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😅

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

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.

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

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

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

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

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

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

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…”

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

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.

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

"we shouldn't let machines rule our lives" -the man writing and using a wordle bot Love the video!

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.

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

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

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

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

This video is why I got my first 1/6 score today 😁😁😁

"Ignoring its recommendation, because we can't let machines rule our lives" I love this!!!

18:39-18:58 I love this paragraph! Love this wordplay, brings back VSauce memories!

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

I have religiously been using crane since I saw this video, TODAYS OUR DAY GUYS!!!!!🎉

Tares is a verb! "He tares the scale". It means setting a scale to zero with something on it. That way you can weigh something in a container without weighing the container! You use it a lot in chemistry.

As an information theorist (a PhD student working on the field), I am amazed by this video. It is so interesting and well-organized. The information i(x) = -log2(p(x)) is also called "surprisal". I like this terminology a lot, because, really, the larger i(x) is, the more you get surprized by the outcome x.

All of us crane openers got it in 1 today

Well today's word was CRANE. Have to give this the award for best thumbnail ever

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!

I love how you opened with the idea that "4 guesses is par and 3 guesses is birdie", then in your comment at the end (29:26) you note that consistently getting 3 guesses is basically impossible. That's so cool how the math matches our human intuition about the puzzle!

6/21/2023, i opened youtube, saw this on my homepage, opened wordle, typed in crane and got it correct first try

Today is a momentous occasion - the word IS **CRANE** today! Happy 1-shot day to a lot of people.

This 30 minute video taught me more about entropy than an entire section on entropy from my machine learning course. Bravo!

The most useful and enlightening definition of entropy I've ever encountered came from neuroscientist Terrence Deacon, who frames it as the dissipation of constraints. Anything at maximum entropy is maximally UN-constrained. Be it energy levels in the statistical distribution of particles in an ideal gas (Boltzmann) or the resolution of uncertainty in the answer of any given question (Shannon). It also helps to frame how entropy doesn't simply rely on the contents of a container (2 black, and 2 red checkers on a 2 x 2 checker board, for example) but the possibility space conferred onto those arrangements by the SIZE of the container (considerably larger if those same checker pieces end up transposed onto a standard 8 x 8 board). Constraints man, they're big time (gravity vs. Inflation being my all time fav example).

Finally after using crane as my opening for a year, I'm so grateful i didnt miss wordle 732!

I randomly got recommended this again today so I decided to do wordle and it was in fact crane

This reminds me of "mastermind" a game of the early 70's. In stead of words you have 4 different colored pins. And for the error/success feedback there is two pins in black and white. It is played by two people where one player is the guesser and the other one checks the guess and gives feedback.

(18:46) Just brilliant! ‘FIRST is “which” after WHICH THERE's “their” and “there.” “First” itself is not FIRST but ninth, and it makes sense that THESE OTHER words COULD come ABOUT more often. WHERE those AFTER first are “after,” “where,” and “those,” ... BEING just a little bit less common.’

This video has finally fulfilled its purpose

Good to see you all here 😀

Edit: For more details on how the "best" opener was chosen, and why there was a slight mistake here such that CRANE actually drops to #6, see the follow-on video ukposts.info/have/v-deo/noKWmGaPpJljuJs.html For a human playing Wordle, I'm not sure I'd actually recommend starting with CRANE, or any of the ones best for one of these algorithms, since it requires also knowing what it will do for second guesses. For example, here's the start of the mapping for what it does with that second guess: ⬛⬛⬛⬛⬛ -> sloth ⬛⬛🟨⬛⬛ -> toils ⬛⬛⬛⬛🟨 -> spilt ⬛🟨⬛⬛🟨 -> rosit ⬛⬛⬛⬛🟩 -> toils ⬛🟨⬛⬛⬛ -> shout ⬛🟨🟨⬛⬛ -> party ⬛⬛⬛🟩⬛ -> gluts ⬛⬛⬛🟨🟨 -> lemon ⬛⬛⬛🟨⬛ -> pilot 🟨⬛⬛⬛⬛ -> kutis ⬛🟩⬛⬛⬛ -> pilot ⬛🟨🟨⬛🟨 -> patly ⬛⬛🟩⬛⬛ -> slipt ⬛⬛🟨⬛🟩 -> lambs ⬛⬛🟨🟨⬛ -> toils ⬛⬛🟨⬛🟨 -> tepal ⬛⬛🟩⬛🟩 -> glost ⬛🟨⬛⬛🟩 -> south

This video is so good and the fact that you implemented and did affort to basically have any visual / stasttical point of view to any version of solver is just incredible

Ever since seeing this video over 1 year ago, I have been EXCLUSIVELY using CRANE as my opener. EVERY. SINGLE. DAY. And finally….. Today was the day, 6/21/2023 The Wordle was CRANE, I have never been so happy to guess the Wordle, and of course I started off with CRANE, and boom! FIRST TRY, IT WAS FINALLY CRANES DAY TO SHINE!!

