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Solving Wordle using information theory

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3Blue1Brown

3Blue1Brown

Күн бұрын

Пікірлер: 8 900
@leumasarc4180
@leumasarc4180 2 жыл бұрын
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😅
@lilydiring4295
@lilydiring4295 2 жыл бұрын
making this video is just an excuse to prove his friend is stupid mathematically lol
@Acc_Expired
@Acc_Expired 2 жыл бұрын
To be fair, the friend did have the best possible explanation for it. They maximized expected joy rather than information.
@teeforever1
@teeforever1 2 жыл бұрын
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).
@anasimron
@anasimron 2 жыл бұрын
@@teeforever1 wat
@ralphcrewe374
@ralphcrewe374 2 жыл бұрын
His friend is probably pretty awesome
@lumisussy
@lumisussy 2 жыл бұрын
Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!
@Strange-Loooop
@Strange-Loooop 2 жыл бұрын
🤣🤣🤣
@dylnn-music
@dylnn-music 2 жыл бұрын
gold
@sullivannick
@sullivannick 2 жыл бұрын
Same but FARTS
@sunritroykarmakar4406
@sunritroykarmakar4406 2 жыл бұрын
Lmao
@lildevil362003
@lildevil362003 2 жыл бұрын
You might like Lewdle, the lewd version. (Penis is my first guess on it every day)
@RazAnime
@RazAnime 2 жыл бұрын
creating an algorithm for this and comparing them against each other sounds like it would have made a great programming competition
@bigbadwolf4075
@bigbadwolf4075 2 жыл бұрын
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.
@mitikox
@mitikox 2 жыл бұрын
well, a bit further from wordle, with the same intent, there's the Hutter prize
@sudevsen
@sudevsen 2 жыл бұрын
Polygon already did it
@tiagoaoa
@tiagoaoa 2 жыл бұрын
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!
@oelarnes
@oelarnes 2 жыл бұрын
@@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)
@tztztz-vp4ty
@tztztz-vp4ty 2 жыл бұрын
The amount of preparation work in order to produce a video like this is unbelievable.. truly impressive work.
@ParadanMusic-cn7ym
@ParadanMusic-cn7ym 7 ай бұрын
even if i'm there i'm always listening out for these specific locations for a better d'andre type of speaking throughout these special and widly ranged with the ability to be truly free
@clickbaitking6770
@clickbaitking6770 2 жыл бұрын
I love those sketches you put in when depicting real life situations, like the conversation between Von Neumann and Shannon 12:01!
@mrfeliscatus3236
@mrfeliscatus3236 2 жыл бұрын
I love how the sketch showed up as I read your comment
@lindsaybeyerstein7096
@lindsaybeyerstein7096 2 жыл бұрын
The art takes a fascinating discussion to the next level. Well done.
@shoam2103
@shoam2103 2 жыл бұрын
But how are they done? Looks almost like made from 2D Fourier Transform curves
@paradoxicallyexcellent5138
@paradoxicallyexcellent5138 2 жыл бұрын
@@shoam2103 what about the drawing made it seem that way?
@paradoxicallyexcellent5138
@paradoxicallyexcellent5138 2 жыл бұрын
Timestamp comments like this!
@AlphaPhoenixChannel
@AlphaPhoenixChannel 2 жыл бұрын
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…”
@chiragkumar9060
@chiragkumar9060 2 жыл бұрын
Hi alpha I love your videos huge science fan!
@imbw267
@imbw267 2 жыл бұрын
Pros watch at 2x speed
@AlphaPhoenixChannel
@AlphaPhoenixChannel 2 жыл бұрын
@@imbw267 nah 1x. I want to appreciate it in its entirety
@shoam2103
@shoam2103 2 жыл бұрын
I knew it was a 30 min video when it started. Couldn't believe it was already over.
@daney-tv
@daney-tv 2 жыл бұрын
ngl I did the same thing with the speed of motion
@lindybeige
@lindybeige 2 жыл бұрын
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.
@figgahh5823
@figgahh5823 2 жыл бұрын
the word is never a plural fyi
@lindybeige
@lindybeige 2 жыл бұрын
@@figgahh5823 Oh really? It accepts guesses of plurals, such as NAILS which is used as an example in this video. Good to know, thanks.
@figgahh5823
@figgahh5823 2 жыл бұрын
Lindybeige no worries! I only found out yesterday too
@laurie_guilbeau
@laurie_guilbeau 2 жыл бұрын
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.'
@andrewedgecombe
@andrewedgecombe 2 жыл бұрын
@@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"? ;-)
@blackholevortex
@blackholevortex 2 жыл бұрын
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.
@Oberon4278
@Oberon4278 Жыл бұрын
Possibly fun fact: GEB is why I'm an atheist.
@hackkitts9254
@hackkitts9254 Жыл бұрын
@@Oberon4278 cringe alert
@nephastgweiz1022
@nephastgweiz1022 Жыл бұрын
​@@hackkitts9254why ?
@cstatic01123
@cstatic01123 Жыл бұрын
​@@Oberon4278reductionism only gets you so far
@marcuskissinger3842
@marcuskissinger3842 8 ай бұрын
@@Oberon4278what argument convinced you?
@Bismuth9
@Bismuth9 2 жыл бұрын
18:38 I bet you had a lot of fun writing that bit
@eboone
@eboone 2 жыл бұрын
Hello
@NoriMori1992
@NoriMori1992 2 жыл бұрын
That's two different KZbinrs that I've been watching recently that have commented on this video. (You and AlphaPhoenix.) I love that!
