for implementing new solve strategies. Feel free to send a PR with your own (just subclass the Player class)!

Terminology:

1. Perfect guess: a guess that uses all previous information available, including knowledge about correct positions, unused letters, and used letters

Initial Fixed Guesses with Successive Greedy Choices

This algorithm takes a list of one, two, three, etc. initial guesses and always does them in order. This strategy lets you maximize the number of unique letters you can get information (e.g., if you pick three words, you can potentially get information about 15 letters in the standard 5-column variant of the game). However, this strategy sacrifices the positional information learned during these guesses as they are not used.

After the initial guesses, the algorithm tabulates all the constraints it learned (e.g., which letters are in the right position, which letters are present but in the wrong position, and what letters are not present). It then reads through the dictionary and picks the first word that matches all the constraints. If this isn't the winner, it updates the constraints and continues. This works quite well!

The obvious follow-up questions are:

1. How often does this work?
2. How many initial words do I need?
3. What are the best words?
4. Can this algorithm be improved?

The answer to 4 is yes: rather than picking just the first word, you can rank all the remaining words by "entropy" and pick the highest one. But now let's look at the other questions for different possible 1, 2, and 3-word fixed initial guesses. Each word is given an entropy score by first calculating the letter frequencies across all words of the given length then performing a weighted sum of the unique letters in a word based on their frequencies. Therefore, words containing a larger variety of frequent letters get the highest entropy scores.

One Fixed Guess

For each of the ~3.5 5-letter words in the English dictionary, I chose that word as the initial word, then ran the fixed guess with successive greedy choices algorithm for all possible Wordle games starting with all words. Then I calculated the number of games where the algorithm was successful. The following chart shows entropy score of each initial guess vs. the percentage success rate across all games on all words. I was expecting a weak linear relation between score and success, but there almost isn't one at all. It turns out, if you're a perfect guesser, then Wordle is just too easy most of the time. I bet that the few failures were due to the naïveté of the algorithm, which could be improved the way I described above.

Three Fixed Guesses

We actually got into this whole thing because we thought that we needed three letters to start it off. Mamma Hoyt said she had picked Ariel, thump, and gowns as her initial guesses. I hadn't even considered doing this at the moment, so I was off to the races. My sister came up with the same idea, and had chosen weary, ghost, lions.

This strategy involves deterministically guessing three words that cover a wide variety of vowels and consonants. For example, (lunch, metro, daisy) covers all five vowels and 10 different consonants.

It's pretty likely that with these choices, you will be able to deterministically solve for the word after one more perfect guess. It turns out that with this example, you can solve 96.9% of the time with an average of 4.27 guesses. That's pretty surprising, but also assumes you have computer-like recall of words.

I haven't quite got around to scoring all the possible 3-letter starts. First, it will take a loooong time, and I'm not willing to leave Python to finish this (it will then stop being fun). Second, I haven't yet determined if the following statement is true or not:

The best performing word in the 1 word variant of this algorithm will also appear in the best performing pair of words in the 2 word variant

If this is true, then all of those considerations of implementation will go out the window, so I will need to think about it a bit more!