Can confirm “crane” is the best opener.

You ever watch a video that's so good you actually watch the end screen

Try to work out your friends' first words from their scoring patterns - Metawordle :) The worst starter word? "Eerie" - unless it's correct!. Anyone got a worse one?

I LOVE THIS!! Made a Wordle solver myself before seeing this video, but the level of maths you’re using here and the knowledge you need to pull it off THIS way is just incredible. 3B1B, that’s another score there. Thanks for this vid! 🙏

Thanks for making and sharing more exciting math content like this; you're doing really great to make them so interesting!

I JUST started a college class on information theory. I'll have to watch this again a couple of times but its so helpful to have a real world example!

Awesome breakdown as usual. I'm surprised you didn't comment more about the effect of "hard mode" and the reduction in information available when you need to reuse correct information.

I know you came back later and decided that you miscalculated and this wasn't the best opener. But I've been using it anyway, and I can tell you that *today* it's the best opener!

I like to start with “Faint”, which is usually followed by “Ouphe”, and they both remove vowels (excluding “Y”), and I usually end up with enough info to finish the word, but if I do not, then I follow up with “Byrls”. Which removes “Y” and four extra, fairly common letters. This strategy will usually get you the letters by the fourth guess. The strategy I used to follow was a “House” “Paint” combo, and after a while I felt like I could get more efficient and swapped to “Faint, Ouphe, Byrls”.

Grant that little bit you did with "these is in the eighth position" etc was absolutely brilliant. Great video as ever, thank you.

I played Wordle for the first time just a few minutes ago and used "Other" as my opener and got a 1/6 thanks man

today, 6/21/23, crane is an especially good guess

What a momentous day

Some thoughts on CRANE as first guess... I usually guess stare first (an anagram of tares, which your first algorithm likes) but started guessing crate, with the reasoning that a C often comes with an H or K, so finding a C feels like it gives more information even though it's a less likely letter. Essentially, letters that are weighted towards appearing in certain types of words or in certain letter combinations should be more valuable guesses than their simple frequency should predict. C is probably at a sweet spot where it's not too uncommon a letter, and enjoys a big boost from giving you a lot of bonus information if you do find one. Further to this, if you have, say, two certain letters that often appear in combination, it makes sense strategically to include one of these letters and not both in an early guess, as the odds of these letters appearing in the word are far from being independent odds, so guessing one gives you information on the probability of the other - bonus information from just one guessed letter. Hence, since CH and CK are very common associations of letters in common English words, guessing a C but not an H or a K in your first word seems to make a lot of sense from an information standpoint, and I'm not surprised that an algorithm found that guessing a word containing a C first was smart, despite C being quite a way down the letter frequency list.

My friend and I like AUDIO/STERN as a double opening. It covers all traditional vowels without repeat letters and tests S in the first slot which is the most common starting letter for 5 letter words.

THE DAY IS FINALLY HERE! TODAY’S THE DAY

I never touched it when Wordle was a big deal, but watching you talk about the maths is making me want to try it for the first time. Congrats on that.

Making a word game about math. I LOVE IT

I would like to see a Hard Mode version of this analysis and how the algorithm reacts to it.

the letters „first naive ideas“ tending to the word „start“ is such a nice detail! well done video!

Today, I thank you.

Would love to see how you would approach tackling Wordle’s “Hard Mode.” Loved it, thanks so much for making this

This whole video is great but I have to say I liked the cute word play around 19:00 quite a lot.

i am so thankful for the quality of your educational content. It is amazing to learn so much from just one person.

3blue1brown fans having a great Wordle day today.

Such clarity in explaining things, is why I love this channel. Plus, you do a ton of work to make it visually interesting!

Here's an interesting alternate goal: what if rather than optimizing for fewest guesses, you built a bot that attempted to maximize the amount of times it could guess the answer in 2 guesses, and only after failing to do so would try to minimize its remaining score. Basically a risk-taking bot that's more in it for the bragging rights of the unlikely got-it-in-two situation more than it cares about reliably doing well.

Just wanted to thank you for this video I got wordle in 1 yesterday. Guess it’s time to change my word to Salet. ;)

amazing video as always! please don't ever stop producing them !!

Wordle has existed in Dutch as "Lingo" for probably 30 or so years as a public tevelision show, with variable word length too. Near one of its last shows there were two brothers who developed an algorithm to guess these words during the show which they could play out in their head and they won literally every round and after they won they put their full way of thinking on internet.

I don’t know why, but this was the most calming video I’ve ever watched… math can be so relaxing sometimes

Thanks for the great video! I think a great addition to this algorithm would be the removal of already used words in previous wordles. This would decrease the overall entropy a little since some pretty common words were already used. Anyways, great video, I always learn so much from you!!

