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

It takes courage to admit a self-made error, and in this case, an extra effort to make a video explaining it. Thank you Grant, this says, directly and indirectly, a lot of good things about you.

I always start with, "ADIEU" since it has four vowels. My second guess is, "STOMP" since it has the fifth vowel along with S,T,M,P, which are letters that are more commonly used.

Admitting a mistake and correcting it is the pinnacle of studying math and/or coding. I love how "noble" this channel is.

just so y'all know: 1) six words have been removed from the official answer set so it's now down to 2,309 words. The words that were removed: AGORA, PUPAL, FIBRE, LYNCH, SLAVE, WENCH 2) no answer word ever repeats. So as time goes on ... that list of 2,309 is shrinking by one every day. Ideally if you wanted to play the optimal first word, you'd rerun your code on a daily basis!

My mom plays Wordle, and she opens with the word “audio” every time to get the vowels. She tries to use the letter “E” in her second word. She’s only ever lost once.

It's interesting that SOARE keeps showing up in your lists, because it's also the top word from a simpler and more arbitrary method by Bertrand Fan ("The Best Starting Word in WORDLE"). They just counted how many green and yellow tiles you get from each starting guess if you use that guess on the whole answer list, but gave greens twice as much weight as yellows.

I started playing wordle really late, about 7 months ago, and on my own came up with a group of starting wordles that seemed intuitive to me based on my experiences watching Wheel of Fortune growing up. And my list is SLATE STALE STEAL LEAST TALES I was honestly super proud of myself for coming this close to the best answer just by thinking about how other word games work

An excellent follow up video. Came for an answer, but stuck all the way through and gained some insights.

Yeah, as a real human playing the game, I actually aim to find the most consonants, and ideally the first letter of the word, as this helps my brain think of possibilities more readily, instead of having just vowels and maybe a letter somewhere in the middle. So statistically "best" and "best for me to use when trying to solve the puzzle" are likely to be very different.

There are two joys in solving a puzzle: The first is finding the solution; the second is exploring the process. Applying information theory to the process is a joy in itself, and for some a joy greater than finding an answer. Similar feats are done that result in Rubik’s cubes being solved by robots, or machines that can sink a basketball from anywhere on the half court. The mechanics of invention are not finding a solution, but in finding a new puzzle in the process that leads to a better solution. Farming is advanced not by figuring out how to make it rain or have longer days to work, but on solving problems of yield and disease. Transportation is advanced not by breading better horses, but making cars, trucks, and airplanes. This is true out-of-the-box thinking, looking at the problem with eyes that are larger or smaller than the problem in its original form requires. There is a joy here that needs no apology, because the exercise is in its own right a challenge to be met and the consequences of such exploration may yield innovations with far greater benefits than knowing the answer to today’s Wordle.

Your esence of linear algebra has helped me so much honestly, please make esence of basic analysis🙏🙏🙏 The linear algebra series has made me from barley getting through exams to acing them with ease, as it so much easier now to study, mor fun, and it makes sense. Before I was just memorizing everything to get through and to pass the exam.

I always like to look around my location and use the first 5-letter word I find. If it contains common letters then it's possible to get more green and yellow letters. If it contains more uncommon letters like Q and X, if they're right, then it narrows down the guess opportunities.

Public corrections show a dedication to intellectual integrity. I am so grateful we have creators on RU-vid who are dedicated to quality and honesty. Keep it up, Grant!

I always like to start with "Share", usually followed by "Point" if the first guess produces all greys. Seeing "soare" as such a highly rated first guess is a bit reassuring.

My favourite starting word is 'adieu' as it shows four out of the five vowels immediately. You can tell a lot about a word by the placement of its vowels.

