6 ms·

3Blue1Brown: The mathematically optimal Wordle strategy

92 points by herbstein 5y ago

nyc111 5y ago
I love his animations, I wonder what programs he is using. He can do animations and calculations at the same time and it's all visually appealing. Most of his videos are amazing and fun to watch.
- awesomelvin 5y ago
  He's generally using his own tool called 'manim'. All of his code/animations are open-source. The code for this specific video can be found here: https://github.com/3b1b/videos/blob/master/_2022/wordle.py https://github.com/3b1b/videos/blob/master/_2022/wordle.py
  - nyc111 5y ago
    Amazing! So he does not have a visual user interface? This is Python, right?
    - FractalHQ 5y ago
      As far as I know, that is correct!
  - smoe 5y ago
    There is also the community fork of manim https://github.com/ManimCommunity/manim/ https://github.com/ManimCommunity/manim/ According to 3b1b on the original repo: "Note, there are two versions of manim. This repository began as a personal project by the author of 3Blue1Brown for the purpose of animating those videos, with video-specific code available here. In 2020 a group of developers forked it into what is now the community edition, with a goal of being more stable, better tested, quicker to respond to community contributions, and all around friendlier to get started with." https://github.com/3b1b/manim https://github.com/3b1b/manim
Syzygies 5y ago
At 17:05 he shows two possibilities left, ABBAS and ABYSS. In the actual implementation of Wordle, ABYSS is the only remaining possibility. (I recommend his videos to my students, who love them!) I don't know anyone who has actually read the Wordle JavaScript, but there are two word lists. The first list consists of more familiar words, ordered by date to provide secret words for each day. The second list consists of other words in alphabetical order that are also accepted as guesses. One reverse-engineers this code by figuring this out; one can experiment by resetting the computer clock to a new day. The standard assumption in any analysis of Wordle as actually played is that we don't know what day it is. Otherwise, the game is deterministic. Various of us have written code that agrees that SOARE is the best first guess using Shannon entropy for how Wordle is actually played (RAISE is close and easier to remember), and TARES is the best first guess for the most common misunderstanding for how Wordle is played. I don't recognize his first guess, so I don't recognize what he's doing. There isn't actually any proof that Shannon entropy is mathematically optimal here. I searched the literature for a relevant theorem after getting annoyed that so many online approaches were improvised. The trouble is that five letter words have a fixed, known, lumpy distribution, an artifact of human choice. If the game randomized both the secret word and the word lists themselves, and one could query an oracle to measure bin sizes for each candidate guess, ... but that's cooking the conclusion. If one took a limit as word length went to infinity, with a regular definition of what constitutes a word, there would likely be an optimality proof. On the other hand, after choosing an objective function one could entirely solve this finite game, as some have done, and entropy doesn't even come up. A refined variant on entropy that would be computationally feasible in cases where one can't solve completely would be to look ahead several steps. For each possible response to each first guess word (in practice one need only consider the strongest, and a partial search is nearly optimal as my Dad noticed programming JOTTO on Kodak's computers in the 1960s), find the optimal next guess using Shannon entropy. Now measure the entropy of the bins after both guesses, to value the first guess.
- udbhavs 5y ago
  I wonder if the virality of the game would have been boosted if the word list was stored server-side and not readable from the client source. Although I'm not on twitter so I don't know if future word spoilers are an issue.
bspammer 5y ago
There's something so gratifying about seeing your mental models of entropy and probability explained so visually. I wish all maths was taught with interactive diagrams, but it's not fair to expect everyone to be able to make 3b1b-level animations.
netcat99 5y ago
It's a bit disappointing to see "mathematically optimal" in the title when the strategy is based on a heuristic (granted, a very intuitive and effective one). For actual optimality results this article is good: https://www.poirrier.ca/notes/wordle-optimal/ https://www.poirrier.ca/notes/wordle-optimal/ In particular, max entropy heuristic + beam search will derive the optimal (now proven) strategy in terms of minimizing expected number of guesses
__s 5y ago
http://sonorouschocolate.com/notes/index.php?title=The_best_strategies_for_Wordle http://sonorouschocolate.com/notes/index.php?title=The_best_... This site ranks CRANE 6th, & 8th in hard mode. Includes other parameters like PALET being optimal start if only 5 guesses were allowed
schmorptron 5y ago
Slightly off-topic: 3Blue1Brown is such a treasure. I've been preparing for an exam for the past few days and only really discovered his LinAlg videos. They're incredible to get the reasoning behind a lot of what's happening.

