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😅
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).
the fact that such a competition would be possible tells us that the use of "optimal" in the title is incorrect. :P that being said, that competition would be interesting!
@@tiagoaoa I think for this reason a competition would not be interesting. As far as I can tell the algorithm is optimal for the objective it defines (which is slightly modified from the original puzzle but only for greater generality)
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
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 роки тому+19
I came to say this. It is, most likely, the best presentation I have ever witnessed.
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.
I have also thought about not only the letters of your first word but the placement. I either use 'STERN' or 'RENTS.' Since 'rents' ends in S, it will rule out most plural words. But then I think that plural words don't tend to be the words used in Wordle. So I usually just go with 'stern.'
@@lindybeige Maybe it rejects "nails" if you enter it as the plural of nail, but it accepts it if you enter "nails" as the past tense of the verb "nail"? ;-)
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
@@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
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
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).
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
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.
As an information theorist (a PhD student working on the field), I am amazed by this video. It is so interesting and well-organized. The information i(x) = -log2(p(x)) is also called "surprisal". I like this terminology a lot, because, really, the larger i(x) is, the more you get surprized by the outcome x.
I 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
The most useful and enlightening definition of entropy I've ever encountered came from neuroscientist Terrence Deacon, who frames it as the dissipation of constraints. Anything at maximum entropy is maximally UN-constrained. Be it energy levels in the statistical distribution of particles in an ideal gas (Boltzmann) or the resolution of uncertainty in the answer of any given question (Shannon). It also helps to frame how entropy doesn't simply rely on the contents of a container (2 black, and 2 red checkers on a 2 x 2 checker board, for example) but the possibility space conferred onto those arrangements by the SIZE of the container (considerably larger if those same checker pieces end up transposed onto a standard 8 x 8 board). Constraints man, they're big time (gravity vs. Inflation being my all time fav example).
The definition that I use (I think I got it from PBS Space Time) is a measure of how much *unknown* information - according to certain defined properties like particle position/velocity, quantum properties, etc. - is present in a given system. Deacon's definition is definitely more concise though!
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).
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.
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.
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!
This reminds me of "mastermind" a game of the early 70's. In stead of words you have 4 different colored pins. And for the error/success feedback there is two pins in black and white. It is played by two people where one player is the guesser and the other one checks the guess and gives feedback.
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).
Tares is a verb! "He tares the scale". It means setting a scale to zero with something on it. That way you can weigh something in a container without weighing the container! You use it a lot in chemistry.
Fun fact: (not Fun at all actually) in portuguese its "tara", but the word for "pervert" is "tarado", where -do is a suffix, meaning "perversion" is "tara" as well
@@joaomatheus6222 How interesting! I looked up the etymology of "tare", to see if it might explain why "tara" has two different meanings in Portuguese. I found that the medieval Latin word "tara" comes from the Arabic word "tarah", meaning "thing deducted or rejected, that which is thrown away", which is derived from "taraha", meaning "to reject". Perhaps perversion became associated with rejection at some point in the history of the Portuguese language.
the Gospel: the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell. our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d). in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@MelodiousThunk I suspect you are on the money about that. In Spanish we also have the verb "tarar": to set a scale to zero. Also we have a "tarado" (male) and "tarada" (female) but it translates as stupid or idiot. In fact, it's a participle. It's like saying "tared": The scale was tared // La balanza fue tarada. I wouldn't be surprise if your explanation is also valid for Spanish. Just remember the complex history Spain and Portugal have with each other. Specially during the Al Andalus times.
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.
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 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 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
@@kidalan I go for the naïve frequency analysis-based route. 'orate' is my go-to atm, but it used to be 'opera'. That is not to say by any means it is optimal.
@@__a_4444 I like those openers! I usually open with adieu or ourie. I like to establish which vowels I’m working with, then use that foundation to shoot down consonants. If there was a word with five vowels, I’d use that every time. 😆
(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.’
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.
My friend and I like AUDIO/STERN as a double opening. It covers all traditional vowels without repeat letters and tests S in the first slot which is the most common starting letter for 5 letter words.
I use 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.
Just realised WORDLE now has a "hard mode" where you MUST use existing information in future guesses (i.e. if you get a green first letter and yellow fourth letter, future guesses HAVE to start with that same first letter and mix that other letter around). Curious how this would affect the amount of information obtained at each guess, particularly with an algorithm looking ahead multiple guesses.
I've lost only a couple times; once because I got the last 4 letters, but there were more possibilities for the first letter than I had guesses left. that would be a case to use a word that doesn't include the results from previous guesses.
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)
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.
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 ua-cam.com/video/fRed0Xmc2Wg/v-deo.html For a human playing Wordle, I'm not sure I'd actually recommend starting with CRANE, or any of the ones best for one of these algorithms, since it requires also knowing what it will do for second guesses. For example, here's the start of the mapping for what it does with that second guess: ⬛⬛⬛⬛⬛ -> sloth ⬛⬛🟨⬛⬛ -> toils ⬛⬛⬛⬛🟨 -> spilt ⬛🟨⬛⬛🟨 -> rosit ⬛⬛⬛⬛🟩 -> toils ⬛🟨⬛⬛⬛ -> shout ⬛🟨🟨⬛⬛ -> party ⬛⬛⬛🟩⬛ -> gluts ⬛⬛⬛🟨🟨 -> lemon ⬛⬛⬛🟨⬛ -> pilot 🟨⬛⬛⬛⬛ -> kutis ⬛🟩⬛⬛⬛ -> pilot ⬛🟨🟨⬛🟨 -> patly ⬛⬛🟩⬛⬛ -> slipt ⬛⬛🟨⬛🟩 -> lambs ⬛⬛🟨🟨⬛ -> toils ⬛⬛🟨⬛🟨 -> tepal ⬛⬛🟩⬛🟩 -> glost ⬛🟨⬛⬛🟩 -> south
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?
couple more questions on this super interesting video: 1. i note that the information you are gaining each time seems more based on letter frequency while not really considering letter placement frequency (as your suggested guesses often include words with letters in incorrect places, albeit with 0 probability of being right). that may be another avenue for info gain - ie, doing some analysis on how often a given letter occurs in a specific location. 2. strongly defining what is optimal as it may mean different things to different ppl. you seem to have defined it as lowering the expected number of guesses until being correct. however, another might reasonably define optimal as never missing a puzzle which i suspect would change the strategy being used. and of course my previous question of looking at the puzzle in hard mode would also affect how the previous two points are considered. cheers and thanks for the informative video!
Huh, I ran a much more naive calculation of the best first guess (matching every word in the worlde dictonary against every other word, calculating yellow and green clues, and generating a weighted average score with green clues being a bit more valuable than yellow) and I also came up with SOARE as the best first guess.
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 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.