Excellent point towards the end about overfitting to the answer list not being a good strategy long term, since it's now got an editor who's theoretically going to be picking an answer each day, similar to how crosswords are human generated rather than procedural, rather than having an official answer list (I think the allowed guesses list is the same?) I think they're committing to keeping to the 'no add an s plurals' for what they pick as answers, mind. This also allows them to do thematic answers - Maybe on the 25th of December Carol will be more likely to be the answer than it would be around July, for example. (I rarely play Wordle. I do often find myself playing squardle, which is a grid of 6 criss-crossing wordle puzzles in a waffle shaped pattern, three vertical, three horizontal, where clues can give you help on other answers alongside the one you put it in - so an E will tell you if there's an E both in the clue you guessed it and the clues going the other direction that 'see' that letter and your answering one horizontal and one vertical each time where my opening is usually point, clear, mushy - which is also my opening for the weekly puzzle (which fills in the holes to make it 25 simultaneous, crisscrossing, wordle puzzles))

Curious how things would differ if this system was applied to hard mode (i.e. always use all known info)

i mean a lot of it just takes time to analyze, it's good that you were able to identify this

This was very interesting as an information theory thing. I have come up with Scart, being folky as my "optimal" starting strategy. Thanks and keep up the good work.

The algorithm gave this to me yesterday and today I am blessed.

<a href="#" class="seekto" data-time="535">08:55</a> it's like in chess. Computers have solved so many openings and movesets, but often the optimal move is totally not the best move, because you can't follow up with a random movement pattern thinking 8 rounds ahead

I've been using "crane" since the first video came out, and it works alright for me. I use "pious" as my second guess if the first guess doesnt turn up much yellows or greens, cus it uses the remaining vowels and some common consonants.

Hey Grant, Excellent video - thank you. I've enjoyed the information theory aspects and the comparison of different search strategies. One thing I'm surprised about is that no one has yet tried to tackle an analysis that involves "hard mode" - in which there are two further requirements: 1) any correct guesses (green) have to remain in future guesses, and 2) and correct letters (yellow) have to be included in future guesses. The question I've had is not which word gets the best overall score but which word has the fewest possible outcomes in which you cannot guess in 6 tries. For example, guessing vowel-heavy words (think ADIEU) is a bad idea - you easily get caught knowing the vowels and not the consonants and don't have enough remaining guesses to distinguish between all possible words.

After watching this video, I immediately played today's wordle on 4 July 2023, and opened with the word "CRATE". It just so happened that the last 4 letters - "RATE" were all Green !! A very well made and explained duo of wordle videos. Looking forward to more!

I've actually never played Wordle and just wanted to know how this clever man cracked the game with math....

It is interesting that "CRATE" and "TRACE" deliver pretty much the same result, but "SALET" and "STALE" don't. That being said the positions of the letters matter and the odd case in this is "CRATE/TRACE" matching in score rather than "SALET/STALE" not matching in score. This calls for a follow-up video.

There are very similar opening words used in both this presentation and how I make an opening choice. I use the official Scrabble (TM) dictionary and filter out all the 5 letter words (12972). Then count the frequency of each letter in all those words, the first 5 letters and frequency are {s, 6665}, {e, 6662}, {a, 5990}, {o, 4438}, {r, 4158} and of all the words in the dictionary that contain those 5 letters are {aeros, arose, soare}.

Oh wow, I've been using soare for a couple of weeks after reading an article listing a few good words. The amount of vowels but also very frequent consonants made me go with it, I half expected to see it here, that's fun

When this game came out, I immediately thought of its extremely similarity to cracking WW2 Enigma code, especially the part used to find "cribs" from ciphertext. The pre-computed lookup table is analogous to diagonal board used on the improved Bombe machine which basically serves as a 5*5 string comparision circuit.

After seeing all those articles and social media posts about your last video, I am hugely impressed with your honesty and humility to call out how that is actually wrong. Didn't think my respect for you could go much higher. Loved the last video and love this one too - thank you :)

The idea of quantifying information was fantastic. It'd be awesome to have the long awaited Inverse Fourier Transform video sometime soon too :)

This kept showing up on my feed and last night I wanted a starting word so I chose CRANE. I now have a first round completion.

this makes sense, when i implemented it i got that list with soare, roate, and raise at the top so i was confused. Glad i didn’t just miss the point some how

My initial approach was to do the "Wheel of Fortune" strategy and try guesses that use as much of R, S, T, L, N, and E as possible for my first 2 guesses, and I see those letters appearing a lot in the top suggested guesses from your bot. It may have been interesting to see how choosing guesses based on letter frequency (rather than word frequency) affected the results.

