Solving Wordle using information theory
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- Опубликовано: 30 апр 2024
- An excuse to teach a lesson on information theory and entropy.
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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:
www.powerlanguage.co.uk/wordle/
Music by Vincent Rubinetti.
www.vincentrubinetti.com/
Shannon and von Neumann artwork by Kurt Bruns.
/ czprkhmjnd6
Code for this video:
github.com/3b1b/videos/tree/m...
These animations are largely made using a custom python library, manim. See the FAQ comments here:
www.3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
github.com/3b1b/videos/
Thanks to these viewers for their contributions to translations
German: Thadaeus, styrix560, wolfsgier
------------------
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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😅
making this video is just an excuse to prove his friend is stupid mathematically lol
To be fair, the friend did have the best possible explanation for it. They maximized expected joy rather than information.
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@teeforever1 wat
His friend is probably pretty awesome
creating an algorithm for this and comparing them against each other sounds like it would have made a great programming competition
I was thinking the same! In fact I actually was researching for a hash table for all 5 letter words and was going to start my algo.
well, a bit further from wordle, with the same intent, there's the Hutter prize
Polygon already did it
the fact that such a competition would be possible tells us that the use of "optimal" in the title is incorrect. :P that being said, that competition would be interesting!
@@tiagoaoa I think for this reason a competition would not be interesting. As far as I can tell the algorithm is optimal for the objective it defines (which is slightly modified from the original puzzle but only for greater generality)
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.
the word is never a plural fyi
@@figgahh5823 Oh really? It accepts guesses of plurals, such as NAILS which is used as an example in this video. Good to know, thanks.
Lindybeige no worries! I only found out yesterday too
I have also thought about not only the letters of your first word but the placement. I either use 'STERN' or 'RENTS.' Since 'rents' ends in S, it will rule out most plural words. But then I think that plural words don't tend to be the words used in Wordle. So I usually just go with 'stern.'
@@lindybeige Maybe it rejects "nails" if you enter it as the plural of nail, but it accepts it if you enter "nails" as the past tense of the verb "nail"? ;-)
Never have I ever been tricked into enjoying a math class like this. I wish I had you instead of all my college professors
I mean I'm sure he had to go through what you did to get to the fun things he does now.
@@malachiduncan6104 this, also learning anything you don’t wanna learn will ALWAYS be worse than something you are motivated to do.
Hear, Hear.
@@malachiduncan6104oh i heard the lecture about information theory. And you can teach all of this real boring
Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!
🤣🤣🤣
gold
Same but FARTS
Lmao
You might like Lewdle, the lewd version. (Penis is my first guess on it every day)
thanks for making this. now people will stop asking me to make this video, lol
Lol, would still appreciate your take! Thanks jan
People still won’t stop asking you, lets be honest.
You’re contractually obligated to remake this video in toki pona using seximal notation.
Do the same thing but instead of the bit, you have -log base 6 of p(x).
@@Anonymous-df8it You mean -log base 10 of 1/p(x), right?
A year later and my blind devotion to your original video has paid off. Thank you kindly!
All Greens.
I guessed crane time since I saw this video, I never thought the day would finally come
What do we start with now?
I watched this only a week or so before adopting it and it being correct on the first guess.
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!
I love how the sketch showed up as I read your comment
The art takes a fascinating discussion to the next level. Well done.
But how are they done? Looks almost like made from 2D Fourier Transform curves
@@shoam2103 what about the drawing made it seem that way?
Timestamp comments like this!
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…”
Hi alpha I love your videos huge science fan!
Pros watch at 2x speed
@@imbw267 nah 1x. I want to appreciate it in its entirety
I knew it was a 30 min video when it started. Couldn't believe it was already over.
ngl I did the same thing with the speed of motion
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.
I've lost only a couple times; once because I got the last 4 letters, but there were more possibilities for the first letter than I had guesses left. that would be a case to use a word that doesn't include the results from previous guesses.
