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😅
@lilydiring42952 жыл бұрын
making this video is just an excuse to prove his friend is stupid mathematically lol
@Acc_Expired2 жыл бұрын
To be fair, the friend did have the best possible explanation for it. They maximized expected joy rather than information.
@teeforever12 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).
@anasimron2 жыл бұрын
@@teeforever1 wat
@ralphcrewe3742 жыл бұрын
His friend is probably pretty awesome
@lumisussy2 жыл бұрын
Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!
@Strange-Loooop2 жыл бұрын
🤣🤣🤣
@dylnn-music2 жыл бұрын
gold
@sullivannick2 жыл бұрын
Same but FARTS
@sunritroykarmakar44062 жыл бұрын
Lmao
@lildevil3620032 жыл бұрын
You might like Lewdle, the lewd version. (Penis is my first guess on it every day)
@RazAnime2 жыл бұрын
creating an algorithm for this and comparing them against each other sounds like it would have made a great programming competition
@bigbadwolf40752 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.
@mitikox2 жыл бұрын
well, a bit further from wordle, with the same intent, there's the Hutter prize
@sudevsen2 жыл бұрын
Polygon already did it
@tiagoaoa2 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!
@oelarnes2 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-vp4ty2 жыл бұрын
The amount of preparation work in order to produce a video like this is unbelievable.. truly impressive work.
@ParadanMusic-cn7ym7 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
@clickbaitking67702 жыл бұрын
I love those sketches you put in when depicting real life situations, like the conversation between Von Neumann and Shannon 12:01!
@mrfeliscatus32362 жыл бұрын
I love how the sketch showed up as I read your comment
@lindsaybeyerstein70962 жыл бұрын
The art takes a fascinating discussion to the next level. Well done.
@shoam21032 жыл бұрын
But how are they done? Looks almost like made from 2D Fourier Transform curves
@paradoxicallyexcellent51382 жыл бұрын
@@shoam2103 what about the drawing made it seem that way?
@paradoxicallyexcellent51382 жыл бұрын
Timestamp comments like this!
@AlphaPhoenixChannel2 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…”
@chiragkumar90602 жыл бұрын
Hi alpha I love your videos huge science fan!
@imbw2672 жыл бұрын
Pros watch at 2x speed
@AlphaPhoenixChannel2 жыл бұрын
@@imbw267 nah 1x. I want to appreciate it in its entirety
@shoam21032 жыл бұрын
I knew it was a 30 min video when it started. Couldn't believe it was already over.
@daney-tv2 жыл бұрын
ngl I did the same thing with the speed of motion
@lindybeige2 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.
@figgahh58232 жыл бұрын
the word is never a plural fyi
@lindybeige2 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.
@figgahh58232 жыл бұрын
Lindybeige no worries! I only found out yesterday too
@laurie_guilbeau2 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.'
@andrewedgecombe2 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"? ;-)
@blackholevortex2 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 Жыл бұрын
Possibly fun fact: GEB is why I'm an atheist.
@hackkitts9254 Жыл бұрын
@@Oberon4278 cringe alert
@nephastgweiz1022 Жыл бұрын
@@hackkitts9254why ?
@cstatic01123 Жыл бұрын
@@Oberon4278reductionism only gets you so far
@marcuskissinger38428 ай бұрын
@@Oberon4278what argument convinced you?
@Bismuth92 жыл бұрын
18:38 I bet you had a lot of fun writing that bit
@eboone2 жыл бұрын
Hello
@NoriMori19922 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!
@dannyb218922 жыл бұрын
I come to the comments to write this and see my boy bismuth beating me to the punch
@devonm85782 жыл бұрын
I spit out my tea at "Where those after first are after, where and those, being just a little bit less common."
@NoNTr1v1aL2 жыл бұрын
These nuts haha gotem. Someone end me pls.