@dannyb21892
@dannyb21892 2 жыл бұрын
I come to the comments to write this and see my boy bismuth beating me to the punch
@devonm8578
@devonm8578 2 жыл бұрын
I spit out my tea at "Where those after first are after, where and those, being just a little bit less common."
@NoNTr1v1aL
@NoNTr1v1aL 2 жыл бұрын
These nuts haha gotem. Someone end me pls.
@HBMmaster
@HBMmaster 2 жыл бұрын
thanks for making this. now people will stop asking me to make this video, lol
@RobBot00
@RobBot00 2 жыл бұрын
Lol, would still appreciate your take! Thanks jan
@lillianruan9801
@lillianruan9801 2 жыл бұрын
People still won’t stop asking you, lets be honest.
@shinydino
@shinydino 2 жыл бұрын
You’re contractually obligated to remake this video in toki pona using seximal notation.
@Anonymous-df8it
@Anonymous-df8it 2 жыл бұрын
Do the same thing but instead of the bit, you have -log base 6 of p(x).
@AlienValkyrie
@AlienValkyrie 2 жыл бұрын
@@Anonymous-df8it You mean -log base 10 of 1/p(x), right?
@nipungupta8846
@nipungupta8846 2 жыл бұрын
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!
2 жыл бұрын
I came to say this. It is, most likely, the best presentation I have ever witnessed.
@robchan2604
@robchan2604 2 жыл бұрын
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.
@sabnarose
@sabnarose 2 жыл бұрын
He deserves the wordl(e)
@kilianschabort2354
@kilianschabort2354 Жыл бұрын
A year later and my blind devotion to your original video has paid off. Thank you kindly!
@BrandonSmith-mj9nf
@BrandonSmith-mj9nf Жыл бұрын
All Greens.
@YungPetee
@YungPetee Жыл бұрын
I guessed crane time since I saw this video, I never thought the day would finally come
@maxking65
@maxking65 Жыл бұрын
What do we start with now?
@robeik
@robeik Жыл бұрын
I watched this only a week or so before adopting it and it being correct on the first guess.
@DrTrefor
@DrTrefor 2 жыл бұрын
Came for the wordle, stayed for the awesome lesson on information theory. Cool!
@dariuskianersi4350
@dariuskianersi4350 2 жыл бұрын
love your videos!
@FranFerioli
@FranFerioli 2 жыл бұрын
Your playlist on discrete math is up next on my list...
@edwardsulitzer3738
@edwardsulitzer3738 2 жыл бұрын
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
@DrTrefor
@DrTrefor 2 жыл бұрын
@@edwardsulitzer3738 hey cool! Small internet lol
@teeforever1
@teeforever1 2 жыл бұрын
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).
@AlexDings
@AlexDings 2 жыл бұрын
4:00 note that the list used in Wordle is the exact list of words allowed in international tournament Scrabble. It's called CSW19.
@helenross3037
@helenross3037 2 жыл бұрын
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
@rowanlivengood
@rowanlivengood 2 жыл бұрын
sounds like a virus
@tomribbens4860
@tomribbens4860 2 жыл бұрын
@@helenross3037 The allowed words list is the full list. The possible answers is the curated by the partner list.
@trefwoordpunk2225
@trefwoordpunk2225 2 жыл бұрын
@@helenross3037 Threw out 10,000 words.... yet kept American spellings of words despite being British. Pfft... snowflakes
@tsumikiminiwa4603
@tsumikiminiwa4603 2 жыл бұрын
@@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
@berryesseen
@berryesseen 2 жыл бұрын
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.
@iain_nakada
@iain_nakada 2 жыл бұрын
I like that.
@shreyasunil9204
@shreyasunil9204 2 жыл бұрын
why use he log base 2?? bcs always we cant get half observation in my space of probabilities
@gwenturo9550
@gwenturo9550 Жыл бұрын
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
@3blue1brown
@3blue1brown 2 жыл бұрын
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 kzbin.info/www/bejne/nIPIlWOOoshljck 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
@0x19
@0x19 2 жыл бұрын
:O btw really nice video! The animations were amazing and they made it very fun to watch! Keep it up!
@MaxxDW
@MaxxDW 2 жыл бұрын
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?
@jaekim7514
@jaekim7514 2 жыл бұрын
will we see a follow-up with hard mode consideration?
@jaekim7514
@jaekim7514 2 жыл бұрын
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!
@darthrainbows
@darthrainbows 2 жыл бұрын
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.
@Paul_MacK
@Paul_MacK 2 жыл бұрын
Never have I ever been tricked into enjoying a math class like this. I wish I had you instead of all my college professors
@malachiduncan6104
@malachiduncan6104 2 жыл бұрын
I mean I'm sure he had to go through what you did to get to the fun things he does now.
@melody3741
@melody3741 Жыл бұрын
@@malachiduncan6104 this, also learning anything you don’t wanna learn will ALWAYS be worse than something you are motivated to do.
@CloneDaddy
@CloneDaddy Жыл бұрын
Hear, Hear.
@liechtenstein6775
@liechtenstein6775 8 ай бұрын
​@@malachiduncan6104oh i heard the lecture about information theory. And you can teach all of this real boring
@I_am_Itay
@I_am_Itay 2 жыл бұрын
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
@Hydratz
@Hydratz Жыл бұрын
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
@zangeh
@zangeh 2 жыл бұрын
"we shouldn't let machines rule our lives" -the man writing and using a wordle bot Love the video!
@karakenio
@karakenio 2 жыл бұрын
HAHAHA I was going to bring that up. Super funny.
@corneasp9418
@corneasp9418 2 жыл бұрын
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.