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
It's not exclusive to this particular video of his, but there is something strangely refreshing about learning about things I don't understand. Like the prime numbers video of the monster, it's so refreshing to hear someone talk so plainly and expositorily yet still pass way over my head. I love learning how little I actually know, and this channel (among others) refreshes my brain so well. Please accept my sleepy and sincere appreciation. TL:DR ~ I like your funny words magic man
this was a fun problem to solve :) my friend and I essentially constructed a solver with the same methods but we conceptualized it in a very different way. really cool video!
Some thoughts on CRANE as first guess... I usually guess stare first (an anagram of tares, which your first algorithm likes) but started guessing crate, with the reasoning that a C often comes with an H or K, so finding a C feels like it gives more information even though it's a less likely letter. Essentially, letters that are weighted towards appearing in certain types of words or in certain letter combinations should be more valuable guesses than their simple frequency should predict. C is probably at a sweet spot where it's not too uncommon a letter, and enjoys a big boost from giving you a lot of bonus information if you do find one. Further to this, if you have, say, two certain letters that often appear in combination, it makes sense strategically to include one of these letters and not both in an early guess, as the odds of these letters appearing in the word are far from being independent odds, so guessing one gives you information on the probability of the other - bonus information from just one guessed letter. Hence, since CH and CK are very common associations of letters in common English words, guessing a C but not an H or a K in your first word seems to make a lot of sense from an information standpoint, and I'm not surprised that an algorithm found that guessing a word containing a C first was smart, despite C being quite a way down the letter frequency list.
on that note, i feel like the _position_ of the letter within the 5 could also be valuable. i believe that's why 'tares' is valued over 'stare' because presumably there are more words ending with s, which might be pretty informative.
@@alveolate yeah, letter positioning must be valuable. I actually initially preferred stare over rates (same logic applies to tares) because I thought the wordle would never be a plural so an S in the last position would be bad! Maybe vowels in positions 2 and 4 are better than in positions 3 and 5?
This ^^^. You can easily see it, if you guess a word with "U" and "U" is not in the word, then "Q" isn't either. In code breaking, you'd see a word that ended in "Y" and guess one that ends in "LY" (hard mode) because that's a likely 2 letter combination. I don't have the table of common 2 letter combinations but it's available.
Yeah if we’re playing to eliminate two letter combinations word final s also informs us in situations of “es” (as in tares. just as word initial c would inform us of possible ch words
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!
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?
20:10 It is interesting and I think people should keep in mind how even in highly mathematic scenarios, human preference is still involved not always, but not never
Yeah, and the more nuanced version of this is that human preference is used where a heuristic is more cost-efficient than more computing. In this case, Grant used his intuition to feel where the cut-off point is. However by the definitions given in this video, this cut-off point should certainly be able to be found in the game-theoretic sense. A quick naive approach would be to try different iterations of the bot using different cut-off points and over millions of iterations find the optimal point. But you see that's exactly why Grant used his intuition as a heuristic instead, because the expected gains from running said millions of iterations is very little compared to what his best guess would do. And as an alternative, if Grant used another method (not brute force simulations) to try to get the exact game-theoretic optimal point, it would be a lot of thinking time used for not much effect.
In 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 :)
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.
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. :)
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 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.
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!
I’ve never played this but if that’s the restrictions of hard mode, it seems more like dumb mode.. which I suppose you could also refer to as hard mode
@@Jay22222 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.
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:)
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.
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.
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.
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).
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.
9:28 I think this is the perfect explanation to the whole concept of Akinator. Yes, it also cheats by just using a user-created database but getting to the answer in less number of questions is the real challenge.
I 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.
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.
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.
wouldnt that exponentially increase the complexity of the computation. Is it even solvable within 2 steps ? I think grant mentions something along the same lines.
@@adityapalve3752 I don't know why you think the computation would be far more complex since you're only looking 1/2 guesses into the future. It isn't solvable within 2 steps, but you can try to solve it within 2 steps as much as possible (likely by increasing the weighting of the frequencies of the words; this gives you less information in the long term but increases the chance that you get lucky on the second guess). Hopefully this makes sense lol.
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.
Thanks for the great video! I think a great addition to this algorithm would be the removal of already used words in previous wordles. This would decrease the overall entropy a little since some pretty common words were already used. Anyways, great video, I always learn so much from you!!
I 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”.
@@treverfox1280 Doesn't work if your Wordle requires entering only guesses that are words, like cell phone Wordle from Lion Studios Plus. Also fails for goal words requiring trial and error, like batch/match/patch/watch/hatch/latch/catch, which can't be reliably guessed even if all six lines were used.
'I like to start with “Faint” ' Not optimal, because the consonant F is not a frequent one. Saint would be better, and including E in the first word would be best.
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.
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.
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.
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.
This made me discover absurdle. I was extremely aggrivated by it at first until I saw the explanation on their page. Basically all the words I was getting were "kitty" "jiffy" "dizzy". But that's because my first two guesses were always Crane and then Buoys to knock out as many vowels as possible.
That's what's so interesting about absurdle! Having the same first few guesses can really back it into a corner. I really wonder if it's possible to force any given word out of it. With how restrictive and deterministic it is, it's not obvious that this should be the case
@@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.
@@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.
While playing the game, just like you considered the "common word probability", I consider the "common character probability" as well. I propose scoring the words on the basis of how frequent each letter comes at each of the 5 positions in all the 5-letter words. For example, you mentioned the NAILS vs SNAIL choice. SNAIL has an A in the middle (as in ~1200 5 letter words), whereas NAILS has A on the 2nd position (as in ~2100 5 letter words). Clearly, the A in NAILS gives you higher information (getting those greens on the board).
Yes, as david said, this is already accounted for in Grant's information-related approach. We know intuitively that a green is better than a yellow but how does Grant's program know that? Because it counts the remaining possibilities. The remaining possibilities after a green clue are much more restricted than after a yellow clue, so that algorithm will naturally rank guesses that give green clues more often as more useful.
@@kentanggulung But your method is better for the human brain which does not contain the list of possible words, nor can do the entropy calculations on the fly. I use AROSE, UNITS as my first two words no matter what, it gets rid of a lot of common letters and all the vowels.
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
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
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.
@@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.
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!!
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
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.
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).