@HBMmaster2 жыл бұрын
thanks for making this. now people will stop asking me to make this video, lol
@RobBot002 жыл бұрын
Lol, would still appreciate your take! Thanks jan
@lillianruan98012 жыл бұрын
People still won’t stop asking you, lets be honest.
@shinydino2 жыл бұрын
You’re contractually obligated to remake this video in toki pona using seximal notation.
@Anonymous-df8it2 жыл бұрын
Do the same thing but instead of the bit, you have -log base 6 of p(x).
@AlienValkyrie2 жыл бұрын
@@Anonymous-df8it You mean -log base 10 of 1/p(x), right?
@nipungupta88462 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.
@robchan26042 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.
@sabnarose2 жыл бұрын
He deserves the wordl(e)
@kilianschabort2354 Жыл бұрын
A year later and my blind devotion to your original video has paid off. Thank you kindly!
@BrandonSmith-mj9nf Жыл бұрын
All Greens.
@YungPetee Жыл бұрын
I guessed crane time since I saw this video, I never thought the day would finally come
@maxking65 Жыл бұрын
What do we start with now?
@robeik Жыл бұрын
I watched this only a week or so before adopting it and it being correct on the first guess.
@DrTrefor2 жыл бұрын
Came for the wordle, stayed for the awesome lesson on information theory. Cool!
@dariuskianersi43502 жыл бұрын
love your videos!
@FranFerioli2 жыл бұрын
Your playlist on discrete math is up next on my list...
@edwardsulitzer37382 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
@DrTrefor2 жыл бұрын
@@edwardsulitzer3738 hey cool! Small internet lol
@teeforever12 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).
@AlexDings2 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.
@helenross30372 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
@rowanlivengood2 жыл бұрын
sounds like a virus
@tomribbens48602 жыл бұрын
@@helenross3037 The allowed words list is the full list. The possible answers is the curated by the partner list.
@trefwoordpunk22252 жыл бұрын
@@helenross3037 Threw out 10,000 words.... yet kept American spellings of words despite being British. Pfft... snowflakes
@tsumikiminiwa46032 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
@berryesseen2 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_nakada2 жыл бұрын
I like that.
@shreyasunil92042 жыл бұрын
why use he log base 2?? bcs always we cant get half observation in my space of probabilities
@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
@3blue1brown2 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
@0x192 жыл бұрын
:O btw really nice video! The animations were amazing and they made it very fun to watch! Keep it up!
@MaxxDW2 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?
@jaekim75142 жыл бұрын
will we see a follow-up with hard mode consideration?
@jaekim75142 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!
@darthrainbows2 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_MacK2 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
@malachiduncan61042 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 Жыл бұрын
@@malachiduncan6104 this, also learning anything you don’t wanna learn will ALWAYS be worse than something you are motivated to do.
@CloneDaddy Жыл бұрын
Hear, Hear.
@liechtenstein67758 ай бұрын
@@malachiduncan6104oh i heard the lecture about information theory. And you can teach all of this real boring
@I_am_Itay2 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 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
@zangeh2 жыл бұрын
"we shouldn't let machines rule our lives" -the man writing and using a wordle bot Love the video!
@karakenio2 жыл бұрын
HAHAHA I was going to bring that up. Super funny.
@corneasp94182 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.
@zangeh2 жыл бұрын
I know what it means, Corne, lol
@maanitarora11727 ай бұрын
exactly! he's just iconic!
@maanitarora11727 ай бұрын
exactly! he's just iconic!
@MrSamwise252 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!
@koktszfung2 жыл бұрын
I think it is experience rather than intuition
@SpeedOfDarknesss2 жыл бұрын
@@koktszfung Isn't most of intuition simply what you expect based on experience? 😛
@randomsoul2942 жыл бұрын
@@koktszfung Intuition is experience-driven
@lambdaman32282 жыл бұрын
@@koktszfung You got schooled in the comments.
@TheJunky2282 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
@stephaniecass65672 жыл бұрын
"Ignoring its recommendation, because we can't let machines rule our lives" I love this!!!