?. SZwa*=+
he has that at the end of the vid
he does a zip on the guesses and patterns, look at the source code:
if hard_mode:
for guess, pattern in zip(guesses, patterns):
choices = get_possible_words(guess, pattern, choices)
Oh. That's just how I've been playing normally...
I could've never had forgiven my self had I not played Wordle today. Been using crane since this video came about.
Came here for this, was not disappointed.
Also I believe NYT has updated the Wordle words list, would love to see an updated video with the latest best starter.
@@lpeabody yeah idk if it's public though?
@jonaslarsson5279 it might be the the source code somewhere
18:38 I bet you had a lot of fun writing that bit
Hello
That's two different RUclipsrs that I've been watching recently that have commented on this video. (You and AlphaPhoenix.) I love that!
I come to the comments to write this and see my boy bismuth beating me to the punch
I spit out my tea at "Where those after first are after, where and those, being just a little bit less common."
These nuts haha gotem. Someone end me pls.
"we shouldn't let machines rule our lives" -the man writing and using a wordle bot
Love the video!
HAHAHA I was going to bring that up. Super funny.
Funny if you take it the wrong way yeah but the meaning of that saying is to not blindly follow a machine's decision, which is exactly what he's doing by taking into account the bot suggestion but ultimately making his own choice with what info he has available aka the word list and his personal preference.
I know what it means, Corne, lol
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.
Possibly fun fact: GEB is why I'm an atheist.
@@Oberon4278 cringe alert
@@hackkitts9254why ?
@@Oberon4278reductionism only gets you so far
@@Oberon4278what argument convinced you?
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.
I believe that the original list had all available scrabble five letter words, but the coder's partner went through and took out all the truly ridiculous and obscure ones
sounds like a virus
@@helenross3037 The allowed words list is the full list. The possible answers is the curated by the partner list.
@@helenross3037 Threw out 10,000 words.... yet kept American spellings of words despite being British. Pfft... snowflakes
@@trefwoordpunk2225 Isn't Scrabble (or at least Scrabble tournaments) US centric? I feel like it's more likely the Scrabble tournament people removed those words
Came for the wordle, stayed for the awesome lesson on information theory. Cool!
love your videos!
Your playlist on discrete math is up next on my list...
Professor Bazett! You were my professor while I was at UofT and just wanted to say you were hands down one of the best math teachers I've had, I still remember your infectious enthusiasm for the topic
@@edwardsulitzer3738 hey cool! Small internet lol
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
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 😁😁😁
I also was here for that
No spoilers 😂
I used crane today. Got it on first word.
Lol
Coming in with the -4 (WordleBot did it in 5 that day)
"Ignoring its recommendation, because we can't let machines rule our lives"
I love this!!!
L
Yesss, I laughed out loud at this part too!
18:39-18:58 I love this paragraph! Love this wordplay, brings back VSauce memories!
I really liked it as well :)
Yea, brillaint stuff
That part made me smile. You could tell he was having fun with it :)
Grant is a fucking genius lmao
Reminds me a of CGP Grey video personally with the wordplay and semi-rhythmic nature
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.
Fun fact: (not Fun at all actually) in portuguese its "tara", but the word for "pervert" is "tarado", where -do is a suffix, meaning "perversion" is "tara" as well
@@joaomatheus6222 How interesting! I looked up the etymology of "tare", to see if it might explain why "tara" has two different meanings in Portuguese. I found that the medieval Latin word "tara" comes from the Arabic word "tarah", meaning "thing deducted or rejected, that which is thrown away", which is derived from "taraha", meaning "to reject". Perhaps perversion became associated with rejection at some point in the history of the Portuguese language.
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@MelodiousThunk I suspect you are on the money about that. In Spanish we also have the verb "tarar": to set a scale to zero. Also we have a "tarado" (male) and "tarada" (female) but it translates as stupid or idiot. In fact, it's a participle. It's like saying "tared":
The scale was tared // La balanza fue tarada.