Many thanks for your great videos. And I suggest making video about non-integer base of numeration.

I usually shake things up with my starter words, but I was happy to see several of my starters on the list. Stare, arise, raise, roast for example

“Maybe it’s not about the optimal opener… but the Information Theory we learned along the way” 🧐 - 3Blue1Brown (paraphrased 😅)

I always open with "DAISY", and if that doesn't give much information, I follow with "OUNCE", which gives me all vowels including Y. It's not perfect by any means, but it gives me some comfort to know all the possible vowels are included so in the worst case I'll have at least one clue.

Great graphic design, great content!

I absolutely never start with a consistent word. Everyday I stare at the puzzle and pull a credible word out of the sky. Hasn’t failed me yet. I’ve been playing for many months.

I like starting with “young”, because it helps me with letters and patterns that trip me up if I DON’T get them, and I can infer more common letters more easily if the uncommon ones are already in place. I also play in hard more so I don’t have a standard second guess, but I will usually try to get as many vowels as possible in the second guess :)

I think you have the right idea. I’ve learned much about information theory and I appreciate that you not only let us know about an error, but that you took the analysis further out of curiosity. I love your content - keep doing what you do!

This is so excellent thank you

I usually use audio since it has 4 vowels in it. Each vowel has a silent e 5 word that you can use to follow up. It works most of the time for me. (Shame,prune,shine,shone are just examples.)

I always respect when a content creator realizes a flaw and acts to correct it. I also entirely agree that these technically optimal words are rather irrelevant for human players. I always get the best results by eliminating most vowels early, so I was surprised by crane, unsurprised by soare and again surprised by salet. I'm incidentally a medieval enthusiast, so I do consider it a word. However, I do consider the word to be spelled with 2 "L"s, making it fake anyway. In my vowel elimination strategy, I am a bit disappointed I never thought of "audio" before seeing it at the end of this video.

I always start with “stare”. It gets out the s, t, and r which are probably the most used consonants and then the a and e for the vowels. Yeah, it’s boring but I almost always solve the word puzzle so it works for me :)

I enjoyed this explanation, and the previous one. I was looking at how WordleBot does it, and I did not understand the 'expected information' in its analysis. I was just using its same idea of [color] groups. I am amused and sympathetic with your issue of the combinations of yellow letters with duplicated letters, as that has been the main difficulty with my programming efforts. I think I finally have fixed those issues. As far as the 2315/12546 word lists go, that ship sailed long ago, with the 2309/14855 lists the NYT uses today, combined with the fact that it occasionally uses final answer words that are not in the 2309-word list. (Like on June 9) I started out this programming project (and I am not a serious programmer) with the idea of finding the 'best' word, but I am finding that the difference between a word with 3.402 average guesses being better than a word with 3.405 average guesses similar to the fact that the 13th of the month is more often a Friday- statistically true, but essentially meaningless. I do, however, test SALET every day, along with 20 or so other words. I am leaning towards LEAST for my computer, and CREST for my personal use (I like consonants, especially combining consonants), but am still finalizing my programming,

I often use crane as my second guess. Right after guild. Those give me a solid amount of info. Glad I came to a reasonably optimal answer on my own

In recognition for your brilliant first attempt, "crane" should henceforth be known as the Sanderson Opener (in reference to the Parker Square)!

I bet discovering this mistake felt mortifying. We've all been there; most of us are fortunate that our mistakes aren't seen by millions of people. Thanks for publishing the correction so quickly and transparently!

I've been starting with SAINE for about a month now. I looked at letter frequency in each position for the 2315 Wordle answers (found on a web page somewhere) and this was the highest scoring word I could come up with. I think it is slightly more likely get some green which I think helps solve the puzzle.

I was starting with snare and pilot; but recently I've switched to slate and groin. Just looking at scrabble letter scoring can tell you the commonality of each letter and getting all the 1 point letters in two guesses is pretty efficient for human players.

I've worked with and have read a lot on information theory, yours was by far the best in explaining what bits are and what the formula for entropy means. Great video!

I appreciate that you correct your mistake with more knowledge and exhaustive explanation. That's the correct way of doing science and I hope you do more in the future!