@zangeh
@zangeh 2 жыл бұрын
I know what it means, Corne, lol
@maanitarora1172
@maanitarora1172 7 ай бұрын
exactly! he's just iconic!
@maanitarora1172
@maanitarora1172 7 ай бұрын
exactly! he's just iconic!
@MrSamwise25
@MrSamwise25 2 жыл бұрын
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!
@koktszfung
@koktszfung 2 жыл бұрын
I think it is experience rather than intuition
@SpeedOfDarknesss
@SpeedOfDarknesss 2 жыл бұрын
@@koktszfung Isn't most of intuition simply what you expect based on experience? 😛
@randomsoul294
@randomsoul294 2 жыл бұрын
@@koktszfung Intuition is experience-driven
@lambdaman3228
@lambdaman3228 2 жыл бұрын
@@koktszfung You got schooled in the comments.
@TheJunky228
@TheJunky228 2 жыл бұрын
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
@stephaniecass6567
@stephaniecass6567 2 жыл бұрын
"Ignoring its recommendation, because we can't let machines rule our lives" I love this!!!
@AuRoBoss
@AuRoBoss 2 жыл бұрын
L
@lordbattletax6772
@lordbattletax6772 2 жыл бұрын
Yesss, I laughed out loud at this part too!
@jonaslarsson5279
@jonaslarsson5279 Жыл бұрын
I could've never had forgiven my self had I not played Wordle today. Been using crane since this video came about.
@jonaslarsson5279
@jonaslarsson5279 Жыл бұрын
@@lpeabody yeah idk if it's public though?
@connorwallace5274
@connorwallace5274 Жыл бұрын
​@jonaslarsson5279 it might be the the source code somewhere
@DrZedDrZedDrZed
@DrZedDrZedDrZed 2 жыл бұрын
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).
@aaron552au
@aaron552au 2 жыл бұрын
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!
@JaxsobThe3rd
@JaxsobThe3rd 2 жыл бұрын
@@aaron552au sussy
@silentofthewind
@silentofthewind 2 жыл бұрын
What the heck is happening here 😭
@paulkiat
@paulkiat 2 жыл бұрын
Compound Pivot. Dead Hands. Finesse Swing. 730, 900, 1030 swings. Makes complete sense @David
@teeforever1
@teeforever1 2 жыл бұрын
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).
@caspg
@caspg 2 жыл бұрын
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!
@EscurKo
@EscurKo 2 жыл бұрын
real worlde example :D
@caspg
@caspg 2 жыл бұрын
@@EscurKo haha yes yes, you get it. Its not a book exercise.
@RoanCritter
@RoanCritter 2 жыл бұрын
18:39-18:58 I love this paragraph! Love this wordplay, brings back VSauce memories!
@vez3834
@vez3834 2 жыл бұрын
I really liked it as well :)
@jamiepayton1574
@jamiepayton1574 2 жыл бұрын
Yea, brillaint stuff
@necromac
@necromac 2 жыл бұрын
That part made me smile. You could tell he was having fun with it :)
@nakulgoyal2879
@nakulgoyal2879 2 жыл бұрын
Grant is a fucking genius lmao
@kingkory2
@kingkory2 2 жыл бұрын
Reminds me a of CGP Grey video personally with the wordplay and semi-rhythmic nature
@CorpseEater.
@CorpseEater. Ай бұрын
I'm sure one day your friend will get "weary" as a word and that day is gonna be the best of his life
@binaryalgorithm
@binaryalgorithm 2 жыл бұрын
Such clarity in explaining things, is why I love this channel. Plus, you do a ton of work to make it visually interesting!
@teeforever1
@teeforever1 2 жыл бұрын
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).
@leovin00
@leovin00 2 жыл бұрын
This 30 minute video taught me more about entropy than an entire section on entropy from my machine learning course. Bravo!
@seanvinsick
@seanvinsick 2 жыл бұрын
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.
@suparki123
@suparki123 2 жыл бұрын
Honestly, machine learning is really not the best context to get an intuitive understanding of entropy.
@rahuldewangan1064
@rahuldewangan1064 2 жыл бұрын
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.
@rishikeshchapekar4481
@rishikeshchapekar4481 2 жыл бұрын
Same. I learn more maths, better maths in a few 3b1b videos than I do at school
@beckettmw
@beckettmw 2 жыл бұрын
(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.’
@lawislaw2585
@lawislaw2585 2 жыл бұрын
I also thought that was brilliant. Such awesome word play and creativity for such a small moment
@shibno01
@shibno01 2 жыл бұрын
As soon as I heard it I looked for this comment
@lawislaw2585
@lawislaw2585 2 жыл бұрын
@@shibno01 same lol
@widmur
@widmur 2 жыл бұрын
I thought I was having a neurological event.
@charmingpea
@charmingpea 2 жыл бұрын
WHOSE on FIRST?
@EeveeFromAlmia
@EeveeFromAlmia Жыл бұрын
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.
@oweneastwood3445
@oweneastwood3445 2 жыл бұрын
Grant that little bit you did with "these is in the eighth position" etc was absolutely brilliant. Great video as ever, thank you.
@grandtheftlemon301
@grandtheftlemon301 2 жыл бұрын
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.
@joaomatheus6222
@joaomatheus6222 2 жыл бұрын
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
@MelodiousThunk
@MelodiousThunk 2 жыл бұрын
@@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.
@teeforever1
@teeforever1 2 жыл бұрын
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).
@LucianoRobino
@LucianoRobino 2 жыл бұрын
@@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.