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! 🙏
Data Scientist here: Just wanted to add another perspective on entropy & the way we quantify information, as this topic is often fairly confusing for beginners. So 1, where did all this theory & stuff come from? Information theory comes from trying to measure the efficiency of communication of information. So the key idea is that, if we want to quantify information, really what we're doing is trying to measure how well one actor is communicating to another actor about an event. So the two actors need to come up with some dictionary, or what is often called an "encoding" in order to communicate events to one another. The the second key idea, is that It takes more energy to communicate with more symbols ("symbols" could be words, bits, smoke signals, whatever is your base unit of information). Therefore, our objective is to assign the least amount of symbols to all the possible events, so we should encode according to how common different events are. More common events, should use less symbols. The inverse of a probability has this great name, called "the surprisal", the idea is that the higher the number, the more "surprising" an event is. Like if I were to tell you the sky just instantly changed from blue to magenta, that event would have a wildly high surprisal, because it has a really low probability. The reason we put a log on the surprisal is to get "how many symbols do we need in order to communicate this event?", the base of your log determines the number of symbols available to you, most commonly we use base 2 because we're usually thinking of this in bits. The entropy of a probability distribution is the average number of bits required to communicate events in said probability distribution. Hope someone else found that interesting! None of this stuff made sense to me until I understood that.
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.
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.
A very nice video! A fun fact: Finding an actual "mathematically optimal strategy" is probably pretty hard. Similar problems, like Mastermind, are known to lead to provably hard problems (at least NP-complete, potentially even harder!). This does not mean it cannot be solved, though. For example, Donald Knuth bruteforced optimal mastermind solution in 1976. :) EDIT: Thanks darci peeps and Tim Fischer for clarification: Knuth bruteforced optimal *worst case* solution for Mastermind (with 4 pegs). If you care about the average number of moves, this was solved only later.
Donald Knuth’s algorithm used minimax, a greedy algorithm which was not most optimal. It was Kenji Koyama and Tony W. Lai that performed the first an exhaustive depth-first search in 1993. I agree that 3b1b’s strategy is not THE most optimal, but it’s robust to other versions of wordle which is cool.
I did an exhaustive search on hard-mode Wordle, but using only the 2315 word dictionary the game uses for its own choices. I optimized for average number of moves. Here are the top five starting words & the average game length they lead to: 3.51922 trace 3.52009 slate 3.52181 least 3.52700 crate 3.53391 crane Allowing the full 12972 word dictionary would add a lot more searching, though the search could potentially be pruned, depending on what question you were trying to answer.
I always use “audio” and then “entry”. Those two words cover all of the vowels and some common consonants. Once I know which vowels are in the word I can usually figure it out.
@@WanderTheNomad that is so smart. I also try to get my vowels out of the way with adieu, then sport to get my “o” and then chewy to get my “y”, but you get the o and y in one shot with story. I will try that next time!!
Imagine Grant's friend innocently telling him that his Wordle opener was "weary", only for him to publish a 30-minute essay on why that's stupid a week later😅
making this video is just an excuse to prove his friend is stupid mathematically lol
To be fair, the friend did have the best possible explanation for it. They maximized expected joy rather than information.
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@teeforever1 wat
His friend is probably pretty awesome
Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!
🤣🤣🤣
gold
Same but FARTS
Lmao
You might like Lewdle, the lewd version. (Penis is my first guess on it every day)
creating an algorithm for this and comparing them against each other sounds like it would have made a great programming competition
I was thinking the same! In fact I actually was researching for a hash table for all 5 letter words and was going to start my algo.
well, a bit further from wordle, with the same intent, there's the Hutter prize
Polygon already did it
the fact that such a competition would be possible tells us that the use of "optimal" in the title is incorrect. :P that being said, that competition would be interesting!
@@tiagoaoa I think for this reason a competition would not be interesting. As far as I can tell the algorithm is optimal for the objective it defines (which is slightly modified from the original puzzle but only for greater generality)
The amount of preparation work in order to produce a video like this is unbelievable.. truly impressive work.
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
I love those sketches you put in when depicting real life situations, like the conversation between Von Neumann and Shannon 12:01!
I love how the sketch showed up as I read your comment
The art takes a fascinating discussion to the next level. Well done.
But how are they done? Looks almost like made from 2D Fourier Transform curves
@@shoam2103 what about the drawing made it seem that way?
Timestamp comments like this!
You deserve the world. The amount of effort that went into making those smooth slick animations, the wordle UI to run simulations on, the code that you wrote is IMMEDIATELY apparent. Production quality is off the charts as always, and the video is filled to the brim with information, pun intented. Keep up the good work, you are amazing!
I came to say this. It is, most likely, the best presentation I have ever witnessed.
Really cool presentation.
Laughed at the words Crane and Shtik when they came out. Reminds me of a thing I saw a few days ago called joincrane.
He deserves the wordl(e)
The position of letters is a factor. For example, I prefer TALES over SALET ( SALET is recommended by others who have done computer analysis of this game) because if I do NOT get a green S, then that rules out a huge number of plural four-letter nouns with an S on the end, like BOOMS. Note that I am getting a lot of information out an absence of a match there. Though Y is a fairly rare letter, it turns up at the end of a lot of five-letter words. Letters like L, R and H are important beyond their commonness because they often combine with other consonants as in BLAND, PROSE, and CHAIR.
the word is never a plural fyi
@@figgahh5823 Oh really? It accepts guesses of plurals, such as NAILS which is used as an example in this video. Good to know, thanks.
Lindybeige no worries! I only found out yesterday too
I have also thought about not only the letters of your first word but the placement. I either use 'STERN' or 'RENTS.' Since 'rents' ends in S, it will rule out most plural words. But then I think that plural words don't tend to be the words used in Wordle. So I usually just go with 'stern.'
@@lindybeige Maybe it rejects "nails" if you enter it as the plural of nail, but it accepts it if you enter "nails" as the past tense of the verb "nail"? ;-)
A year later and my blind devotion to your original video has paid off. Thank you kindly!
All Greens.
I guessed crane time since I saw this video, I never thought the day would finally come
What do we start with now?
I watched this only a week or so before adopting it and it being correct on the first guess.
4:00 note that the list used in Wordle is the exact list of words allowed in international tournament Scrabble. It's called CSW19.
I believe that the original list had all available scrabble five letter words, but the coder's partner went through and took out all the truly ridiculous and obscure ones
sounds like a virus
@@helenross3037 The allowed words list is the full list. The possible answers is the curated by the partner list.
@@helenross3037 Threw out 10,000 words.... yet kept American spellings of words despite being British. Pfft... snowflakes
@@trefwoordpunk2225 Isn't Scrabble (or at least Scrabble tournaments) US centric? I feel like it's more likely the Scrabble tournament people removed those words
Came for the wordle, stayed for the awesome lesson on information theory. Cool!
love your videos!
Your playlist on discrete math is up next on my list...
Professor Bazett! You were my professor while I was at UofT and just wanted to say you were hands down one of the best math teachers I've had, I still remember your infectious enthusiasm for the topic
@@edwardsulitzer3738 hey cool! Small internet lol
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
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
This video is so well done.
The word play at 18:40, the hidden messages in the game at 25:25... This video gives me "Gödel, Escher, Bach" vibes, and that is something that has never happened to me since I read that book. Awesome.