I appreciate the analysis from an information theory standpoint. There might be an interesting point to be made from the best theoretical analysis to develop a solid strategy in wordle. I believe the best theory would be one from a linguistic standpoint. For example, we know that (in the English language) nearly every word needs a vowel. So early words that eliminate all the vowels are handy - adieu, ouija, etc. For a 5 letter word, you can probably expect 2 vowels, frequently 1 vowel, but rarely 3 or more. Clear follow up words that eliminate any remaining vowels (if necessary) as well as picking up on letters that commonly form consonant blends are useful. In a 5 letter word with 1-2 vowels there will have to be a consonant blend or two. S, R, L, H, and rarely w are our letters commonly used to form consonant blends. You might decide that it's unnecessary to eliminate all the vowels in the first 2 guesses, and that it's better to eliminate the more common vowels and letters used in consonant blends on the first guess instead. Therefore, SHARE is actually a very useful word as a first guess. It picks up 3 of the most common letters used in consonant blends, as well as the common A vowel - and perhaps the most useful vowel, E. Of course, a curve ball can always come your way. You need to remember the use of double letters, and there are the consonant digraphs that are tricky such as KN, NG, or MB. A linguistic analysis may not get you the absolute best starting word, but it can give you the tools needed to beat the game better. It would be interesting to see whether information theory or linguistic knowledge gets better results overall.

Interesting. I'd been using Steal, which is an anagram of Salet, as my first guess to pretty good results.

I'm curious to know how the bot performs on Hard Mode, where every subsequent guess must include the letters you've found before. Since that restricts how much information you can gather on later guesses, can the bot still maintain an average 3.4 score?

Love the ending! So interesting that the computer algorithms are optimized for words with lots of vowels. My personal strategy is to start with words with lots of consonants, since I will likely "accidentally" guess the right vowels eventually if I use a different one each time. Having a couple consonants is more helpful for me to guess the word than, for example, knowing that "e" is the fourth letter. Very interesting.

I loved how similar the theory behind the wordle probability is to poker theory! Maybe an idea for a video..?😬

ABOUT followed by STICK and then RHYME< is the best for me. just because it covers all the vowels and the top 3 constants, i think. S, T and H

A very interesting 3-word opening sequence that a friend taught me was: Ideal, Snort, Chump. Works like a charm, but it's not the best to get the answer in as few guesses as possible.

This was such an interesting video! I learned about overfitting, heuristics and entropy in uni earlier this year, and being able to place all of that here felt so satisfying :)

Route, snail was my go to. Great game with many great strategies.

Just found this video, and I must say I find it both amusing and vindicating. I’ve been using LEAST as my opener almost since day one. Sometimes I’ll mix it up with STALE or another anagram, but the letters are the same. Must be a good one, because I’ve never lost. Maybe I’ll throw SALET in as another of the anagrams.

This second video is so great, Something that is missing in the age of online self-presentation: admitting errors and failure and then fixing it. Brilliant video! Really good!

The double "E" problem happened to me last semester in high school coding! I didn't know how to solve it but and I asked my teacher, but she said to not worry about it. This helped though!

I'm so glad you put out this video! I feel validated. I have a few friends that kept telling me "crane" was the best opener, but I was like "eh really?". I picked a word that I liked that I felt gave me more information with each word including common letter patterns. This algorithm made sense, but I felt like the thing this missed was the information you can gain from grey letters and common word patterns. For example, I like using the word 'Horse' because words that have a H, typically start with H or it is part of a pairing (TH, SH, CH, PH). If the H is yellow I will use a word that has all the rest of the pairing letters. Also, it doesn't account for the way each person thinks. Thank you so much for updating!

i usually start with trace or stale, so I now feel very validated

I have such a deep respect for this channel… I’ve always hated math but ever since I started watching this channel about 2 years ago I can definitely begin to see its beauty… the Fourier transform series is just amazing . Really paired nicely with Varitasium’s latest video on calculating tides and nondigital computers. Your animations are awesome and your voice is lol very soothing.

Even when you're wrong, it's still great to watch and learn from you! Way to go Grant! Keep up the good work!