I wouldn't be surprise if your explanation is also valid for Spanish. Just remember the complex history Spain and Portugal have with each other. Specially during the Al Andalus times.
I always wondered why the scales I use to brew my coffee had a "T" written on the button that zeroes the scales 😂
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.
I like that.
why use he log base 2??
bcs always we cant get half observation in my space of probabilities
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 came to say this. It is, most likely, the best presentation I have ever witnessed.
Really cool presentation.
Laughed at the words Crane and Shtik when they came out. Reminds me of a thing I saw a few days ago called joincrane.
He deserves the wordl(e)
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!
I think it is experience rather than intuition
@@koktszfung Isn't most of intuition simply what you expect based on experience? 😛
@@koktszfung Intuition is experience-driven
@@koktszfung You got schooled in the comments.
oh I thought he said 3 was dirty, as in you're using outside info or likely cheating. continuing the golf terms make more sense lol
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!
reducible has some pretty good videos on it, especially the compression video. He uses grant's library, so they look like 3b1b but instead of a focus on math, it's on cs.
Honestly, machine learning is really not the best context to get an intuitive understanding of entropy.
Machine learning in IMHO is a wrong introduction for Information Theory. Shannon's paper "A mathematical theory of Communication" and Hamming's Paper on Error correction and Detection are really worth reading and easily approachable in few sitting.
Same. I learn more maths, better maths in a few 3b1b videos than I do at school
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).
The definition that I use (I think I got it from PBS Space Time) is a measure of how much *unknown* information - according to certain defined properties like particle position/velocity, quantum properties, etc. - is present in a given system.
Deacon's definition is definitely more concise though!
@@aaron552au sussy
What the heck is happening here 😭
Compound Pivot. Dead Hands. Finesse Swing. 730, 900, 1030 swings. Makes complete sense @David
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
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.
played it, loved it
Actually I wrote an algorithm to play mastermind using this exact approach!
I thought I was the only one compare it to that game
was thinking the same thing!
i still have that board game!!
(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.’
I also thought that was brilliant. Such awesome word play and creativity for such a small moment
As soon as I heard it I looked for this comment
@@shibno01 same lol
I thought I was having a neurological event.
WHOSE on FIRST?
Good to see you all here 😀
This video has finally fulfilled its purpose
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 ruclips.net/video/fRed0Xmc2Wg/видео.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
:O btw really nice video! The animations were amazing and they made it very fun to watch! Keep it up!
I find it very interesting that in all three of these words, 'A' finds itself in the third position. Is that just a thing where most 5 letter words containing an 'A' have it in the third position or is that meant as a guess to provide most information - or bits?
will we see a follow-up with hard mode consideration?
couple more questions on this super interesting video:
1. i note that the information you are gaining each time seems more based on letter frequency while not really considering letter placement frequency (as your suggested guesses often include words with letters in incorrect places, albeit with 0 probability of being right). that may be another avenue for info gain - ie, doing some analysis on how often a given letter occurs in a specific location.
2. strongly defining what is optimal as it may mean different things to different ppl. you seem to have defined it as lowering the expected number of guesses until being correct. however, another might reasonably define optimal as never missing a puzzle which i suspect would change the strategy being used.
and of course my previous question of looking at the puzzle in hard mode would also affect how the previous two points are considered.
cheers and thanks for the informative video!
Huh, I ran a much more naive calculation of the best first guess (matching every word in the worlde dictonary against every other word, calculating yellow and green clues, and generating a weighted average score with green clues being a bit more valuable than yellow) and I also came up with SOARE as the best first guess.
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
More like "you ever watch a video that is too long you actually SKIP to the end screen" 😅 Yeah no way am I sticking around for 30 minutes trying to get info on the best start word to use.