@williamsmith3817
@williamsmith3817 2 жыл бұрын
I always wondered why the scales I use to brew my coffee had a "T" written on the button that zeroes the scales 😂
@Cheetahhh
@Cheetahhh 2 жыл бұрын
You ever watch a video that's so good you actually watch the end screen
@AzureSteel
@AzureSteel 2 жыл бұрын
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.
@dogmouthhorse
@dogmouthhorse 2 жыл бұрын
@@AzureSteel why would you look to an in-depth mathematics channel for wordle tips?
@havocike2400
@havocike2400 2 жыл бұрын
Wait Cheetahh. Lol. Holy crap. Weird to find a bridge player here lol
@AzureSteel
@AzureSteel 2 жыл бұрын
@@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.
@ziggy_starz
@ziggy_starz 2 жыл бұрын
@@AzureSteel The word is in the thumbnail, if you don't like math this was an easy skip lmao
@furretwalky
@furretwalky Жыл бұрын
Today is a momentous occasion - the word IS **CRANE** today! Happy 1-shot day to a lot of people.
@Geosquare8128
@Geosquare8128 2 жыл бұрын
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!
@cutewavelets
@cutewavelets 2 жыл бұрын
hi geo
@dunnperfect8567
@dunnperfect8567 2 жыл бұрын
Thank you for your service geo
@drummike
@drummike 2 жыл бұрын
hey it’s the big cactus guy
@CraftyMasterman
@CraftyMasterman 2 жыл бұрын
you mean you did and matt was watching chess lmao
@bcarpyy2739
@bcarpyy2739 2 жыл бұрын
hi minecraft man
@bored_pyro
@bored_pyro 2 жыл бұрын
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.
@rantingrodent416
@rantingrodent416 2 жыл бұрын
I wonder if looking ahead at the next guess is all you really need for hard mode.
@psymar
@psymar 2 жыл бұрын
@@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...
@AntonioDoukas
@AntonioDoukas 2 жыл бұрын
Am I the only one that finds hard mode easier?
@Codan3
@Codan3 2 жыл бұрын
@@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
@dalmationblack
@dalmationblack 2 жыл бұрын
Hard mode is actually a lot easier to write a bot for, in my experience
@quai8193
@quai8193 2 жыл бұрын
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
@dannyhpy_me
@dannyhpy_me 2 жыл бұрын
The same thing literally happend to me RIGHT NOW, I was shocked lmao!!
@charlieoxspring545
@charlieoxspring545 2 жыл бұрын
ahaha me too
@slinky7696
@slinky7696 2 жыл бұрын
I got 4/6
@NovaaZR
@NovaaZR 2 жыл бұрын
oh
@malleckmelon2086
@malleckmelon2086 2 жыл бұрын
@@NovaaZR he meant tht day the actual word was *OTHER* so he got it right on the first try lol
@Mathefurdullies
@Mathefurdullies Жыл бұрын
the letters „first naive ideas“ tending to the word „start“ is such a nice detail! well done video!
@naspleo2252
@naspleo2252 2 жыл бұрын
This whole video is great but I have to say I liked the cute word play around 19:00 quite a lot.
@justincalfo1486
@justincalfo1486 2 жыл бұрын
Would love to see how you would approach tackling Wordle’s “Hard Mode.” Loved it, thanks so much for making this
@jermudgeon
@jermudgeon 2 жыл бұрын
I’d love to see the changes hard mode creates as well.
@kidalan
@kidalan 2 жыл бұрын
Ditto! What’s the best first word in Hard Mode? Great video! (but none of it applies to my game lol)
@themaincheese5897
@themaincheese5897 2 жыл бұрын
@@kidalan lol😐
@__a_4444
@__a_4444 2 жыл бұрын
@@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.
@kidalan
@kidalan 2 жыл бұрын
@@__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. 😆
@JordanBeagle
@JordanBeagle 2 жыл бұрын
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
@lekhakaananta5864
@lekhakaananta5864 2 жыл бұрын
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.
@ssz8946
@ssz8946 2 жыл бұрын
In WordHoot, a variant of Wordle, where speed matters, I see people consistently beat bots.
@jonathanbaxter5821
@jonathanbaxter5821 2 жыл бұрын
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 :)
@christianhinge7196
@christianhinge7196 2 жыл бұрын
The use of priors (prior beliefs) for making predictions is quite often used in some areas of statistics and machine learning. :)
@w花b
@w花b 2 жыл бұрын
@@lekhakaananta5864 it's basically a password cracker bot but a bit more chill
@vedparekh2170
@vedparekh2170 Жыл бұрын
Finally after using crane as my opening for a year, I'm so grateful i didnt miss wordle 732!
@LeonardoDaVinci01
@LeonardoDaVinci01 2 жыл бұрын
I don’t know why, but this was the most calming video I’ve ever watched… math can be so relaxing sometimes
@monkiram
@monkiram 2 жыл бұрын
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
@bentationfunkiloglio
@bentationfunkiloglio 2 жыл бұрын
By far, my absolute favorite 3b1b video. No uncertainty! I really like that the discussion didn't get bogged down with decision tree specifics. Instead, focus was on deriving an appropriate metric for the problem at hand. Perfect context to discuss entropy, information gain, uncertainty, etc. Nicely done! Giving you a virtual standing ovation.
@dudedude6892
@dudedude6892 2 жыл бұрын
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.
