Solving Wordle using information theory

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

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)

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

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"? ;-)

🤣🤣🤣

gold

Same but FARTS

Lmao

You might like Lewdle, the lewd version. (Penis is my first guess on it every day)

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

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.

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!

Hello

That's two different KRplusrs 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.

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...

Possibly fun fact: GEB is why I'm an atheist.

@@Oberon4278 cringe alert

​@@hackkitts9254why ?

​@@Oberon4278reductionism only gets you so far

@@Oberon4278what argument convinced you?

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

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?

Came here for this, was not disappointed.

Also I believe NYT has updated the Wordle words list, would love to see an updated video with the latest best starter.

@@lpeabody yeah idk if it's public though?

​@jonaslarsson5279 it might be the the source code somewhere

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

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)

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).

L

Yesss, I laughed out loud at this part too!

I also was here for that

No spoilers 😂

I used crane today. Got it on first word.

Lol

Coming in with the -4 (WordleBot did it in 5 that day)

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!!

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

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.

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 😂

I like that.

why use he log base 2??
bcs always we cant get half observation in my space of probabilities

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

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 would love to see a follow-up with hard mode considered.

I wonder if looking ahead at the next guess is all you really need for hard mode.

@@rantingrodent416 definitely gotta look ahead at more than one guess; it's easy to get stuck with 4 letters solved and 4-5 options for the last letter and if you don't have enough guesses left...

Am I the only one that finds hard mode easier?

@@AntonioDoukas hardmode is definitely harder, so I assume you are. if you get stuck on a word with 4 greens and one grey, that could have several possibilities for the last one, you're boned

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).

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. 😆

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

real worlde example :D

@@EscurKo haha yes yes, you get it. Its not a book exercise.

Yeah, and the more nuanced version of this is that human preference is used where a heuristic is more cost-efficient than more computing.
In this case, Grant used his intuition to feel where the cut-off point is. However by the definitions given in this video, this cut-off point should certainly be able to be found in the game-theoretic sense. A quick naive approach would be to try different iterations of the bot using different cut-off points and over millions of iterations find the optimal point.
But you see that's exactly why Grant used his intuition as a heuristic instead, because the expected gains from running said millions of iterations is very little compared to what his best guess would do. And as an alternative, if Grant used another method (not brute force simulations) to try to get the exact game-theoretic optimal point, it would be a lot of thinking time used for not much effect.

In WordHoot, a variant of Wordle, where speed matters, I see people consistently beat bots.

In this case he's using a heuristic to approximate the true word distribution which is zero for words not in the wordle list and 1/N for words that are in the wordle list (where N is the size of the wordle list).
It's kluge in the sense that he could just use the wordle list for this purpose, but he decided that's off-limits side-information, so he goes ahead and finds a different source of side-information that he can use to approximate the wordle list distribution.
The real lesson is that if you require human preference, the problem is likely ill-posed :)

The use of priors (prior beliefs) for making predictions is quite often used in some areas of statistics and machine learning. :)

@@lekhakaananta5864 it's basically a password cracker bot but a bit more chill

I loved that book as a kid

goated book

@@kylemcleod4115 same

I will be checking that out

favorite book ever

Yeah I was like damn not even playing hard mode. Gotta step up

@@oldcouchcushion1545 Not playing hard mode = weaksauce

i like anime and shout

you can always do:
GLENT
BRICK
JUMPY
VOZHD
WAQFS
this eliminates 25/26 letters and just leaves X

: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.

don't get too excited - it's just conceptual baloney.

@@JamesHawkeKRplus Conceptual? He tested it; it's quite evidential.

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

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 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 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?

Use AUDIO and EYING to get all of the vowels

@@dave9012 I just learned that you guys consider "y" a vowel.

@@LuckyLex_ WAY back in school, we learned that the vowels were: "AEIOU and sometimes Y". Dunno what they teach the kids these days.

@@ColinFox In terms of wordle I think it's totally valid to put it into the same category as other vowels. With how you construct words in english not considering y a vowel with this kinda game is just going to cause frustration and possible confusion.

@@LuckyLex_ Only sometimes

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

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

Except that the order matters, as the video maker argues convincingly. Still, though, great intuition!

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?

hi evan

Hi Evan

@Ex Japan you're lucky,

I lost $1500 trading with an unprofessional trader.

There are lots of good experts out there but most offer little ROI's. I will advise trading with Mr Nicholas Burke-Gaffney's team as I make over $35,000 on average per month from their trading bots.

I 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.

"fewer"

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

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.

I do that too!

timestamp please

@@joseville 18:40

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

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

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

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.