Possibly fun fact: GEB is why I'm an atheist.
@@Oberon4278 cringe alert
@@hackkitts9254why ?
@@Oberon4278reductionism only gets you so far
@@Oberon4278what argument convinced you?
As an information theorist (a PhD student working on the field), I am amazed by this video. It is so interesting and well-organized. The information i(x) = -log2(p(x)) is also called "surprisal". I like this terminology a lot, because, really, the larger i(x) is, the more you get surprized by the outcome x.
I like that.
why use he log base 2??
bcs always we cant get half observation in my space of probabilities
18:38 I bet you had a lot of fun writing that bit
Hello
That's two different UA-camrs that I've been watching recently that have commented on this video. (You and AlphaPhoenix.) I love that!
I come to the comments to write this and see my boy bismuth beating me to the punch
I spit out my tea at "Where those after first are after, where and those, being just a little bit less common."
These nuts haha gotem. Someone end me pls.
Never have I ever been tricked into enjoying a math class like this. I wish I had you instead of all my college professors
I mean I'm sure he had to go through what you did to get to the fun things he does now.
@@malachiduncan6104 this, also learning anything you don’t wanna learn will ALWAYS be worse than something you are motivated to do.
Hear, Hear.
@@malachiduncan6104oh i heard the lecture about information theory. And you can teach all of this real boring
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
The most useful and enlightening definition of entropy I've ever encountered came from neuroscientist Terrence Deacon, who frames it as the dissipation of constraints. Anything at maximum entropy is maximally UN-constrained. Be it energy levels in the statistical distribution of particles in an ideal gas (Boltzmann) or the resolution of uncertainty in the answer of any given question (Shannon). It also helps to frame how entropy doesn't simply rely on the contents of a container (2 black, and 2 red checkers on a 2 x 2 checker board, for example) but the possibility space conferred onto those arrangements by the SIZE of the container (considerably larger if those same checker pieces end up transposed onto a standard 8 x 8 board). Constraints man, they're big time (gravity vs. Inflation being my all time fav example).
The definition that I use (I think I got it from PBS Space Time) is a measure of how much *unknown* information - according to certain defined properties like particle position/velocity, quantum properties, etc. - is present in a given system.
Deacon's definition is definitely more concise though!
@@aaron552au sussy
What the heck is happening here 😭
Compound Pivot. Dead Hands. Finesse Swing. 730, 900, 1030 swings. Makes complete sense @David
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
This 30 minute video taught me more about entropy than an entire section on entropy from my machine learning course. Bravo!
reducible has some pretty good videos on it, especially the compression video. He uses grant's library, so they look like 3b1b but instead of a focus on math, it's on cs.
Honestly, machine learning is really not the best context to get an intuitive understanding of entropy.
Machine learning in IMHO is a wrong introduction for Information Theory. Shannon's paper "A mathematical theory of Communication" and Hamming's Paper on Error correction and Detection are really worth reading and easily approachable in few sitting.
Same. I learn more maths, better maths in a few 3b1b videos than I do at school
I love how you opened with the idea that "4 guesses is par and 3 guesses is birdie", then in your comment at the end (29:26) you note that consistently getting 3 guesses is basically impossible. That's so cool how the math matches our human intuition about the puzzle!
I think it is experience rather than intuition
@@koktszfung Isn't most of intuition simply what you expect based on experience? 😛
@@koktszfung Intuition is experience-driven
@@koktszfung You got schooled in the comments.
oh I thought he said 3 was dirty, as in you're using outside info or likely cheating. continuing the golf terms make more sense lol
I could've never had forgiven my self had I not played Wordle today. Been using crane since this video came about.
@@lpeabody yeah idk if it's public though?
@jonaslarsson5279 it might be the the source code somewhere
thanks for making this. now people will stop asking me to make this video, lol
Lol, would still appreciate your take! Thanks jan
People still won’t stop asking you, lets be honest.
You’re contractually obligated to remake this video in toki pona using seximal notation.
Do the same thing but instead of the bit, you have -log base 6 of p(x).
@@Anonymous-df8it You mean -log base 10 of 1/p(x), right?
I JUST started a college class on information theory. I'll have to watch this again a couple of times but its so helpful to have a real world example!
real worlde example :D
@@EscurKo haha yes yes, you get it. Its not a book exercise.
This reminds me of "mastermind" a game of the early 70's. In stead of words you have 4 different colored pins. And for the error/success feedback there is two pins in black and white. It is played by two people where one player is the guesser and the other one checks the guess and gives feedback.
played it, loved it
Actually I wrote an algorithm to play mastermind using this exact approach!
I thought I was the only one compare it to that game
was thinking the same thing!
i still have that board game!!
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
Grant: “this video’s getting kinda long.”
Me: “what are we at, like 10? 15 minutes? He’s got plenty of time!”
Me after checking clock: “oh…”
Hi alpha I love your videos huge science fan!
Pros watch at 2x speed
@@imbw267 nah 1x. I want to appreciate it in its entirety
I knew it was a 30 min video when it started. Couldn't believe it was already over.
ngl I did the same thing with the speed of motion
Such clarity in explaining things, is why I love this channel. Plus, you do a ton of work to make it visually interesting!
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
Grant that little bit you did with "these is in the eighth position" etc was absolutely brilliant. Great video as ever, thank you.
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.
Tares is a verb! "He tares the scale". It means setting a scale to zero with something on it. That way you can weigh something in a container without weighing the container! You use it a lot in chemistry.
Fun fact: (not Fun at all actually) in portuguese its "tara", but the word for "pervert" is "tarado", where -do is a suffix, meaning "perversion" is "tara" as well
@@joaomatheus6222 How interesting! I looked up the etymology of "tare", to see if it might explain why "tara" has two different meanings in Portuguese. I found that the medieval Latin word "tara" comes from the Arabic word "tarah", meaning "thing deducted or rejected, that which is thrown away", which is derived from "taraha", meaning "to reject". Perhaps perversion became associated with rejection at some point in the history of the Portuguese language.
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@MelodiousThunk I suspect you are on the money about that. In Spanish we also have the verb "tarar": to set a scale to zero. Also we have a "tarado" (male) and "tarada" (female) but it translates as stupid or idiot. In fact, it's a participle. It's like saying "tared":
The scale was tared // La balanza fue tarada.
I wouldn't be surprise if your explanation is also valid for Spanish. Just remember the complex history Spain and Portugal have with each other. Specially during the Al Andalus times.
I always wondered why the scales I use to brew my coffee had a "T" written on the button that zeroes the scales 😂
"we shouldn't let machines rule our lives" -the man writing and using a wordle bot
Love the video!
HAHAHA I was going to bring that up. Super funny.