@kylemcleod4115
@kylemcleod4115 2 жыл бұрын
I loved that book as a kid
@prodtheontar
@prodtheontar 2 жыл бұрын
goated book
@blockmath_2048
@blockmath_2048 2 жыл бұрын
@@kylemcleod4115 same
@infiniteplanes5775
@infiniteplanes5775 2 жыл бұрын
I will be checking that out
@natalie-ih1wc
@natalie-ih1wc 2 жыл бұрын
favorite book ever
@Willieg2008
@Willieg2008 Жыл бұрын
I have religiously been using crane since I saw this video, TODAYS OUR DAY GUYS!!!!!🎉
@admiralcapn
@admiralcapn 2 жыл бұрын
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.
@sandal_thong8631
@sandal_thong8631 2 жыл бұрын
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.
@kgratia4748
@kgratia4748 Жыл бұрын
?. SZwa*=+
@22tfortnitevevo
@22tfortnitevevo Жыл бұрын
he has that at the end of the vid
@Kyle-oe2vs
@Kyle-oe2vs Жыл бұрын
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)
@_P2M_
@_P2M_ Жыл бұрын
Oh. That's just how I've been playing normally...
@sabertag6992
@sabertag6992 2 жыл бұрын
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
@JamesHawkeYouTube
@JamesHawkeYouTube 2 жыл бұрын
don't get too excited - it's just conceptual baloney.
@TheDSasterX
@TheDSasterX 2 жыл бұрын
@@JamesHawkeKZbin Conceptual? He tested it; it's quite evidential.
@evan
@evan 2 жыл бұрын
Making a word game about math. I LOVE IT
@christa.mp4
@christa.mp4 2 жыл бұрын
hi evan
@harrypotterina
@harrypotterina 2 жыл бұрын
Hi Evan
@อภิษฎาคนขยัน
@อภิษฎาคนขยัน 2 жыл бұрын
@Ex Japan you're lucky,
@อภิษฎาคนขยัน
@อภิษฎาคนขยัน 2 жыл бұрын
I lost $1500 trading with an unprofessional trader.
@marvinkinnel2920
@marvinkinnel2920 2 жыл бұрын
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.
@tobybartels8426
@tobybartels8426 Жыл бұрын
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!
@JimmyJJJohnson
@JimmyJJJohnson 2 жыл бұрын
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.
@alveolate
@alveolate 2 жыл бұрын
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.
@JimmyJJJohnson
@JimmyJJJohnson 2 жыл бұрын
@@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?
@garyp.7501
@garyp.7501 2 жыл бұрын
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.
@mopanda81
@mopanda81 2 жыл бұрын
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
@yaseen157
@yaseen157 2 жыл бұрын
Beautiful watching as always, thanks Grant! I enjoyed the confusing word skit at 18:40 haha
@pallenda
@pallenda 2 жыл бұрын
This is PERFECT for me! Over the past week I have been fiddling with my own Python wordle "bot". I first made a small text mode version of the game to I could play more, and have slowly worked on my solver. It find skip letters and remove candidates with those letters. It can collect correct letter(bad position) and perfect letters. Yesterday I started going into putting some "weight" to the candidates left, nut I have some funky issues. So this video is a PERFECT next step for me to study. :)
@AxxLAfriku
@AxxLAfriku 2 жыл бұрын
I am being humble when I am telling you that I am the most powerful strongest coolest smartest most famous greatest funniest Y*uTub3r of all time! That's the reason I have multiple girlfriends and I show them off all the time! Bye bye pa
@lolajuliet2662
@lolajuliet2662 2 жыл бұрын
this is so cool i want to try making a wordle bot in python too !!
@aluisious
@aluisious 2 жыл бұрын
@@lolajuliet2662 I made one this morning because I was bored. I figured out one relatively easy way is using regular expressions to check the possibilities and spit out a list that could fit the information at hand. Then I just pick one. Also working on weighting the results.
@YungPetee
@YungPetee Жыл бұрын
This video has finally fulfilled its purpose
@BorinUltimatum
@BorinUltimatum 2 жыл бұрын
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.
@nigelong1779
@nigelong1779 2 жыл бұрын
I use IRATE/SOUND myself
@Tabroski
@Tabroski 2 жыл бұрын
Nice. ADIEU/SHORT is mine. So instead of the N I’m guessing the H. Other than that it’s the same letters.
@simoncarter3541
@simoncarter3541 2 жыл бұрын
@@nigelong1779 I was irate and pound but will definitely switch to sound now
@Stereomoo
@Stereomoo 2 жыл бұрын
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.
@WhitestOC
@WhitestOC 2 жыл бұрын
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
@anderslauridsen601
@anderslauridsen601 2 жыл бұрын
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!
@joseville
@joseville 2 жыл бұрын
timestamp please
@sleinbuyt402
@sleinbuyt402 2 жыл бұрын
@@joseville 18:40
@karlosfy
@karlosfy 2 жыл бұрын
I have studied information theory in top level engineering school and I had never seen this explained as clear as this, not even close. This video makes me wonder about the future of education.
@Ida20
@Ida20 6 ай бұрын
I can’t imagine the work involved in creating this video. It is so refreshing to see something professionally done.
@RJTheBikeGuy
@RJTheBikeGuy 2 жыл бұрын
Cool video! Loved the math! It would be different for hard mode though where you can't ignore the clues you already have.
@rkeating
@rkeating 2 жыл бұрын
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
@Jay22222
@Jay22222 2 жыл бұрын
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
@מיכאלרחמילביץ-ד2ק
@מיכאלרחמילביץ-ד2ק 2 жыл бұрын
@@Jay22222 true
@kaazma
@kaazma 2 жыл бұрын
@@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.
@NikitaOnline17
@NikitaOnline17 2 жыл бұрын
@@Jay22222 why tho lol
@dkursada
@dkursada 2 жыл бұрын
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.