@@AzureSteel why would you look to an in-depth mathematics channel for wordle tips?
Wait Cheetahh. Lol. Holy crap. Weird to find a bridge player here lol
@@dogmouthhorse Pretty sure this video was recommended to me (and probably to a lot of other people given the views this has relative to his other videos in the past year) through YT's algorithm because of the recent Wordle hype.
@@AzureSteel The word is in the thumbnail, if you don't like math this was an easy skip lmao
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 do this
If you know someone starts with the same every time, then you can use their scoring pattern to unlock information yourself. Bit cheaty though
@@seastilton7912 I do it to pass the time between puzzles but you make an excellent point.
I do this. It's pretty fun
"queue" must be pretty bad.
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!
real worlde example :D
@@EscurKo haha yes yes, you get it. Its not a book exercise.
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 would love to see a follow-up with hard mode considered.
I wonder if looking ahead at the next guess is all you really need for hard mode.
@@rantingrodent416 definitely gotta look ahead at more than one guess; it's easy to get stuck with 4 letters solved and 4-5 options for the last letter and if you don't have enough guesses left...
Am I the only one that finds hard mode easier?
@@AntonioDoukas hardmode is definitely harder, so I assume you are. if you get stuck on a word with 4 greens and one grey, that could have several possibilities for the last one, you're boned
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”.
the issue is that you will never get the word in two or three guesses like that, so it maximizes your chances of winning but not your score
you can always do:
GLENT
BRICK
JUMPY
VOZHD
WAQFS
this eliminates 25/26 letters and just leaves X
I'm with you, find the vowels first ...
@@treverfox1280 Doesn't work if your Wordle requires entering only guesses that are words, like cell phone Wordle from Lion Studios Plus. Also fails for goal words requiring trial and error, like batch/match/patch/watch/hatch/latch/catch, which can't be reliably guessed even if all six lines were used.
'I like to start with “Faint” ' Not optimal, because the consonant F is not a frequent one. Saint would be better, and including E in the first word would be best.
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
The same thing literally happend to me RIGHT NOW, I was shocked lmao!!
ahaha me too
I got 4/6
oh
@@NovaaZR
he meant tht day the actual word was *OTHER* so he got it right
on the first try lol
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.
on that note, i feel like the _position_ of the letter within the 5 could also be valuable. i believe that's why 'tares' is valued over 'stare' because presumably there are more words ending with s, which might be pretty informative.
@@alveolate yeah, letter positioning must be valuable. I actually initially preferred stare over rates (same logic applies to tares) because I thought the wordle would never be a plural so an S in the last position would be bad! Maybe vowels in positions 2 and 4 are better than in positions 3 and 5?
This ^^^. You can easily see it, if you guess a word with "U" and "U" is not in the word, then "Q" isn't either.
In code breaking, you'd see a word that ended in "Y" and guess one that ends in "LY" (hard mode) because that's a likely 2 letter combination. I don't have the table of common 2 letter combinations but it's available.
Yeah if we’re playing to eliminate two letter combinations word final s also informs us in situations of “es” (as in tares. just as word initial c would inform us of possible ch words
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.
I use IRATE/SOUND myself
Nice. ADIEU/SHORT is mine. So instead of the N I’m guessing the H. Other than that it’s the same letters.
@@nigelong1779 I was irate and pound but will definitely switch to sound now
I use AUDIO/LYRES, I did a very non-scientific survey of digraphs and found that S (as first letter), L or R (as second letter) have the most distinct ones, so far I'm averaging 4 so I'm maybe doing as well as a simple robot.
I did exactly these 2 as well, have not had a single misser and played since start. We stopped using it as it became too easy to play with these 2
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
hi evan
Hi Evan
@Ex Japan you're lucky,
I lost $1500 trading with an unprofessional trader.
There are lots of good experts out there but most offer little ROI's. I will advise trading with Mr Nicholas Burke-Gaffney's team as I make over $35,000 on average per month from their trading bots.