Funny if you take it the wrong way yeah but the meaning of that saying is to not blindly follow a machine's decision, which is exactly what he's doing by taking into account the bot suggestion but ultimately making his own choice with what info he has available aka the word list and his personal preference.
I know what it means, Corne, lol
exactly! he's just iconic!
exactly! he's just iconic!
"Ignoring its recommendation, because we can't let machines rule our lives"
I love this!!!
L
Yesss, I laughed out loud at this part too!
the letters „first naive ideas“ tending to the word „start“ is such a nice detail!
well done video!
18:39-18:58 I love this paragraph! Love this wordplay, brings back VSauce memories!
I really liked it as well :)
Yea, brillaint stuff
That part made me smile. You could tell he was having fun with it :)
Grant is a fucking genius lmao
Reminds me a of CGP Grey video personally with the wordplay and semi-rhythmic nature
Awesome breakdown as usual. I'm surprised you didn't comment more about the effect of "hard mode" and the reduction in information available when you need to reuse correct information.
I wonder if looking ahead at the next guess is all you really need for hard mode.
@@rantingrodent416 definitely gotta look ahead at more than one guess; it's easy to get stuck with 4 letters solved and 4-5 options for the last letter and if you don't have enough guesses left...
Am I the only one that finds hard mode easier?
@@AntonioDoukas hardmode is definitely harder, so I assume you are. if you get stuck on a word with 4 greens and one grey, that could have several possibilities for the last one, you're boned
Hard mode is actually a lot easier to write a bot for, in my experience
Would love to see how you would approach tackling Wordle’s “Hard Mode.” Loved it, thanks so much for making this
I’d love to see the changes hard mode creates as well.
Ditto! What’s the best first word in Hard Mode?
Great video! (but none of it applies to my game lol)
@@kidalan lol😐
@@kidalan I go for the naïve frequency analysis-based route. 'orate' is my go-to atm, but it used to be 'opera'.
That is not to say by any means it is optimal.
@@__a_4444 I like those openers! I usually open with adieu or ourie. I like to establish which vowels I’m working with, then use that foundation to shoot down consonants. If there was a word with five vowels, I’d use that every time. 😆
Finally after using crane as my opening for a year, I'm so grateful i didnt miss wordle 732!
(18:46) Just brilliant! ‘FIRST is “which” after WHICH THERE's “their” and “there.” “First” itself is not FIRST but ninth, and it makes sense that THESE OTHER words COULD come ABOUT more often. WHERE those AFTER first are “after,” “where,” and “those,” ... BEING just a little bit less common.’
I also thought that was brilliant. Such awesome word play and creativity for such a small moment
As soon as I heard it I looked for this comment
@@shibno01 same lol
I thought I was having a neurological event.
WHOSE on FIRST?
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.
My friend and I like AUDIO/STERN as a double opening. It covers all traditional vowels without repeat letters and tests S in the first slot which is the most common starting letter for 5 letter words.
I use IRATE/SOUND myself
Nice. ADIEU/SHORT is mine. So instead of the N I’m guessing the H. Other than that it’s the same letters.
@@nigelong1779 I was irate and pound but will definitely switch to sound now
I use AUDIO/LYRES, I did a very non-scientific survey of digraphs and found that S (as first letter), L or R (as second letter) have the most distinct ones, so far I'm averaging 4 so I'm maybe doing as well as a simple robot.
I did exactly these 2 as well, have not had a single misser and played since start. We stopped using it as it became too easy to play with these 2
I have religiously been using crane since I saw this video, TODAYS OUR DAY GUYS!!!!!🎉
I played Wordle for the first time just a few minutes ago and used "Other" as my opener and got a 1/6
thanks man
The same thing literally happend to me RIGHT NOW, I was shocked lmao!!
ahaha me too
I got 4/6
oh
@@NovaaZR
he meant tht day the actual word was *OTHER* so he got it right
on the first try lol
Just realised WORDLE now has a "hard mode" where you MUST use existing information in future guesses (i.e. if you get a green first letter and yellow fourth letter, future guesses HAVE to start with that same first letter and mix that other letter around). Curious how this would affect the amount of information obtained at each guess, particularly with an algorithm looking ahead multiple guesses.
I've lost only a couple times; once because I got the last 4 letters, but there were more possibilities for the first letter than I had guesses left. that would be a case to use a word that doesn't include the results from previous guesses.
?. SZwa*=+
he has that at the end of the vid
he does a zip on the guesses and patterns, look at the source code:
if hard_mode:
for guess, pattern in zip(guesses, patterns):
choices = get_possible_words(guess, pattern, choices)
Oh. That's just how I've been playing normally...
I learned about entropy from a graphic novel called Meanwhile. It's a choose your own adventure revolving around a scientist and three inventions, the kill everyone button, a time machine, and a memory transfer machine, highly reccomend, more of a puzzle than a book.
Great video as always!
Edit: Author's Name is Jason Shiga.
I loved that book as a kid
goated book
@@kylemcleod4115 same
I will be checking that out
favorite book ever
I can’t imagine the work involved in creating this video. It is so refreshing to see something professionally done.
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 ua-cam.com/video/fRed0Xmc2Wg/v-deo.html
For a human playing Wordle, I'm not sure I'd actually recommend starting with CRANE, or any of the ones best for one of these algorithms, since it requires also knowing what it will do for second guesses. For example, here's the start of the mapping for what it does with that second guess:
⬛⬛⬛⬛⬛ -> sloth
⬛⬛🟨⬛⬛ -> toils
⬛⬛⬛⬛🟨 -> spilt
⬛🟨⬛⬛🟨 -> rosit
⬛⬛⬛⬛🟩 -> toils
⬛🟨⬛⬛⬛ -> shout
⬛🟨🟨⬛⬛ -> party
⬛⬛⬛🟩⬛ -> gluts
⬛⬛⬛🟨🟨 -> lemon
⬛⬛⬛🟨⬛ -> pilot
🟨⬛⬛⬛⬛ -> kutis
⬛🟩⬛⬛⬛ -> pilot
⬛🟨🟨⬛🟨 -> patly
⬛⬛🟩⬛⬛ -> slipt
⬛⬛🟨⬛🟩 -> lambs
⬛⬛🟨🟨⬛ -> toils
⬛⬛🟨⬛🟨 -> tepal
⬛⬛🟩⬛🟩 -> glost
⬛🟨⬛⬛🟩 -> south
:O btw really nice video! The animations were amazing and they made it very fun to watch! Keep it up!
I find it very interesting that in all three of these words, 'A' finds itself in the third position. Is that just a thing where most 5 letter words containing an 'A' have it in the third position or is that meant as a guess to provide most information - or bits?
will we see a follow-up with hard mode consideration?
couple more questions on this super interesting video:
1. i note that the information you are gaining each time seems more based on letter frequency while not really considering letter placement frequency (as your suggested guesses often include words with letters in incorrect places, albeit with 0 probability of being right). that may be another avenue for info gain - ie, doing some analysis on how often a given letter occurs in a specific location.