I really like this approach. Since you can calculate all these state on every possible guess vs every possible solution. Which is an O(n^2) algorithm and can be efficiently computed. I didn't think of that at first for some reason I thought it might not be possible to computer this kind of information.

20:10 It is interesting and I think people should keep in mind how even in highly mathematic scenarios, human preference is still involved not always, but not never

I learned about entropy from a graphic novel called Meanwhile. It's a choose your own adventure revolving around a scientist and three inventions, the kill everyone button, a time machine, and a memory transfer machine, highly reccomend, more of a puzzle than a book. Great video as always! Edit: Author's Name is Jason Shiga.

This is great. I was using AISLE, and sometimes use COUNT as my second since both words cover all the vowels and both have different consonants that I thought were somewhat common. Turns out my intuition was correct since they're all near the top of that popularity list!

I always start with RAISE and POUND. That uses all the vowels except Y, and gives you a lot of information about the rest of the letters. I usually score 4, and often 3.

Wordle literally saved a woman's life when the daughter realized the mother hadn't sent her a wordle for the day. Turns out the mother had someone break in to her house and was being held hostage. She was saved by police after the daughters tip.

Data Scientist here: Just wanted to add another perspective on entropy & the way we quantify information, as this topic is often fairly confusing for beginners. So 1, where did all this theory & stuff come from? Information theory comes from trying to measure the efficiency of communication of information. So the key idea is that, if we want to quantify information, really what we're doing is trying to measure how well one actor is communicating to another actor about an event. So the two actors need to come up with some dictionary, or what is often called an "encoding" in order to communicate events to one another. The the second key idea, is that It takes more energy to communicate with more symbols ("symbols" could be words, bits, smoke signals, whatever is your base unit of information). Therefore, our objective is to assign the least amount of symbols to all the possible events, so we should encode according to how common different events are. More common events, should use less symbols. The inverse of a probability has this great name, called "the surprisal", the idea is that the higher the number, the more "surprising" an event is. Like if I were to tell you the sky just instantly changed from blue to magenta, that event would have a wildly high surprisal, because it has a really low probability. The reason we put a log on the surprisal is to get "how many symbols do we need in order to communicate this event?", the base of your log determines the number of symbols available to you, most commonly we use base 2 because we're usually thinking of this in bits. The entropy of a probability distribution is the average number of bits required to communicate events in said probability distribution. Hope someone else found that interesting! None of this stuff made sense to me until I understood that.

This video taught me more about information theory in 30min than two university courses on AI did in half a year. I wish I had seen it back when i was learning about that

Thank you, just got it on first try tonight lol

It's not exclusive to this particular video of his, but there is something strangely refreshing about learning about things I don't understand. Like the prime numbers video of the monster, it's so refreshing to hear someone talk so plainly and expositorily yet still pass way over my head. I love learning how little I actually know, and this channel (among others) refreshes my brain so well. Please accept my sleepy and sincere appreciation. TL:DR ~ I like your funny words magic man

this was a fun problem to solve :) my friend and I essentially constructed a solver with the same methods but we conceptualized it in a very different way. really cool video!

I really thought that I was the only guy on the planet willing to go through so much analysis, math, and tool development just to win a video game. Thanks for making me feel slightly less weird.

The word play with the top 13 5 letter words was awesome!

That wordplay in the sorted list of most common words broke my brain more than any math you've ever presented on this channel. Great work, lovely video!

Such clarity in explaining things

This video randomly appeared in my recommendations, I decided to play Wordle and today’s word of the day is the «Crane»? Bro no way 😭😭😭

After incorporating Relative Word Frequencies of all words, a next step may be to rank relative letter frequency for each letter position, 1, 2, 3, 4, and 5 (noting that letter-frequencies for five-letter words is different than for all words: "soare" rates higher than "arose"). The letter distributions also change for each step for the 'remaining' possible words.

9:28 I think this is the perfect explanation to the whole concept of Akinator. Yes, it also cheats by just using a user-created database but getting to the answer in less number of questions is the real challenge.

I think this also shows how amazing the human mind is, because even without knowing all this, we can sort of figure out that four is normal, three takes skill, and two is just lucky.

today’s word was crane so i got it first try lol

It's clear that people develop different methods to solve the puzzle. For me I start with "adieu". My second word is "story". This way I get all the vowels covered and some major consonants. I have found getting a good start goes a long way towards solving the puzzle.

This made me discover absurdle. I was extremely aggrivated by it at first until I saw the explanation on their page. Basically all the words I was getting were "kitty" "jiffy" "dizzy". But that's because my first two guesses were always Crane and then Buoys to knock out as many vowels as possible.

Cool video! Loved the math! It would be different for hard mode though where you can't ignore the clues you already have.

Interesting. I happen to have been using TASER as a first try, which is just an anagram of TARES!

Really great video. Helped clarify and solidify some of my thoughts regarding information theory. Wordle was also a nice familiar subject choice.