I would like to see a Hard Mode version of this analysis and how the algorithm reacts to it.
Yeah I was like damn not even playing hard mode. Gotta step up
@@oldcouchcushion1545 Not playing hard mode = weaksauce
the letters „first naive ideas“ tending to the word „start“ is such a nice detail!
well done video!
Today, I thank you.
This whole video is great but I have to say I liked the cute word play around 19:00 quite a lot.
Would love to see how you would approach tackling Wordle’s “Hard Mode.” Loved it, thanks so much for making this
I’d love to see the changes hard mode creates as well.
Ditto! What’s the best first word in Hard Mode?
Great video! (but none of it applies to my game lol)
@@kidalan lol😐
@@kidalan I go for the naïve frequency analysis-based route. 'orate' is my go-to atm, but it used to be 'opera'.
That is not to say by any means it is optimal.
@@__a_4444 I like those openers! I usually open with adieu or ourie. I like to establish which vowels I’m working with, then use that foundation to shoot down consonants. If there was a word with five vowels, I’d use that every time. 😆
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!
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
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.
why even bother going beyond 2 guesses? didnt get it in 2, you failed.
wouldnt that exponentially increase the complexity of the computation. Is it even solvable within 2 steps ? I think grant mentions something along the same lines.
@@adityapalve3752 I don't know why you think the computation would be far more complex since you're only looking 1/2 guesses into the future.
It isn't solvable within 2 steps, but you can try to solve it within 2 steps as much as possible (likely by increasing the weighting of the frequencies of the words; this gives you less information in the long term but increases the chance that you get lucky on the second guess).
Hopefully this makes sense lol.
Especially with the long tails it is definitely possible to trade 'get it in 3 or less more than x% of the time' for the average score
That just means doing the first two guesses in hard mode and the continuing normally. Which in reality just means the set of guessable words on the second guess is smaller.
amazing video as always! please don't ever stop producing them !!
Just wanted to thank you for this video I got wordle in 1 yesterday. Guess it’s time to change my word to Salet. ;)
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.
Could you give a link to that please? Klinkt heel erg interessant!
Also been around as a tv show called "MOTUS" in France
You might be interested to know Lingo actually started in the US in 1987 and has had international versions in at least 15 countries.
Those two brother remind me of Michael Larson who memorized the pattern of the Press Your Luck board and used it to beat the system.
Also very similar to the game “Mastermind” that uses colored pegs instead of letters.
Link?
I don’t know why, but this was the most calming video I’ve ever watched… math can be so relaxing sometimes
His voice is extremely soothing. I'm going to check out his other videos just because of that 😂
Edit: I discovered this is a math channel. While I enjoyed this video, I'll have to reconsider because math and I have not historically had a great relationship
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
Yeah, and the more nuanced version of this is that human preference is used where a heuristic is more cost-efficient than more computing.
In this case, Grant used his intuition to feel where the cut-off point is. However by the definitions given in this video, this cut-off point should certainly be able to be found in the game-theoretic sense. A quick naive approach would be to try different iterations of the bot using different cut-off points and over millions of iterations find the optimal point.
But you see that's exactly why Grant used his intuition as a heuristic instead, because the expected gains from running said millions of iterations is very little compared to what his best guess would do. And as an alternative, if Grant used another method (not brute force simulations) to try to get the exact game-theoretic optimal point, it would be a lot of thinking time used for not much effect.
In WordHoot, a variant of Wordle, where speed matters, I see people consistently beat bots.
In this case he's using a heuristic to approximate the true word distribution which is zero for words not in the wordle list and 1/N for words that are in the wordle list (where N is the size of the wordle list).
It's kluge in the sense that he could just use the wordle list for this purpose, but he decided that's off-limits side-information, so he goes ahead and finds a different source of side-information that he can use to approximate the wordle list distribution.