@AuRoBoss2 жыл бұрын
L
@lordbattletax67722 жыл бұрын
Yesss, I laughed out loud at this part too!
@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 Жыл бұрын
@@lpeabody yeah idk if it's public though?
@connorwallace5274 Жыл бұрын
@jonaslarsson5279 it might be the the source code somewhere
@DrZedDrZedDrZed2 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).
@aaron552au2 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!
@JaxsobThe3rd2 жыл бұрын
@@aaron552au sussy
@silentofthewind2 жыл бұрын
What the heck is happening here 😭
@paulkiat2 жыл бұрын
Compound Pivot. Dead Hands. Finesse Swing. 730, 900, 1030 swings. Makes complete sense @David
@teeforever12 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).
@caspg2 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!
@EscurKo2 жыл бұрын
real worlde example :D
@caspg2 жыл бұрын
@@EscurKo haha yes yes, you get it. Its not a book exercise.
@RoanCritter2 жыл бұрын
18:39-18:58 I love this paragraph! Love this wordplay, brings back VSauce memories!
@vez38342 жыл бұрын
I really liked it as well :)
@jamiepayton15742 жыл бұрын
Yea, brillaint stuff
@necromac2 жыл бұрын
That part made me smile. You could tell he was having fun with it :)
@nakulgoyal28792 жыл бұрын
Grant is a fucking genius lmao
@kingkory22 жыл бұрын
Reminds me a of CGP Grey video personally with the wordplay and semi-rhythmic nature
@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
@binaryalgorithm2 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!
@teeforever12 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).
@leovin002 жыл бұрын
This 30 minute video taught me more about entropy than an entire section on entropy from my machine learning course. Bravo!
@seanvinsick2 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.
@suparki1232 жыл бұрын
Honestly, machine learning is really not the best context to get an intuitive understanding of entropy.
@rahuldewangan10642 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.
@rishikeshchapekar44812 жыл бұрын
Same. I learn more maths, better maths in a few 3b1b videos than I do at school
@beckettmw2 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.’
@lawislaw25852 жыл бұрын
I also thought that was brilliant. Such awesome word play and creativity for such a small moment
@shibno012 жыл бұрын
As soon as I heard it I looked for this comment
@lawislaw25852 жыл бұрын
@@shibno01 same lol
@widmur2 жыл бұрын
I thought I was having a neurological event.
@charmingpea2 жыл бұрын
WHOSE on FIRST?
@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.
@oweneastwood34452 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.
@grandtheftlemon3012 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.
@joaomatheus62222 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
@MelodiousThunk2 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.
@teeforever12 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).
@LucianoRobino2 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.
@williamsmith38172 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 😂
@Cheetahhh2 жыл бұрын
You ever watch a video that's so good you actually watch the end screen
@AzureSteel2 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.
@dogmouthhorse2 жыл бұрын
@@AzureSteel why would you look to an in-depth mathematics channel for wordle tips?
@havocike24002 жыл бұрын
Wait Cheetahh. Lol. Holy crap. Weird to find a bridge player here lol
@AzureSteel2 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_starz2 жыл бұрын
@@AzureSteel The word is in the thumbnail, if you don't like math this was an easy skip lmao
@furretwalky Жыл бұрын
Today is a momentous occasion - the word IS **CRANE** today! Happy 1-shot day to a lot of people.
@Geosquare81282 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!
@cutewavelets2 жыл бұрын
hi geo
@dunnperfect85672 жыл бұрын
Thank you for your service geo
@drummike2 жыл бұрын
hey it’s the big cactus guy
@CraftyMasterman2 жыл бұрын
you mean you did and matt was watching chess lmao
@bcarpyy27392 жыл бұрын
hi minecraft man
@bored_pyro2 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.
@rantingrodent4162 жыл бұрын
I wonder if looking ahead at the next guess is all you really need for hard mode.
@psymar2 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...
@AntonioDoukas2 жыл бұрын
Am I the only one that finds hard mode easier?