Crane is the best starting word today!

Soare being the best one-step-deep opener pleasantly surprised me seeing as my prefered opener is "share"; just one letter off. I quite like "share" as an opener because of the fact that eliminating the H early on means that i can also eliminate clusters such as TH, CH, PH and so on… great video as always!

I love this take on videos - wanting to get a cool fundamental point across but also "knowing how the internet works..." and having to address the "technically correct" question even when it's totally irrelevant. I think I saw someone in your comments on the first video pull an "Um actually..." saying that they'd run the entire word list at full depth and "wordle was a solved game" - but that doesn't teach you anything! I don't even remember what word they said was the best opener, but I remember your information theory arguments, which are so much more interesting and useful. I can't tell you how many comments I got on a video reply to Veritasium that said "Well I just got to the end and I'm not sure If Derek was wrong. Was Darek wrong??" and I want to reply to all of them "IT DOESN'T MATTER who's technically correct! Isn't electricity cool???"

I did an analysis of letter frequency, and scored words based on occurrence of those letters. I didn't use the official Wordle list, I garbed the Linux English dictionary. Then I sort the words in that list by most frequent letter occurrence (I drop duplicates as those don't reveal as much information) and came up with my go-to starting word of "arose" ... then as you play you fill in your grey/green/yellow results, and it builds regex patterns that it then uses to eliminate words from the list, and then sorts the remaining words by letter frequency (of the remaining set) again. That started making Wordle boring, so I switched to Quordle and have never failed to solve it so far. Not as deep a dive as you took to run the game fully for each word, but good enough to give me a likely list of words to pick from.

My strategy with wordle is to start with either Adieu or Audio (whichever works), then to base the second guess on a hopeful vowel catch. There are a lot of words, using the most frequent consonants and just one vowel so it's easy to 1-2 punch a lot of information out. For example, start with ADIEU, then (assuming there is an E) follow with STERN - two guesses with no letter overlap, and 1-4, 6-8, and 12 most frequent letters in the English language. It almost always gives enough information to make a very accurate guess 3rd - with both a lot of letters ruled in/out and placement of the vowel narrowed down considerably. Then it's just about using your knowledge of the structure of English words to guess intelligently - Y is 19th most frequent, which is almost the lower 3rd of the alphabet, however is commonly used as a stand-in vowel, so if you know there's a single vowel at the start or end of a word, it's highly likely that the word either has a repeat vowel and/or a Y in it.

As more of a game theory guy, I'd be curious about applying different goals than just "lowest average score". "Don't Fail" is a logical goal in order to maintain success streaks, and then "Best score without the possibility of failure". Things along those lines.

<a href="#" class="seekto" data-time="560">9:20</a> I can confirm that NYT already changed the list, I used to open with ABOUT, PIERS, and LYNCH depending but now lynch is not in the word list which makes it an unacceptable guess (and completely screwed me over on CYNIC day, when I found this out lol). Could do an updated video with the new word list, if available somewhere!

I based my heuristic on letter frequency per position for five-letter words, which led me to highly value vowels. Word choices like ADIEU and AUDIO stuck out to me, but I had the sense that they overvalued vowels (vowels often bully each other for position, and it's not very common to have many vowels in a word anyway). After a fair bit of trial and error, I settled on AEROS as my primary starter. It was cool to see SOARE matching my starting letters, but arranged in a very different order. My other fun wildcard trick is that I've dedicated some memory to recall about twenty different words that contain four consonants and 'Y'.

I’ve always had great success with “strep” as my opening word. E and S are two of the most common letters that appear in English, and T and R are near the top.

Oh, I don't even play the game. I'm here purely for the math, this stuff is interesting. Please do keep up the great work!

I don't think knowing the "optimal" word ruins the game. What's optimal for a computer is definitely not what's optimal for me, because my brain doesn't work like a computer. I start with "adieu" since it gives me a clue as to which vowels are in the word, then I build off that with which consonants are fairly common. Crane/Salet simple don't work well enough for the process I have to go through to get the word.

