Oh, wait, actually the best Wordle opener is not “crane”…

I find when I am solving world myself, after the first guess I am thinking a lot about phonemes, as opposed to just letters. This for example leads me to strategies like trying to get most of the vowels in the first two gueses (possibbly non optimal...). I wonder if considering groups of letters simultaneously, given the patterns that arise in english, (such as phonemes) alters the recommendations from a trained model significantly ?

James Matheson

I AM

Thanks for the follow-up! Could you use your code to find the optimal word under the additional constraint that one may only use words from the “possible answer” list. That would eliminate the possibility of using an obscure word at some point and thus the answer may be somewhat closer to “best human starting word”.

There is *one* more factor that may impact the "optimal starting word." Not that this warrants a video, but the rules of Hard Mode might throw a wrench in this. Basically, you HAVE to use all clues you were given in subsequent guesses. As far as I know, the previous versions of this program didn't have that? Either way, great video and addendum. I did not know anything about information theory prior to the video, so it was really cool content.

Thanks for the follow up! These videos have definitely altered the way in which I approach Wordle, but I think in way that is really fun and interesting, and it's really satisfying to be able to put the material presented into practice. So not at all "ruining" anything, I would agree! Plus, maximizing the amount of information (to me, intuitively, and I think maybe also actually) means that I often don't reuse letters from my first guess in my second guess. Which looks like witchcraft to my coworkers, so thanks for that too. 🧙‍♀️

Emily Curry

I like toy example here: https://github.com/Yorko/mlcourse.ai/blob/main/jupyter_english/topic03_decision_trees_kNN/topic3_decision_trees_kNN.ipynb#How-to-Build-a-Decision-Tree

Mr. Duck

This was a really good video series! It's surprisingly hard to find good, simple, relatable explanations of the computer-science definition of Entropy, and you've definitely just put yourself in the top-two! (I don't think we want refine any further though, because the other best one is XKCD's English-tweets what-if where we got numbers like ten-thousand eternals years... :D ha ha) But seriously, I really love how easy to understand and how informative your videos are!

Christopher Kemsley

For what it's worth, many of the optimal second-guesses do include u's. For example, following "salet": ⬛⬛⬛⬛⬛ -> courd ⬛⬛⬛🟨⬛ -> drone ⬛⬛⬛🟩⬛ -> rownd ⬛🟨⬛⬛⬛ -> brond ⬛⬛🟨⬛⬛ -> courd ⬛⬛⬛⬛🟨 -> north ⬛🟨⬛🟨⬛ -> beard ⬛🟩⬛⬛⬛ -> corny ⬛🟨🟨⬛⬛ -> corni 🟩⬛⬛⬛⬛ -> unrip ⬛⬛⬛🟨🟨 -> trite ⬛🟨🟨🟨⬛ -> gnarl ⬛⬛🟨🟨⬛ -> deice ⬛⬛🟨🟩⬛ -> bevor 🟨⬛⬛⬛⬛ -> mucho 🟨⬛⬛🟨⬛ -> rhone ⬛⬛⬛⬛🟩 -> groin 🟩⬛⬛🟨⬛ -> prink

3blue1brown

Very interesting, reassuring to see the same numbers I got! It's interesting that few things in the rankings change when you switch from an entropy-based algorithm to a deeper-searching one, but "reast" manages to bump itself up to the second place.

3blue1brown

Next thinking: adversarial wordle. Finding optimal strategy when two players taking turns.

Mr. Duck

[Speaking of coincidences] Just before Wordle came out, I read the book about Shannon: 'A Mind at Play: How Claude Shannon Invented the Information Age'. When Wordle hit the news, my first reaction: duh another boooooring guess game... then wait... this is an information theory problem, then I started writing some code. And now I see the society getting split into two buckets: those who enjoy playing it 'the human' way and those who enjoy it looking at it through the prism of of information theory beauty.

Mr. Duck

Interesting that the vowel 'u' is almost completely absent form all the "best guesses" in the simulations. When i play MasterMind I always use all the available colors in the first two rows (without using any colors form the first row in the second) That gives me the most unambiguous information - I would expect a similar strategy for finding the vowels would be a good strategy in Wordle.

Gregor Shapiro

Thanks for the explainer on the duplicate-letter-coloring rules. That alone was worth a youtube video.

Shawn Van Ness

The color computer was amazing at the time!

Thank you for this awesome follow up video. I am glad you elaborated on what you wished the main takeaway for viewers would be and I wholeheartedly agree. Of course, "entropy of wordle" wouldn't make for a viral headline, so this is a completely understandable and proper use of "click-bait" like thumbnails and titles.

I really enjoyed the Wordle video. I brought me back to the first personal programming project I actually completed and was proud of (on my old Tandy Coco 3!). It was a Mastermind game in BASIC, and it included an AI that would brute-force its way very similarly to yours. I knew nothing about entropy at the time, though! It was simple, but it was trying each time to maximize the number of remaining possibilities it would eliminate.

Vincent Zalzal

There might be a lot of people who concurrently computed the true optimal. I stumbled upon this one by Alex Selby around when the first video went up (code also available on Github): http://sonorouschocolate.com/notes/index.php?title=The_best_strategies_for_Wordle.

I did very briefly show a flash of how the algorithm does on hard mode at the end of the last video. It's actually not much worse, the average is around 3.5

3blue1brown

This is amazing! Love both videos. Your wrap-up about how people like to actually play games is probably a natural place to mention "hard mode" which I know is how a lot of people do wordle. It's sort of interesting because it's (I think!?) pretty strongly non-optimal gameplay, but just a lot of fun!