@Codan32 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
@dalmationblack2 жыл бұрын
Hard mode is actually a lot easier to write a bot for, in my experience
@quai81932 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_me2 жыл бұрын
The same thing literally happend to me RIGHT NOW, I was shocked lmao!!
@charlieoxspring5452 жыл бұрын
ahaha me too
@slinky76962 жыл бұрын
I got 4/6
@NovaaZR2 жыл бұрын
oh
@malleckmelon20862 жыл бұрын
@@NovaaZR he meant tht day the actual word was *OTHER* so he got it right on the first try lol
@Mathefurdullies Жыл бұрын
the letters „first naive ideas“ tending to the word „start“ is such a nice detail! well done video!
@naspleo22522 жыл бұрын
This whole video is great but I have to say I liked the cute word play around 19:00 quite a lot.
@justincalfo14862 жыл бұрын
Would love to see how you would approach tackling Wordle’s “Hard Mode.” Loved it, thanks so much for making this
@jermudgeon2 жыл бұрын
I’d love to see the changes hard mode creates as well.
@kidalan2 жыл бұрын
Ditto! What’s the best first word in Hard Mode? Great video! (but none of it applies to my game lol)
@themaincheese58972 жыл бұрын
@@kidalan lol😐
@__a_44442 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.
@kidalan2 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. 😆
@JordanBeagle2 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
@lekhakaananta58642 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.
@ssz89462 жыл бұрын
In WordHoot, a variant of Wordle, where speed matters, I see people consistently beat bots.
@jonathanbaxter58212 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 :)
@christianhinge71962 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b2 жыл бұрын
@@lekhakaananta5864 it's basically a password cracker bot but a bit more chill
@vedparekh2170 Жыл бұрын
Finally after using crane as my opening for a year, I'm so grateful i didnt miss wordle 732!
@LeonardoDaVinci012 жыл бұрын
I don’t know why, but this was the most calming video I’ve ever watched… math can be so relaxing sometimes
@monkiram2 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
@bentationfunkiloglio2 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.
@dudedude68922 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.
@kylemcleod41152 жыл бұрын
I loved that book as a kid
@prodtheontar2 жыл бұрын
goated book
@blockmath_20482 жыл бұрын
@@kylemcleod4115 same
@infiniteplanes57752 жыл бұрын
I will be checking that out
@natalie-ih1wc2 жыл бұрын
favorite book ever
@Willieg2008 Жыл бұрын
I have religiously been using crane since I saw this video, TODAYS OUR DAY GUYS!!!!!🎉
@admiralcapn2 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_thong86312 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 Жыл бұрын
?. SZwa*=+
@22tfortnitevevo Жыл бұрын
he has that at the end of the vid
@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_ Жыл бұрын
Oh. That's just how I've been playing normally...
@sabertag69922 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
@JamesHawkeYouTube2 жыл бұрын
don't get too excited - it's just conceptual baloney.
@TheDSasterX2 жыл бұрын
@@JamesHawkeKZbin Conceptual? He tested it; it's quite evidential.
@evan2 жыл бұрын
Making a word game about math. I LOVE IT
@christa.mp42 жыл бұрын
hi evan
@harrypotterina2 жыл бұрын
Hi Evan
@อภิษฎาคนขยัน2 жыл бұрын
@Ex Japan you're lucky,
@อภิษฎาคนขยัน2 жыл бұрын
I lost $1500 trading with an unprofessional trader.
@marvinkinnel29202 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 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!
@JimmyJJJohnson2 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.
@alveolate2 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.
@JimmyJJJohnson2 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.75012 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.
@mopanda812 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
@yaseen1572 жыл бұрын
Beautiful watching as always, thanks Grant! I enjoyed the confusing word skit at 18:40 haha
@pallenda2 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. :)
@AxxLAfriku2 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
@lolajuliet26622 жыл бұрын
this is so cool i want to try making a wordle bot in python too !!