92 points by herbstein 5y ago

I love his animations, I wonder what programs he is using. He can do animations and calculations at the same time and it's all visually appealing. Most of his videos are amazing and fun to watch.

awesomelvin 5y ago
He's generally using his own tool called 'manim'. All of his code/animations are open-source. The code for this specific video can be found here: https://github.com/3b1b/videos/blob/master/_2022/wordle.py https://github.com/3b1b/videos/blob/master/_2022/wordle.py
- nyc111 5y ago
  Amazing! So he does not have a visual user interface? This is Python, right?
  - FractalHQ 5y ago
    As far as I know, that is correct!
- smoe 5y ago
  There is also the community fork of manim https://github.com/ManimCommunity/manim/ https://github.com/ManimCommunity/manim/ According to 3b1b on the original repo: "Note, there are two versions of manim. This repository began as a personal project by the author of 3Blue1Brown for the purpose of animating those videos, with video-specific code available here. In 2020 a group of developers forked it into what is now the community edition, with a goal of being more stable, better tested, quicker to respond to community contributions, and all around friendlier to get started with." https://github.com/3b1b/manim https://github.com/3b1b/manim

Syzygies 5y ago

At 17:05 he shows two possibilities left, ABBAS and ABYSS. In the actual implementation of Wordle, ABYSS is the only remaining possibility. (I recommend his videos to my students, who love them!) I don't know anyone who has actually read the Wordle JavaScript, but there are two word lists. The first list consists of more familiar words, ordered by date to provide secret words for each day. The second list consists of other words in alphabetical order that are also accepted as guesses. One reverse-engineers this code by figuring this out; one can experiment by resetting the computer clock to a new day. The standard assumption in any analysis of Wordle as actually played is that we don't know what day it is. Otherwise, the game is deterministic. Various of us have written code that agrees that SOARE is the best first guess using Shannon entropy for how Wordle is actually played (RAISE is close and easier to remember), and TARES is the best first guess for the most common misunderstanding for how Wordle is played. I don't recognize his first guess, so I don't recognize what he's doing. There isn't actually any proof that Shannon entropy is mathematically optimal here. I searched the literature for a relevant theorem after getting annoyed that so many online approaches were improvised. The trouble is that five letter words have a fixed, known, lumpy distribution, an artifact of human choice. If the game randomized both the secret word and the word lists themselves, and one could query an oracle to measure bin sizes for each candidate guess, ... but that's cooking the conclusion. If one took a limit as word length went to infinity, with a regular definition of what constitutes a word, there would likely be an optimality proof. On the other hand, after choosing an objective function one could entirely solve this finite game, as some have done, and entropy doesn't even come up. A refined variant on entropy that would be computationally feasible in cases where one can't solve completely would be to look ahead several steps. For each possible response to each first guess word (in practice one need only consider the strongest, and a partial search is nearly optimal as my Dad noticed programming JOTTO on Kodak's computers in the 1960s), find the optimal next guess using Shannon entropy. Now measure the entropy of the bins after both guesses, to value the first guess.

udbhavs 5y ago
I wonder if the virality of the game would have been boosted if the word list was stored server-side and not readable from the client source. Although I'm not on twitter so I don't know if future word spoilers are an issue.

bspammer 5y ago

There's something so gratifying about seeing your mental models of entropy and probability explained so visually. I wish all maths was taught with interactive diagrams, but it's not fair to expect everyone to be able to make 3b1b-level animations.

netcat99 5y ago

It's a bit disappointing to see "mathematically optimal" in the title when the strategy is based on a heuristic (granted, a very intuitive and effective one). For actual optimality results this article is good: https://www.poirrier.ca/notes/wordle-optimal/ https://www.poirrier.ca/notes/wordle-optimal/ In particular, max entropy heuristic + beam search will derive the optimal (now proven) strategy in terms of minimizing expected number of guesses

__s 5y ago

http://sonorouschocolate.com/notes/index.php?title=The_best_strategies_for_Wordle http://sonorouschocolate.com/notes/index.php?title=The_best_... This site ranks CRANE 6th, & 8th in hard mode. Includes other parameters like PALET being optimal start if only 5 guesses were allowed

schmorptron 5y ago

Slightly off-topic: 3Blue1Brown is such a treasure. I've been preparing for an exam for the past few days and only really discovered his LinAlg videos. They're incredible to get the reasoning behind a lot of what's happening.