I like GHOST as a first answer because it at least has the potential to tell you if any of the common digraphs GH-, SH-, or TH- could be in the word. I usually guess something with the vowels A and E next because there are fewer vowels than consonants. Bear in mind that I have never tested this, but I have an average score under 4 so it seems to work.

I’m glad I saw this, because it’s done me well, 487 games, 366 day streak and (spoiler) my first 1 solve, with the only interruption being a single day that I did Pzazz.

From my understanding "Sallet" actually pronounces the hard t at the end. There is a separate word in french for the helm. But the helm typically covers the top half of the face, with a gorget or... bevah? bever? Covering the lower half of the face. Sometimes they were attached, and other times separate.

Personally, I really like using the word AUDIO as of late, it just gets past nearly all of the vowels for me, and I get through likely consonants based off what I get. If I feel like I need to determine if there's an E, I will of course go for it in my second or third guess. My average score is 3 or 4! I used to use RAISE because it got rid of pesky letters to me. If that was a full blank, I love to RAISE DOUBT on wordle! But that was before I started winning more often with 2 or 3 using audio, it feels good having a strategy that works for me that clearly isn't very orthodox

I don’t really have any desire to discuss Wordle or watch a video on it, but the prospect of an ultimate starter word is pretty cool, and also I wanted to share that for whatever reason I almost always start with “weird”

Thanks for this! It has probably been asked before, but I am curious: Is there a difference between hard mode and normal mode, as to what word would be better to start with? I have a feeling it would.

I usually start with "steal", trying to knock out some of the most common letters, then "chomp" to try to group together some less commonly used letters that are hard to fit into others words

I use AUDIO and STERN as my first 2 opening words. I have a tendency to over analyze and thus take too much time on word games. So these 2 words actually give me just enough info to get it on my 4th word 90% of the time. 9% chance on 3rd. 1% on 5+.

I have a topic suggestion you might be interested in: Homomorphic encryption and what mathematics theories there are that this works. I know it doesn't has anything to do with this video or PI, but I think you can explain this topic very well so that everyone is able to understand the basics.

Something I'd like to see evaluated (forgive me if this exists buried within the comment thread) is how the "Hard" vs Standard mode requirements impact expected score. The "Hard" mode requires players to utilize what is learned in previous guesses, vs. the standard mode which does not force guesses to map to previous information. I play using both models depending on what typically guess one yields. If I get say three unplaced common letters, guess two might be a word totally orthogonal to guess one. Most of my successes in three moves came from this. Curious if a brain clearly bigger than mine had insight on how the strategy would work in theory.

I use a two-word starter: ORATE + JUICY. None of the letters repeat, so I have the benefit of knocking out 10 letters (and every vowel) before I make a real guess. While this sacrifices the opportunity to win on the second guess, I find it significantly raises my (human) ability to win on the 3rd or 4th guess.

This is great

CRATE is the best one for a real mind to think, as it limits the most answer options on average for any word, as you have a very small chance of all greys (follow up with lions or solid) and when you do get a letter, most options with that letter are thrown away by the other letters being there (or not) For people that like combo starters, PARTY SLICE and HOUND/MOUND (M appears eight more times than H, but H is in about 20 more words)so pick which one you like more, it doesn't make much of a difference

personaly speaking i think the best words go in this order regardless of what letters u get right. fjord, waltz, nymph, quick, gybes. that leaves u with one guess but also leaves u with every letter in the English alphabet used accept for two x and v so its pretty easy to get the word after that

I keep it interesting by starting each day with the previous day's answer. I'll never get it in 1, but it keeps it challenging sometimes. Other times, it actually starts of incredibly strong. On the day when the answer was ultra and the previous day's answer was ulcer, there was no way for me to get it on anything but the second guess.

I would be interested in a statistic of how often it's better to choose a word that's already impossible because of the results of the previous guesses.

I like CREST and AUDIO for my first two guesses. Five vowels and most of the common consonants

While I always thought getting the vowels out was most important, my word of choice was Baste. A as second, ends in E, uses B and S... T I think is more common than K. Haven't played in a bit, though. I should try again with my word and yours to see the difference firsthand.

I always tried to maximize the possible digraphs in each guess, as to hopefully strike at two letters to match. STING = ST, SN, NT, NG for example.