2. strongly defining what is optimal as it may mean different things to different ppl. you seem to have defined it as lowering the expected number of guesses until being correct. however, another might reasonably define optimal as never missing a puzzle which i suspect would change the strategy being used.
and of course my previous question of looking at the puzzle in hard mode would also affect how the previous two points are considered.
cheers and thanks for the informative video!
Huh, I ran a much more naive calculation of the best first guess (matching every word in the worlde dictonary against every other word, calculating yellow and green clues, and generating a weighted average score with green clues being a bit more valuable than yellow) and I also came up with SOARE as the best first guess.
You ever watch a video that's so good you actually watch the end screen
More like "you ever watch a video that is too long you actually SKIP to the end screen" 😅 Yeah no way am I sticking around for 30 minutes trying to get info on the best start word to use.
@@AzureSteel why would you look to an in-depth mathematics channel for wordle tips?
Wait Cheetahh. Lol. Holy crap. Weird to find a bridge player here lol
@@dogmouthhorse Pretty sure this video was recommended to me (and probably to a lot of other people given the views this has relative to his other videos in the past year) through YT's algorithm because of the recent Wordle hype.
@@AzureSteel The word is in the thumbnail, if you don't like math this was an easy skip lmao
I don’t know why, but this was the most calming video I’ve ever watched… math can be so relaxing sometimes
His voice is extremely soothing. I'm going to check out his other videos just because of that 😂
Edit: I discovered this is a math channel. While I enjoyed this video, I'll have to reconsider because math and I have not historically had a great relationship
This video has finally fulfilled its purpose
It's not exclusive to this particular video of his, but there is something strangely refreshing about learning about things I don't understand. Like the prime numbers video of the monster, it's so refreshing to hear someone talk so plainly and expositorily yet still pass way over my head. I love learning how little I actually know, and this channel (among others) refreshes my brain so well. Please accept my sleepy and sincere appreciation.
TL:DR ~ I like your funny words magic man
don't get too excited - it's just conceptual baloney.
@@JamesHawkeUA-cam Conceptual? He tested it; it's quite evidential.
this was a fun problem to solve :) my friend and I essentially constructed a solver with the same methods but we conceptualized it in a very different way. really cool video!
hi geo
Thank you for your service geo
hey it’s the big cactus guy
you mean you did and matt was watching chess lmao
hi minecraft man
Some thoughts on CRANE as first guess...
I usually guess stare first (an anagram of tares, which your first algorithm likes) but started guessing crate, with the reasoning that a C often comes with an H or K, so finding a C feels like it gives more information even though it's a less likely letter. Essentially, letters that are weighted towards appearing in certain types of words or in certain letter combinations should be more valuable guesses than their simple frequency should predict. C is probably at a sweet spot where it's not too uncommon a letter, and enjoys a big boost from giving you a lot of bonus information if you do find one.
Further to this, if you have, say, two certain letters that often appear in combination, it makes sense strategically to include one of these letters and not both in an early guess, as the odds of these letters appearing in the word are far from being independent odds, so guessing one gives you information on the probability of the other - bonus information from just one guessed letter. Hence, since CH and CK are very common associations of letters in common English words, guessing a C but not an H or a K in your first word seems to make a lot of sense from an information standpoint, and I'm not surprised that an algorithm found that guessing a word containing a C first was smart, despite C being quite a way down the letter frequency list.
on that note, i feel like the _position_ of the letter within the 5 could also be valuable. i believe that's why 'tares' is valued over 'stare' because presumably there are more words ending with s, which might be pretty informative.
@@alveolate yeah, letter positioning must be valuable. I actually initially preferred stare over rates (same logic applies to tares) because I thought the wordle would never be a plural so an S in the last position would be bad! Maybe vowels in positions 2 and 4 are better than in positions 3 and 5?
This ^^^. You can easily see it, if you guess a word with "U" and "U" is not in the word, then "Q" isn't either.
In code breaking, you'd see a word that ended in "Y" and guess one that ends in "LY" (hard mode) because that's a likely 2 letter combination. I don't have the table of common 2 letter combinations but it's available.
Yeah if we’re playing to eliminate two letter combinations word final s also informs us in situations of “es” (as in tares. just as word initial c would inform us of possible ch words
I know you came back later and decided that you miscalculated and this wasn't the best opener. But I've been using it anyway, and I can tell you that *today* it's the best opener!
I would like to see a Hard Mode version of this analysis and how the algorithm reacts to it.
Yeah I was like damn not even playing hard mode. Gotta step up
@@oldcouchcushion1545 Not playing hard mode = weaksauce
Try to work out your friends' first words from their scoring patterns - Metawordle :) The worst starter word? "Eerie" - unless it's correct!. Anyone got a worse one?
I do this
If you know someone starts with the same every time, then you can use their scoring pattern to unlock information yourself. Bit cheaty though
@@seastilton7912 I do it to pass the time between puzzles but you make an excellent point.
I do this. It's pretty fun
"queue" must be pretty bad.
20:10 It is interesting and I think people should keep in mind how even in highly mathematic scenarios, human preference is still involved not always, but not never
Yeah, and the more nuanced version of this is that human preference is used where a heuristic is more cost-efficient than more computing.
In this case, Grant used his intuition to feel where the cut-off point is. However by the definitions given in this video, this cut-off point should certainly be able to be found in the game-theoretic sense. A quick naive approach would be to try different iterations of the bot using different cut-off points and over millions of iterations find the optimal point.
But you see that's exactly why Grant used his intuition as a heuristic instead, because the expected gains from running said millions of iterations is very little compared to what his best guess would do. And as an alternative, if Grant used another method (not brute force simulations) to try to get the exact game-theoretic optimal point, it would be a lot of thinking time used for not much effect.
In WordHoot, a variant of Wordle, where speed matters, I see people consistently beat bots.
In this case he's using a heuristic to approximate the true word distribution which is zero for words not in the wordle list and 1/N for words that are in the wordle list (where N is the size of the wordle list).
It's kluge in the sense that he could just use the wordle list for this purpose, but he decided that's off-limits side-information, so he goes ahead and finds a different source of side-information that he can use to approximate the wordle list distribution.
The real lesson is that if you require human preference, the problem is likely ill-posed :)
The use of priors (prior beliefs) for making predictions is quite often used in some areas of statistics and machine learning. :)
@@lekhakaananta5864 it's basically a password cracker bot but a bit more chill
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.
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. :)
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
this is so cool i want to try making a wordle bot in python too !!
@@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.