@aluisious2 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 Жыл бұрын
This video has finally fulfilled its purpose
@BorinUltimatum2 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.
@nigelong17792 жыл бұрын
I use IRATE/SOUND myself
@Tabroski2 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.
@simoncarter35412 жыл бұрын
@@nigelong1779 I was irate and pound but will definitely switch to sound now
@Stereomoo2 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.
@WhitestOC2 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
@anderslauridsen6012 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!
@joseville2 жыл бұрын
timestamp please
@sleinbuyt4022 жыл бұрын
@@joseville 18:40
@karlosfy2 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.
@Ida206 ай бұрын
I can’t imagine the work involved in creating this video. It is so refreshing to see something professionally done.
@RJTheBikeGuy2 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.
@rkeating2 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
@Jay222222 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-ד2ק2 жыл бұрын
@@Jay22222 true
@kaazma2 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.
@NikitaOnline172 жыл бұрын
@@Jay22222 why tho lol
@dkursada2 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.
@29BKing2 жыл бұрын
"fewer"
@Dylan52meow2 жыл бұрын
This video is an absolute masterpiece. Especially loved the bit at 18:39 about the most common words. Hilarious!
@owenaspinall20462 жыл бұрын
The ¨bit¨?
@CraftBasti2 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.
@owenaspinall20462 жыл бұрын
@@CraftBasti I made a bad pun about how this is about information theory, which uses the unit the "bit".
@CraftBasti2 жыл бұрын
@@owenaspinall2046 ahh of course, that was the reason for the quotation marks! Good one ^^
@AndrewBackhouse12 жыл бұрын
It was pure genius
@williamdavis694 Жыл бұрын
After 512 days, crane has finally won first try. Thank you
@LifebyBrody4 ай бұрын
got a first try on my go to "purge" and then when they wiped my history after inactivity I stopped
@antonhagelberg74302 жыл бұрын
Absolutely impeccable timing, just went over this concept in a course on Machine Learning, feels great to understand what you're saying!
@psd9932 жыл бұрын
what course and/or what reference have you used specifically for information theory (if you did have separate reference material)
@brettlogeais8492 жыл бұрын
I would like to see a Hard Mode version of this analysis and how the algorithm reacts to it.
@oldcouchcushion15452 жыл бұрын
Yeah I was like damn not even playing hard mode. Gotta step up
@Slamdunka9632 жыл бұрын
@@oldcouchcushion1545 Not playing hard mode = weaksauce
@KayDeeKeySull2 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:)
@geofflulham84602 жыл бұрын
TARES are also a corn/seed used in fishing (in the UK)
@nickalot64362 жыл бұрын
I’m a cashier at a grocery store and I’ve been using “tares” too.
@eduardojuarez98622 жыл бұрын
Im a random kid and I have been using stare which is kinda the same but tares might be better
@isaaclodziak-green63262 жыл бұрын
I also work in a grocery store, but I use the word “rates”
@prockpros2 жыл бұрын
soare is a good starting word too
@cgillespie78 Жыл бұрын
Well today's word was CRANE. Have to give this the award for best thumbnail ever
@AshLordCurry2 жыл бұрын
Crane Shtik combo is absolutely legendary, just tried it, found the word in 3 tries. Absolutely amazing.
@matthewtavani65842 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.
@TimeBucks2 жыл бұрын
Such clarity in explaining things
@supreme-lz5yc2 жыл бұрын
first comment and also feels like botting
@teeforever12 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).
@rottedpotato6452 жыл бұрын
@@teeforever1 no cares about christianity
@jimschott2 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.
@tim40gabby252 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?
@ironknuckle1432 жыл бұрын
I do this
@seastilton79122 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
@ironknuckle1432 жыл бұрын
@@seastilton7912 I do it to pass the time between puzzles but you make an excellent point.
@DeuceBooty2 жыл бұрын
I do this. It's pretty fun
@huellenoperator2 жыл бұрын
"queue" must be pretty bad.
