Solving Wordle using information theory

An excuse to teach a lesson on information theory and entropy.
An equally valuable form of support is to simply share the videos.

Contents:
0:00 - What is Wordle?
2:43 - Initial ideas
8:04 - Information theory basics
18:15 - Incorporating word frequencies
27:49 - Final performance

Original wordle site:

Music by Vincent Rubinetti.

Shannon and von Neumann artwork by Kurt Bruns.

Code for this video:

These animations are largely made using a custom python library, manim. See the FAQ comments here:

You can find code for specific videos and projects here:

Thanks to these viewers for their contributions to translations
German: Thadaeus, styrix560, wolfsgier

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Various social media stuffs:

[leumasarc]

Imagine Grant's friend innocently telling him that his Wordle opener was "weary", only for him to publish a 30-minute essay on why that's stupid a week later😅

[RazAnime]

creating an algorithm for this and comparing them against each other sounds like it would have made a great programming competition

[Paul_MacK]

Never have I ever been tricked into enjoying a math class like this. I wish I had you instead of all my college professors

[lindybeige]

The position of letters is a factor. For example, I prefer TALES over SALET ( SALET is recommended by others who have done computer analysis of this game) because if I do NOT get a green S, then that rules out a huge number of plural four-letter nouns with an S on the end, like BOOMS. Note that I am getting a lot of information out an absence of a match there. Though Y is a fairly rare letter, it turns up at the end of a lot of five-letter words. Letters like L, R and H are important beyond their commonness because they often combine with other consonants as in BLAND, PROSE, and CHAIR.

[lumisussy]

Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!

[clickbaitking]

I love those sketches you put in when depicting real life situations, like the conversation between Von Neumann and Shannon 12:01!

[tztztz-vpty]

The amount of preparation work in order to produce a video like this is unbelievable.. truly impressive work.

[blackholevortex]

This video is so well done.
The word play at 18:40, the hidden messages in the game at 25:25... This video gives me "Gödel, Escher, Bach" vibes, and that is something that has never happened to me since I read that book. Awesome.

[AlphaPhoenixChannel]

Grant: “this video’s getting kinda long.”
Me: “what are we at, like 10? 15 minutes? He’s got plenty of time!”
Me after checking clock: “oh…”

[nipungupta]

You deserve the world. The amount of effort that went into making those smooth slick animations, the wordle UI to run simulations on, the code that you wrote is IMMEDIATELY apparent. Production quality is off the charts as always, and the video is filled to the brim with information, pun intented. Keep up the good work, you are amazing!

[kilianschabort]

A year later and my blind devotion to your original video has paid off. Thank you kindly!

[admiralcapn]

Just realised WORDLE now has a "hard mode" where you MUST use existing information in future guesses (i.e. if you get a green first letter and yellow fourth letter, future guesses HAVE to start with that same first letter and mix that other letter around). Curious how this would affect the amount of information obtained at each guess, particularly with an algorithm looking ahead multiple guesses.

[HBMmaster]

thanks for making this. now people will stop asking me to make this video, lol

[Bismuth]

18:38 I bet you had a lot of fun writing that bit

[jonaslarsson]

I could've never had forgiven my self had I not played Wordle today. Been using crane since this video came about.

[Hydratz]

On Jun 21, 2023 I put down the word CRANE and to my amazement, it was the word of the day! Its the only word I got on my first try

[DrTrefor]

Came for the wordle, stayed for the awesome lesson on information theory. Cool!

[AlexDings]

4:00 note that the list used in Wordle is the exact list of words allowed in international tournament Scrabble. It's called CSW19.

[gwenturo]

I adore your teaching style of gradually building upon simple intuitions until you've reached a rigorous and useful conclusion. It makes so many subjects easier to understand and I hope I get to use it someday

[williamdavis]

After 512 days, crane has finally won first try. Thank you