@29BKing
@29BKing 2 жыл бұрын
"fewer"
@Dylan52meow
@Dylan52meow 2 жыл бұрын
This video is an absolute masterpiece. Especially loved the bit at 18:39 about the most common words. Hilarious!
@owenaspinall2046
@owenaspinall2046 2 жыл бұрын
The ¨bit¨?
@CraftBasti
@CraftBasti 2 жыл бұрын
@@owenaspinall2046 watch that part again, but don't look at the screen. Can you make out which word he claims is how common? Hardly, because he structured the sentence in a way as to incorporate the words he read into it, making it difficult to distinguish between the words used for the sentence and the words in quotes.
@owenaspinall2046
@owenaspinall2046 2 жыл бұрын
@@CraftBasti I made a bad pun about how this is about information theory, which uses the unit the "bit".
@CraftBasti
@CraftBasti 2 жыл бұрын
@@owenaspinall2046 ahh of course, that was the reason for the quotation marks! Good one ^^
@AndrewBackhouse1
@AndrewBackhouse1 2 жыл бұрын
It was pure genius
@williamdavis694
@williamdavis694 Жыл бұрын
After 512 days, crane has finally won first try. Thank you
@LifebyBrody
@LifebyBrody 4 ай бұрын
got a first try on my go to "purge" and then when they wiped my history after inactivity I stopped
@antonhagelberg7430
@antonhagelberg7430 2 жыл бұрын
Absolutely impeccable timing, just went over this concept in a course on Machine Learning, feels great to understand what you're saying!
@psd993
@psd993 2 жыл бұрын
what course and/or what reference have you used specifically for information theory (if you did have separate reference material)
@brettlogeais849
@brettlogeais849 2 жыл бұрын
I would like to see a Hard Mode version of this analysis and how the algorithm reacts to it.
@oldcouchcushion1545
@oldcouchcushion1545 2 жыл бұрын
Yeah I was like damn not even playing hard mode. Gotta step up
@Slamdunka963
@Slamdunka963 2 жыл бұрын
@@oldcouchcushion1545 Not playing hard mode = weaksauce
@KayDeeKeySull
@KayDeeKeySull 2 жыл бұрын
As a chemist, i've been using "tares" (3rd person singular - saves the mass of an empty/full in a scale to determine the difference after doing something with it) for over a month, so i feel accomplished seeing this haha:)
@geofflulham8460
@geofflulham8460 2 жыл бұрын
TARES are also a corn/seed used in fishing (in the UK)
@nickalot6436
@nickalot6436 2 жыл бұрын
I’m a cashier at a grocery store and I’ve been using “tares” too.
@eduardojuarez9862
@eduardojuarez9862 2 жыл бұрын
Im a random kid and I have been using stare which is kinda the same but tares might be better
@isaaclodziak-green6326
@isaaclodziak-green6326 2 жыл бұрын
I also work in a grocery store, but I use the word “rates”
@prockpros
@prockpros 2 жыл бұрын
soare is a good starting word too
@cgillespie78
@cgillespie78 Жыл бұрын
Well today's word was CRANE. Have to give this the award for best thumbnail ever
@AshLordCurry
@AshLordCurry 2 жыл бұрын
Crane Shtik combo is absolutely legendary, just tried it, found the word in 3 tries. Absolutely amazing.
@matthewtavani6584
@matthewtavani6584 2 жыл бұрын
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.
@TimeBucks
@TimeBucks 2 жыл бұрын
Such clarity in explaining things
@supreme-lz5yc
@supreme-lz5yc 2 жыл бұрын
first comment and also feels like botting
@teeforever1
@teeforever1 2 жыл бұрын
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).
@rottedpotato645
@rottedpotato645 2 жыл бұрын
@@teeforever1 no cares about christianity
@jimschott
@jimschott 2 жыл бұрын
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.
@tim40gabby25
@tim40gabby25 2 жыл бұрын
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?
@ironknuckle143
@ironknuckle143 2 жыл бұрын
I do this
@seastilton7912
@seastilton7912 2 жыл бұрын
If you know someone starts with the same every time, then you can use their scoring pattern to unlock information yourself. Bit cheaty though
@ironknuckle143
@ironknuckle143 2 жыл бұрын
@@seastilton7912 I do it to pass the time between puzzles but you make an excellent point.
@DeuceBooty
@DeuceBooty 2 жыл бұрын
I do this. It's pretty fun
@huellenoperator
@huellenoperator 2 жыл бұрын
"queue" must be pretty bad.
@ShrtRndKid
@ShrtRndKid 2 жыл бұрын
Very cool breakdown. It's interesting that in so many cases it chooses a word for the second guess that does not contain a confirmed letter from the first guess. This essentially negates your chance of being correct on the second guess in favor of having more information for the third or fourth guesses. It's basically choosing to fail rather than take the chance at gaining less information.
@valenz1234
@valenz1234 2 жыл бұрын
The likelihood of getting it on second is low, may as well find the most information out and try for third.
@david203
@david203 2 жыл бұрын
After an initial guess, there are cases where subsequent guesses can ignore letter positions, including which letters are already green, and still be excellent guesses. It depends on strategy. In my strategy, I guess all vowels using two words, so I ignore colors and almost always give the two words. In fact, for most Wordles, I automatically enter three words so I can also eliminate the most common consonants. This improves solution speed, too.
@chownc
@chownc 2 жыл бұрын
At 7:20, in answer to your question the. technically there’s “WORRY” but for that game information the R wouldn’t work for position 4. Great video! Thanks
@arnabs2009
@arnabs2009 2 жыл бұрын
I noticed that too, but he was obviously answering (or should i say the program was designed) considering the information of R
@InkablyAU
@InkablyAU Жыл бұрын
Just wanted to thank you for this video I got wordle in 1 yesterday. Guess it’s time to change my word to Salet. ;)
@goodgameproductions3039
@goodgameproductions3039 2 жыл бұрын
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.