@ShrtRndKid2 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.
@valenz12342 жыл бұрын
The likelihood of getting it on second is low, may as well find the most information out and try for third.
@david2032 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.
@chownc2 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
@arnabs20092 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 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. ;)
@goodgameproductions30392 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.
@Moe5Tavern2 жыл бұрын
Could you give a link to that please? Klinkt heel erg interessant!
@JonathanCheseaux2 жыл бұрын
Also been around as a tv show called "MOTUS" in France
@DasVERMiT2 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.
@pokepress2 жыл бұрын
Also very similar to the game “Mastermind” that uses colored pegs instead of letters.
@alejandromesa25782 жыл бұрын
Link?
@jickhertz41242 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
@webx1352 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.
@TheMightyGiantDad2 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
@ThePharphis2 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.
@ShmingsThings2 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.
@iloshwdgac9213Ай 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.
@addymant2 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.
@additionaddict55242 жыл бұрын
entropy is like an advanced average.
@NesrocksGamingVideos2 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.
@Twisol2 жыл бұрын
Your literal wordplay at ~18:55 gives me joy XD
@shrugalic2 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.
@bernie97282 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 Жыл бұрын
I do that too!
@mrevil112 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.
@davidelliott98172 жыл бұрын
I do the same but with audio
@Tysto2 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.
@leonardogoes6832 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.
@firstname13172 жыл бұрын
@@davidelliott9817 SAME!!!
@mikec43082 жыл бұрын
audio is also good. didnt even know adieu was a word lol
@alexander1912972 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! 🙏
@jonaslevyalfie74342 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!
@amaansiddiqui23762 жыл бұрын
Same. But just starting seems such a tedious task.
@jasonx78032 жыл бұрын
@@amaansiddiqui2376 Step one, just pick randomly from all the answers. Then refine. ;)
@PrimeSuperboy3 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
@budge9562 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”.
@joshklapperich94162 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
@treverfox12802 жыл бұрын
you can always do: GLENT BRICK JUMPY VOZHD WAQFS this eliminates 25/26 letters and just leaves X
@jacquescousteau2172 жыл бұрын
I'm with you, find the vowels first ...
@david2032 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.
@david2032 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-mi2ud2 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-ff7jq2 жыл бұрын
You're content and enthusiasm has inspired me to pursue my dreams of learning programming and math, I'm highly grateful.
@ZopcsakFeri2 жыл бұрын
He is neither content nor enthusiasm :)
@hetsmiecht10292 жыл бұрын
@@ZopcsakFeri your funny!
@brongondwana9 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-oi9yv2 жыл бұрын
This is one of the reasons why I went for a double major in Applied Mathematics and Computer Science. Great video.
@napoleonkhan87432 жыл бұрын
All that just to get better at Wordle? That’s dedication
@ethan-loves2 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.
@APromisePast2 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.
@judgeomega2 жыл бұрын
why even bother going beyond 2 guesses? didnt get it in 2, you failed.
@adityapalve37522 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.
@louisrialland25272 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.
@Seeker2657292 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
@motherlove83662 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 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!!
@thegzak2 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!
@Ctulthu002 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?
@thegzak2 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.
@Ctulthu002 жыл бұрын
@@thegzak I see, that makes sense!
@mylonoceda2 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-yr6ig2 жыл бұрын
I hate that quote. It's not even true. If it were accurate it would be like "conditioning can't improve entropy."
@piguy3141592 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.
@teeforever12 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).
@SeppelSquirrel2 жыл бұрын
@@teeforever1 Sorry, "gospel" is 6 letters long.
@StaRScreaM-du6fn2 жыл бұрын
@@krispykremedonut5135 so why do u care?
@StaRScreaM-du6fn2 жыл бұрын
@@krispykremedonut5135 he is obviously trolling
@blubaylon2 жыл бұрын
@@StaRScreaM-du6fn no he's not, just a religious crackhead