That wordplay in the sorted list of most common words broke my brain more than any math you've ever presented on this channel.
Great work, lovely video!
timestamp please
@@joseville 18:40
Cool video! Loved the math! It would be different for hard mode though where you can't ignore the clues you already have.
Was thinking the same thing! I liked the little teaser at the end, but wish the video went into it more as “hard mode” is my preferred way to play
I’ve never played this but if that’s the restrictions of hard mode, it seems more like dumb mode..
which I suppose you could also refer to as hard mode
@@Jay22222 true
@@Jay22222 What do you mean? If your first guess gave you the information that an R and an E are in the word, then your 2nd guess has to have an R and an E in it. That gives you 2 less spots to try new letters. It's significantly harder.
@@Jay22222 why tho lol
Today is a momentous occasion - the word IS **CRANE** today! Happy 1-shot day to a lot of people.
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:)
TARES are also a corn/seed used in fishing (in the UK)
I’m a cashier at a grocery store and I’ve been using “tares” too.
Im a random kid and I have been using stare which is kinda the same but tares might be better
I also work in a grocery store, but I use the word “rates”
soare is a good starting word too
Wordle has existed in Dutch as "Lingo" for probably 30 or so years as a public tevelision show, with variable word length too. Near one of its last shows there were two brothers who developed an algorithm to guess these words during the show which they could play out in their head and they won literally every round and after they won they put their full way of thinking on internet.
Could you give a link to that please? Klinkt heel erg interessant!
Also been around as a tv show called "MOTUS" in France
You might be interested to know Lingo actually started in the US in 1987 and has had international versions in at least 15 countries.
Those two brother remind me of Michael Larson who memorized the pattern of the Press Your Luck board and used it to beat the system.
Also very similar to the game “Mastermind” that uses colored pegs instead of letters.
Link?
Making a word game about math. I LOVE IT
hi evan
Hi Evan
@Ex Japan you're lucky,
I lost $1500 trading with an unprofessional trader.
There are lots of good experts out there but most offer little ROI's. I will advise trading with Mr Nicholas Burke-Gaffney's team as I make over $35,000 on average per month from their trading bots.
After 512 days, crane has finally won first try. Thank you
got a first try on my go to "purge" and then when they wiped my history after inactivity I stopped
Absolutely impeccable timing, just went over this concept in a course on Machine Learning, feels great to understand what you're saying!
what course and/or what reference have you used specifically for information theory (if you did have separate reference material)
Beautiful watching as always, thanks Grant! I enjoyed the confusing word skit at 18:40 haha
Such clarity in explaining things
first comment and also feels like botting
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@teeforever1 no cares about christianity
It's clear that people develop different methods to solve the puzzle. For me I start with "adieu". My second word is "story". This way I get all the vowels covered and some major consonants. I have found getting a good start goes a long way towards solving the puzzle.
I do that too!
9:28 I think this is the perfect explanation to the whole concept of Akinator. Yes, it also cheats by just using a user-created database but getting to the answer in less number of questions is the real challenge.
"fewer"
I 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.
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.
Just wanted to thank you for this video I got wordle in 1 yesterday. Guess it’s time to change my word to Salet. ;)
This whole video is great but I have to say I liked the cute word play around 19:00 quite a lot.
Crane Shtik combo is absolutely legendary, just tried it, found the word in 3 tries. Absolutely amazing.
Here's an interesting alternate goal: what if rather than optimizing for fewest guesses, you built a bot that attempted to maximize the amount of times it could guess the answer in 2 guesses, and only after failing to do so would try to minimize its remaining score. Basically a risk-taking bot that's more in it for the bragging rights of the unlikely got-it-in-two situation more than it cares about reliably doing well.
why even bother going beyond 2 guesses? didnt get it in 2, you failed.
wouldnt that exponentially increase the complexity of the computation. Is it even solvable within 2 steps ? I think grant mentions something along the same lines.
@@adityapalve3752 I don't know why you think the computation would be far more complex since you're only looking 1/2 guesses into the future.
It isn't solvable within 2 steps, but you can try to solve it within 2 steps as much as possible (likely by increasing the weighting of the frequencies of the words; this gives you less information in the long term but increases the chance that you get lucky on the second guess).
Hopefully this makes sense lol.
Especially with the long tails it is definitely possible to trade 'get it in 3 or less more than x% of the time' for the average score
That just means doing the first two guesses in hard mode and the continuing normally. Which in reality just means the set of guessable words on the second guess is smaller.
Thanks for the great video!
I think a great addition to this algorithm would be the removal of already used words in previous wordles. This would decrease the overall entropy a little since some pretty common words were already used. Anyways, great video, I always learn so much from you!!
I like to start with “Faint”, which is usually followed by “Ouphe”, and they both remove vowels (excluding “Y”), and I usually end up with enough info to finish the word, but if I do not, then I follow up with “Byrls”. Which removes “Y” and four extra, fairly common letters. This strategy will usually get you the letters by the fourth guess. The strategy I used to follow was a “House” “Paint” combo, and after a while I felt like I could get more efficient and swapped to “Faint, Ouphe, Byrls”.
the issue is that you will never get the word in two or three guesses like that, so it maximizes your chances of winning but not your score
you can always do:
GLENT
BRICK
JUMPY
VOZHD
WAQFS
this eliminates 25/26 letters and just leaves X
I'm with you, find the vowels first ...
@@treverfox1280 Doesn't work if your Wordle requires entering only guesses that are words, like cell phone Wordle from Lion Studios Plus. Also fails for goal words requiring trial and error, like batch/match/patch/watch/hatch/latch/catch, which can't be reliably guessed even if all six lines were used.
'I like to start with “Faint” ' Not optimal, because the consonant F is not a frequent one. Saint would be better, and including E in the first word would be best.
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.
I do the same but with audio
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.
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.
@@davidelliott9817 SAME!!!
audio is also good. didnt even know adieu was a word lol
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.
The likelihood of getting it on second is low, may as well find the most information out and try for third.
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.
Interesting. I happen to have been using TASER as a first try, which is just an anagram of TARES!
Except that the order matters, as the video maker argues convincingly. Still, though, great intuition!
This made me discover absurdle. I was extremely aggrivated by it at first until I saw the explanation on their page. Basically all the words I was getting were "kitty" "jiffy" "dizzy". But that's because my first two guesses were always Crane and then Buoys to knock out as many vowels as possible.
That's what's so interesting about absurdle! Having the same first few guesses can really back it into a corner. I really wonder if it's possible to force any given word out of it. With how restrictive and deterministic it is, it's not obvious that this should be the case
@@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.
@@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.
While playing the game, just like you considered the "common word probability", I consider the "common character probability" as well. I propose scoring the words on the basis of how frequent each letter comes at each of the 5 positions in all the 5-letter words.