@Moe5Tavern
@Moe5Tavern 2 жыл бұрын
Could you give a link to that please? Klinkt heel erg interessant!
@JonathanCheseaux
@JonathanCheseaux 2 жыл бұрын
Also been around as a tv show called "MOTUS" in France
@DasVERMiT
@DasVERMiT 2 жыл бұрын
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.
@pokepress
@pokepress 2 жыл бұрын
Also very similar to the game “Mastermind” that uses colored pegs instead of letters.
@alejandromesa2578
@alejandromesa2578 2 жыл бұрын
Link?
@jickhertz4124
@jickhertz4124 2 жыл бұрын
Cool! I made a bot that was also based on 'entropy' without knowing its name and definition. It can beat a 5 letter in 5 goes on average (focused on perfect solve rate, rather than quick solves). But I was really glad to know I was on the right lines and find a more optimal method! Fun project all round! Thanks for sharing
@webx135
@webx135 2 жыл бұрын
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.
@TheMightyGiantDad
@TheMightyGiantDad 2 жыл бұрын
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
@ThePharphis
@ThePharphis 2 жыл бұрын
@@TheMightyGiantDad 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.
@ShmingsThings
@ShmingsThings 2 жыл бұрын
@@TheMightyGiantDad 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.
@iloshwdgac9213
@iloshwdgac9213 Ай бұрын
As an engineer, I used Excel to brute force Wordle. I found "slate" as the word with the most unique letters in the most correct spaces. It warms my pi=4 heart knowing that a mathematician likes my opening move.
@addymant
@addymant 2 жыл бұрын
I really like the approach you took to this because it's completely different from how I would've gone about it! I would have treated it almost like a game of Mastermind, and gladly accepted the wordlists. Then, I would've found that strategy which minimizes the _average_ number of moves, while still requiring that any potential series of guesses gets the right answer within the six allowed.
@additionaddict5524
@additionaddict5524 2 жыл бұрын
entropy is like an advanced average.
@NesrocksGamingVideos
@NesrocksGamingVideos 2 жыл бұрын
Yes, one has to wonder what the objective is. If the objective is to maximize wins in 3 or 4 and not care about 6 or losing okay, but if one just wants to not lose the 100% streak then yeah, the unlikely words become all that much scarier.
@Twisol
@Twisol 2 жыл бұрын
Your literal wordplay at ~18:55 gives me joy XD
@shrugalic
@shrugalic 2 жыл бұрын
Having had fun programming a Wordle helper for the past few weeks, I love this video! 😍 My best fast strategy is down to 3.55 average guesses, and the one attempting to get close to optimizing for shortest game is very slow, but a little better, below 3.5.
@bernie9728
@bernie9728 2 жыл бұрын
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.
@echolegend4400
@echolegend4400 Жыл бұрын
I do that too!
@mrevil11
@mrevil11 2 жыл бұрын
I've always started with Adieu as it eliminates almost all the vowels but this really does make me rethink my process. I haven't missed a word yet but i most often get the word in 5 guesses.
@davidelliott9817
@davidelliott9817 2 жыл бұрын
I do the same but with audio
@Tysto
@Tysto 2 жыл бұрын
Yeah, i think there’s more information in guesses with consonants, since you narrow down the possibilities more. Imagine being free to use AEIOU. You’re nearly guaranteed a hit, but since nearly all words (not “tryst”) use at least one of those letters, but you haven’t actually narrowed the possibilities.
@leonardogoes683
@leonardogoes683 2 жыл бұрын
I Like to use "Aurei" first, "Boxty" second and, for the third word, some with 'S' plus the previous matches. Always get in 4 or 5.
@firstname1317
@firstname1317 2 жыл бұрын
@@davidelliott9817 SAME!!!
@mikec4308
@mikec4308 2 жыл бұрын
audio is also good. didnt even know adieu was a word lol
@alexander191297
@alexander191297 2 жыл бұрын
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! 🙏
@jonaslevyalfie7434
@jonaslevyalfie7434 2 жыл бұрын
As a programmer, I actually been thinking a lot about how I would code a solver for this lately. Great vid as always!
@amaansiddiqui2376
@amaansiddiqui2376 2 жыл бұрын
Same. But just starting seems such a tedious task.
@jasonx7803
@jasonx7803 2 жыл бұрын
@@amaansiddiqui2376 Step one, just pick randomly from all the answers. Then refine. ;)
@PrimeSuperboy
@PrimeSuperboy 3 ай бұрын
watching these videos feels like watching the math teacher tell that one student to show their work and when they do, the teacher says, "show the work behind your work" so the student has to recreate math from the beginning
@budge956
@budge956 2 жыл бұрын
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”.
@joshklapperich9416
@joshklapperich9416 2 жыл бұрын
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
@treverfox1280
@treverfox1280 2 жыл бұрын
you can always do: GLENT BRICK JUMPY VOZHD WAQFS this eliminates 25/26 letters and just leaves X
@jacquescousteau217
@jacquescousteau217 2 жыл бұрын
I'm with you, find the vowels first ...
@david203
@david203 2 жыл бұрын
@@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.
@david203
@david203 2 жыл бұрын
'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.
@Me-mi2ud
@Me-mi2ud 2 жыл бұрын
I've been playing Wordle for a month now and was hoping one of my favourite maths channels would upload something about it, very well timed!