The real lesson is that if you require human preference, the problem is likely ill-posed :)
The use of priors (prior beliefs) for making predictions is quite often used in some areas of statistics and machine learning. :)
@@lekhakaananta5864 it's basically a password cracker bot but a bit more chill
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.
I loved that book as a kid
goated book
@@kylemcleod4115 same
I will be checking that out
favorite book ever
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 like anime and shout
you can always do:
GLENT
BRICK
JUMPY
VOZHD
WAQFS
this eliminates 25/26 letters and just leaves X
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
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.
I heard about that
Really happy it worked out well for the family, but I also laughed my ass off when I read it. "Mom didn't send me her Wordle, I gotta call the cops RIGHT NOW"
"911, what's your emergency?"
- "My mother hasn't sent in her wordle today"
"Don't worry ma'm, we'll handle it. *noises* Squad 12, get the tank, we got an anti-wordler!"
*background* "God, another one, hope it doesn't end in an airstrike this time!"
@@sorsocksfake they actually had to get their armored personal carrier out because of the hostage
SAVED was word of the day!
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.
That’s so helpful! Thank you so much.
Yeah, that explanation was very clear to me. Thanks.
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.
Use AUDIO and EYING to get all of the vowels
@@dave9012 I just learned that you guys consider "y" a vowel.
@@LuckyLex_ WAY back in school, we learned that the vowels were: "AEIOU and sometimes Y". Dunno what they teach the kids these days.
@@ColinFox In terms of wordle I think it's totally valid to put it into the same category as other vowels. With how you construct words in english not considering y a vowel with this kinda game is just going to cause frustration and possible confusion.
@@LuckyLex_ Only sometimes
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
don't get too excited - it's just conceptual baloney.
@@JamesHawkeRUclips Conceptual? He tested it; it's quite evidential.
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!
hi geo
Thank you for your service geo
hey it’s the big cactus guy
you mean you did and matt was watching chess lmao
hi minecraft man
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!
timestamp please
@@joseville 18:40
Such clarity in explaining things
first comment and also feels like botting
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@teeforever1 no cares about christianity
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.
today’s word was crane so i got it first try lol
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.
"fewer"
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.
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.
I do that too!
Interesting. I happen to have been using TASER as a first try, which is just an anagram of TARES!
Except that the order matters, as the video maker argues convincingly. Still, though, great intuition!
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.
That's what's so interesting about absurdle! Having the same first few guesses can really back it into a corner. I really wonder if it's possible to force any given word out of it. With how restrictive and deterministic it is, it's not obvious that this should be the case
@@michaelmahoney5677 I'm pretty sure the about page on the website explains the best case scenario (or at least one of them).
I also ran into a similar issue of double consonant words with many many options for a single letter... so I started by guessing things like "wooly" right off the bat to reduce the number of options. Better to make those guesses sooner than later.
@@michaelmahoney5677 QNTM, the author, wrote an algorithm to do just that, and it even works if you can only guess words that can also be actual answers. I think they even got it to work on hard mode? Check the twitter account.
Cool video! Loved the math! It would be different for hard mode though where you can't ignore the clues you already have.
Was thinking the same thing! I liked the little teaser at the end, but wish the video went into it more as “hard mode” is my preferred way to play
I’ve never played this but if that’s the restrictions of hard mode, it seems more like dumb mode..
which I suppose you could also refer to as hard mode
@@Jay22222 true
@@Jay22222 What do you mean? If your first guess gave you the information that an R and an E are in the word, then your 2nd guess has to have an R and an E in it. That gives you 2 less spots to try new letters. It's significantly harder.
@@Jay22222 why tho lol
Really great video. Helped clarify and solidify some of my thoughts regarding information theory. Wordle was also a nice familiar subject choice.
I watched this video for the first time exactly a year ago, came back to watch your youtube explanation on the measure of entropy for my information theory class. The official lecture papers on that topic are so obscure