For example, you mentioned the NAILS vs SNAIL choice. SNAIL has an A in the middle (as in ~1200 5 letter words), whereas NAILS has A on the 2nd position (as in ~2100 5 letter words). Clearly, the A in NAILS gives you higher information (getting those greens on the board).
That's a good idea, but I'm pretty sure it's already included in the entropy calculations.
Surely SNAIL has more information (more bits) because it narrows the choice down more (1,200 versus 2100).
Yes, as david said, this is already accounted for in Grant's information-related approach. We know intuitively that a green is better than a yellow but how does Grant's program know that? Because it counts the remaining possibilities. The remaining possibilities after a green clue are much more restricted than after a yellow clue, so that algorithm will naturally rank guesses that give green clues more often as more useful.
Yes, i always use AUDIO as starter cause it contains 4 vowels and i thought i gives more information, but apparently its not really effective
@@kentanggulung But your method is better for the human brain which does not contain the list of possible words, nor can do the entropy calculations on the fly. I use AROSE, UNITS as my first two words no matter what, it gets rid of a lot of common letters and all the vowels.
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
I noticed that too, but he was obviously answering (or should i say the program was designed) considering the information of R
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
You're content and enthusiasm has inspired me to pursue my dreams of learning programming and math, I'm highly grateful.
He is neither content nor enthusiasm :)
@@ZopcsakFeri your funny!
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.
This video is an absolute masterpiece. Especially loved the bit at 18:39 about the most common words. Hilarious!
The ¨bit¨?
@@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.
@@CraftBasti I made a bad pun about how this is about information theory, which uses the unit the "bit".
@@owenaspinall2046 ahh of course, that was the reason for the quotation marks! Good one ^^
It was pure genius
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!!
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
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.
the Gospel:
the Gospel isn't solely "Jesus loves you and He can do this, this, and that for you." no, the true Biblical Gospel is that all have sinned and fall short of the glory of a holy and just God, and because of this we all deserve death and eternal damnation in hell.
our sins have separated us from God and when we were separated from God, we were sold as slaves to sin, under the captivity and care of the devil, whom we love(d).
in our sinful nature, we're nothing more than wretched, vile sinners in DIRE need of the Savior, but JESUS, the perfect and sinless Lamb of God, came into the world and took the punishment we deserved for our wicked sins and was raised from the dead three days after being buried so that we may have the opportunity of salvation, redemption, adoption, and reconciliation to the Heavenly Father. we ought to repent and believe in the Gospel of our LORD Jesus Christ; we must be born-again. (Mark 8:36,37) (John 3:16), (Acts 17:30), (Romans 6:23), (John 3:5), (Ecclesiastes 12:13), (Mark 1:15).
@@teeforever1 Sorry, "gospel" is 6 letters long.
@@krispykremedonut5135 so why do u care?
@@krispykremedonut5135 he is obviously trolling
@@StaRScreaM-du6fn no he's not, just a religious crackhead
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! 🙏
Well today's word was CRANE. Have to give this the award for best thumbnail ever
As a programmer, I actually been thinking a lot about how I would code a solver for this lately. Great vid as always!
Same. But just starting seems such a tedious task.
@@amaansiddiqui2376 Step one, just pick randomly from all the answers. Then refine. ;)
Data Scientist here:
Just wanted to add another perspective on entropy & the way we quantify information, as this topic is often fairly confusing for beginners.
So 1, where did all this theory & stuff come from? Information theory comes from trying to measure the efficiency of communication of information.
So the key idea is that, if we want to quantify information, really what we're doing is trying to measure how well one actor is communicating to another actor about an event.
So the two actors need to come up with some dictionary, or what is often called an "encoding" in order to communicate events to one another.
The the second key idea, is that It takes more energy to communicate with more symbols ("symbols" could be words, bits, smoke signals, whatever is your base unit of information).
Therefore, our objective is to assign the least amount of symbols to all the possible events, so we should encode according to how common different events are. More common events, should use less symbols.
The inverse of a probability has this great name, called "the surprisal", the idea is that the higher the number, the more "surprising" an event is. Like if I were to tell you the sky just instantly changed from blue to magenta, that event would have a wildly high surprisal, because it has a really low probability.
The reason we put a log on the surprisal is to get "how many symbols do we need in order to communicate this event?", the base of your log determines the number of symbols available to you, most commonly we use base 2 because we're usually thinking of this in bits.
The entropy of a probability distribution is the average number of bits required to communicate events in said probability distribution.
Hope someone else found that interesting! None of this stuff made sense to me until I understood that.
That’s so helpful! Thank you so much.
Yeah, that explanation was very clear to me. Thanks.
I 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.
entropy is like an advanced average.
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.
i am so thankful for the quality of your educational content. It is amazing to learn so much from just one person.
A very nice video! A fun fact: Finding an actual "mathematically optimal strategy" is probably pretty hard. Similar problems, like Mastermind, are known to lead to provably hard problems (at least NP-complete, potentially even harder!). This does not mean it cannot be solved, though. For example, Donald Knuth bruteforced optimal mastermind solution in 1976. :) EDIT: Thanks darci peeps and Tim Fischer for clarification: Knuth bruteforced optimal *worst case* solution for Mastermind (with 4 pegs). If you care about the average number of moves, this was solved only later.
Donald Knuth’s algorithm used minimax, a greedy algorithm which was not most optimal. It was Kenji Koyama and Tony W. Lai that performed the first an exhaustive depth-first search in 1993. I agree that 3b1b’s strategy is not THE most optimal, but it’s robust to other versions of wordle which is cool.
The solution is only for 4 pegs tho, most modern master mind games (each one I ever played) uses 5 pegs!
I did an exhaustive search on hard-mode Wordle, but using only the 2315 word dictionary the game uses for its own choices. I optimized for average number of moves. Here are the top five starting words & the average game length they lead to:
3.51922 trace
3.52009 slate
3.52181 least
3.52700 crate
3.53391 crane
Allowing the full 12972 word dictionary would add a lot more searching, though the search could potentially be pruned, depending on what question you were trying to answer.
I always use “audio” and then “entry”. Those two words cover all of the vowels and some common consonants. Once I know which vowels are in the word I can usually figure it out.
try adieu!!
I like "adieu" and "story" as my first two guesses. Probably cuz I felt that S was more common than N. But my third guess covers that.
audio -> flyer is great too since it also gets the Y
@@WanderTheNomad that is so smart. I also try to get my vowels out of the way with adieu, then sport to get my “o” and then chewy to get my “y”, but you get the o and y in one shot with story. I will try that next time!!
@@WanderTheNomad okay I just tried that and I got avoid in the third guess that's awesome
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!
My favorite starting words are usually TRAINS or TRAMS, getting those basic plural S, the very common TR, and an A