@uncle-ff7jq
@uncle-ff7jq 2 жыл бұрын
You're content and enthusiasm has inspired me to pursue my dreams of learning programming and math, I'm highly grateful.
@ZopcsakFeri
@ZopcsakFeri 2 жыл бұрын
He is neither content nor enthusiasm :)
@hetsmiecht1029
@hetsmiecht1029 2 жыл бұрын
@@ZopcsakFeri your funny!
@brongondwana
@brongondwana 9 күн бұрын
Finally this video appeared in my algorithm some years late. I haven’t noticed anyone pointing it out in the comments yet and I don’t know how it affects your algorithm but a couple of times I’ve noticed it showing 4 green tiles and one yellow which is strictly impossible by the rules because there’s no spot that letter could be misplaced from!
@jb-oi9yv
@jb-oi9yv 2 жыл бұрын
This is one of the reasons why I went for a double major in Applied Mathematics and Computer Science. Great video.
@napoleonkhan8743
@napoleonkhan8743 2 жыл бұрын
All that just to get better at Wordle? That’s dedication
@ethan-loves
@ethan-loves 2 жыл бұрын
At 18:43, he reminds me so much of CGP Grey. That cadence, paired with a nimble navigation of a tongue-twisting utterance... it's nice to see someone else pull off that style.
@APromisePast
@APromisePast 2 жыл бұрын
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.
@judgeomega
@judgeomega 2 жыл бұрын
why even bother going beyond 2 guesses? didnt get it in 2, you failed.
@adityapalve3752
@adityapalve3752 2 жыл бұрын
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.
@louisrialland2527
@louisrialland2527 2 жыл бұрын
@@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.
@Seeker265729
@Seeker265729 2 жыл бұрын
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
@motherlove8366
@motherlove8366 2 жыл бұрын
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.
@KA-lt2tu
@KA-lt2tu Жыл бұрын
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!!
@thegzak
@thegzak 2 жыл бұрын
I was worried you wouldn’t get to the crowning jewel of information theory, which is to show what the theoretical “best” algorithm for something could achieve without having to know the algorithm itself, purely by analyzing the maximum amount of information you can get at each step. But you managed to squeeze it in right at the end, well done!
@Ctulthu00
@Ctulthu00 2 жыл бұрын
Could you refer this fact, please? I think just going for maximum information at each step doesn't work, because it is entirely possible that choices that yield low information initially are rewarded with higher information average later. That's basically why author needs to bruteforce all 2-step combinations, right?
@thegzak
@thegzak 2 жыл бұрын
@@Ctulthu00 you’re right, I overstated the conclusion - in this case he brute forced all possible two steps to show that there can be no guaranteed three-step strategy since there will always be too much uncertainty left over. But the more specific thing I wanted to highlight is that he didn’t have to enumerate all possible three-steps to show that none of them would work - this was done purely by making an information-theoretic argument.
@Ctulthu00
@Ctulthu00 2 жыл бұрын
@@thegzak I see, that makes sense!
@mylonoceda
@mylonoceda 2 жыл бұрын
I was expecting the quote "conditioning reduces entropy" as a reference to conditional entropy. But nevertheless this is arguably one of the most beautiful lessons on information theory I have ever had. Please consider making a full series on information theory, that would be lovely.
@Andrew-yr6ig
@Andrew-yr6ig 2 жыл бұрын
I hate that quote. It's not even true. If it were accurate it would be like "conditioning can't improve entropy."
@piguy314159
@piguy314159 2 жыл бұрын
This video just happened to come out at the same time I was coming up with my own Wordle-solving algorithm: instead of minimizing the average number of guesses, I used minimax to optimize the worst-case scenario. On each turn, I do the following: - Consider all possible words as guesses, including those that are no longer candidates with the information known - For each word in the list, assign a score equal to the number candidate words left in the worst-case scenario (i.e. group the remaining candidates into buckets based on the color pattern they would give for the guess being considered, and use the size of the largest bucket as the score) - Guess whichever word scores lowest (in case of a tie, favor words that are themselves candidates, and if still tied, choose the one that comes first alphabetically) Since I didn't want to see the actual Wordle list, I started by using all 8937 five-letter words in TWL06; with this as the possible word list, I found "serai" to be the best starting guess and got an average of 4.12 guesses, with 17 words that took more than 6 guesses... all of which are either plural nouns or -s verbs ("zills" was the only word that took 8 guesses). If I narrow this list down to the 3841 five-letter words that are among the 50000 most common English words (according to hermitdave's list on github), it goes down to 3.86 guesses on average, never takes more than 6 guesses (with 38 words taking exactly 6), and likes "arose" as an opener. Using random 2315-word subsets (the same size as the Wordle list) of that smaller list, the average tends to vary between 3.59 and 3.66, with 6 guesses being quite rare. So the expected score of my version isn't too far off from "version 2" in the video, but it seems to do better at avoiding the dreaded combo breaker.
@teeforever1
@teeforever1 2 жыл бұрын
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).
@SeppelSquirrel
@SeppelSquirrel 2 жыл бұрын
@@teeforever1 Sorry, "gospel" is 6 letters long.
@StaRScreaM-du6fn
@StaRScreaM-du6fn 2 жыл бұрын
@@krispykremedonut5135 so why do u care?
@StaRScreaM-du6fn
@StaRScreaM-du6fn 2 жыл бұрын
@@krispykremedonut5135 he is obviously trolling
@blubaylon
@blubaylon 2 жыл бұрын
@@StaRScreaM-du6fn no he's not, just a religious crackhead
@alexanderwong4232
@alexanderwong4232 Жыл бұрын
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