Plus, Starting Words for Quordle and Squareword…
Wordle hit the media just as we needed some post-pandemic therapy. Today’s blog is an ode to Josh Wardle’s brilliant game, with trivia, tips and especially, tactics to enhance your fun.
Distinctive Features of Wordle
Either you already know Wordle, or its New York Times link will quickly fill you in.
Transparency. Wordle’s workings are visible to all. A little diligence reveals not only today’s answer, but answers for all the coming days. Wordle does not attract hackers, because looking inside it grants one absolutely no street cred! And no sensible person would gamble money on it because its future answers are so easily available.
Trust. Wordle promotes trust and faith in our fellow human. The game is so easy to cheat that we instantly disregard people who always claim to win in the first or second move. Conversely, we tend to trust those whose scores are believably normal.
Non-Addictiveness. Wardle designed Wordle to present a new puzzle only once per day. It’s one of the few games that does not encourage obsessive repeated play.
Bragging Rights. Wordle allows us to boast to our friends about an especially good score, without revealing the answer and thereby spoiling someone else’s fun. Reportedly, the anonymous “brag screens” for FaceBook and Twitter were invented by Wordle players in New Zealand. When Wardle added this feature, Wordle suddenly became a sensation.
What Are Those Wordle Colors?
This blog discusses not only Wordle, but a number of Wordle-like games. Each of them uses color changes to signal that you’ve found letters that are in the answer.
But there’s something odd that these games have in common: If you click the “?” icon for the game’s rules, the rules don’t name the colors!
If you ask someone what those colors are, they are likely to say:
- Gray, for letters that are not in the answer word
- Yellow, for letters that are in the answer, but in another position
- Green, for letters that are in the answer, in the correct position.
However, the rules given with the games don’t name the colors, they just show examples of them. Why is that, anyway?
- The settings of some of the games allow the player to choose a “High Contrast” or “Color Blind” mode. This makes the game accessible if the player has some degree of color vision deficiency (color blindness). If you choose that option, you’ll see that yellow is replaced with a light blue, and green with a tomatoey red. This blog’s discussion assumes you are not using that setting.
- The yellow and green in the original Wordle game are not “pure” colors, meaning with hexadecimal codes FFFF00 and 00FF00. [In RGB notation, (255, 255, 0) and (0, 255, 0).] Those would be rather harsh to stare at! Instead, Wardle chose a softer palate of colors. According to my PhotoShop, they are:
- 787C7E for “gray”
- 6CA967 for “green”
- C9B35F for “yellow”
- How we see and name colors is to some extent individual. For example, when I look at the Wordle yellow, to me it looks like ochre. But if I called it ochre here, that would confuse readers. So I will simply refer to gray, yellow and green boxes.
Wordle Basic Facts
Wordle was invented by software engineer John Wardle. He was raised in South Wales, received college degrees in UK and USA, and currently lives in Brooklyn. He first created Wordle, a play on his last name, in 2013. It lay dormant until he revisited it in 2021 for entertainment within his family.
His partner Palak Shah played a critical role in making the game user-friendly. She’s American, of Indian-American extraction. From over 12,000 possibilities, she chose approximately 2,500 answer words that would be familiar to most English speakers.
If you or I decided to program a new word game, we might store both the vocabulary and the answer of the day on a protected website. That would discourage cheating, but unfortunately it would also reward hackers! Wardle’s game, cleverly, does neither of these things.
Instead, when you visit a Wordle website, it loads your browser window with the entire list of allowed guess words, the entire list of answer words, and a calendar that tells you when each word will become the answer! And it’s all there for a curious visitor to peruse.
It’s sort of a test of upbringing. The openness allows you to cheat if you want to. But if you prefer to simply play the game, you can congratulate yourself on your self-restraint and good moral character!
Implications of Openness
- Anyone can find an internet article that lists 2,315 answer words and their expected date of use.
- Also, anyone can read an analysis of how the Wordle code works.
- You can even look at the full code yourself. When I consulted it, this version had 2,308 answer words and 10,638 additional allowed guess words.
- Or you can read an article that reveals today’s word before you ever work the puzzle, and also gives hints to the following day’s answer.
- And, you can play tomorrow’s game, or the game for any date you choose, by changing your computer’s calendar date and then visiting the game website. The Wordle program accepts your computer’s opinion for what day it is, and serves up the word programmed for the date your computer is pretending to live in.
Because of openness, there is no payoff to cheating in the game. The maximum personal reward comes from simply playing the game as it’s designed. In fact, the inventor of the game is said to avoid looking ahead, so he too can have the fun of playing each day’s game.
Where Do the Wordle Words Come From?
As a fan of crossword puzzles and Scrabble, I naturally wondered about the source of Wordle’s vocabulary.
The New York Times purchased Wordle in January 2022 and as noted above, still makes the full code available. It allows a total of 12,946 guesses, of which 2,308 are valid answer words.
I have on hand several lists of 5-letter English words:
- The most recent (6th) edition of the Official Scrabble Players dictionary contains 9,332 five-letter words.
- The US Scrabble tournament word list (TWL, The Word List) contains 8,938 five-letter words.
- The European Scrabble tournament word list (known as SOWPODS or Collins Scrabble Words contains 12,478 five-letter words.
Evidently, Wardle started with the Collins list or some similar comprehensive English word list. I decided to compare Wordle’s list with SOWPODS and here’s what I learned.
Comparing the Lists
Wardle’s list adds 507 words to SOWPODS. These are in several categories of which I give only a few examples:
- Words brought in from other languages (abers; achar; arroz; hygge; saags; salut)
- Unusual (to an American) forms (feart, gauch, goest, judgy; kapus; sicky; yobby)
- Slang abbreviations (acros; agros; aight; impro; ixnay; juvie; lemme; newbs; pwned; twerk; vlogs)
- Modern additions (adbot; ayaya; emoji; grrrl; vapes)
- Biological terms (anura; ascon)
- Rude words (aspie; dimbo)
When the New York Times bought Wordle I count 39 words that they deleted from the list. Here are some examples, which I surmise were deleted because they were offensive or had negative connotations (bitch; chink; coons; darky; dykes; homos; kikes; slave; spick; wench), were too foreign (ciaos; fibre; tiyin), too techie (eprom; grenz), too obscure (agora; pupal), or obsolete (heroe; odsos; rivos; swone).
Here’s all that Wordle players need to know:
- Wordle will accept as a guess most five-letter English words;
- The Wordle solution will be a word that most English speakers will readily recognize; and
- You will rarely guess a known word that Wordle doesn’t accept. If your guess is rejected, apparently someone thought that it was NSFW or otherwise unnecessary to the game.
No successful new invention has the stage to itself. Soon a throng of imitators, some brilliant and some not-so, crowd the proscenium. And so it is with Wordle. Here are some notable copycats:
- QUORDLE: You have nine guesses to find four five-letter words. It’s a tough game but if you persist, you can win it. It’s distinctive because a guess that you target toward one of the words also gives you information about the other three.
- SQUAREWORD: Here, you have fifteen guesses to find ten interlocking five-letter words. It takes a little getting used to, but after a while it’s easier than it sounds. Once you find a single word, it gives you information about the five words that cross it. And usually at least four of the ten words end with a vowel or Y.
- WAFFLE: In this game, you are given all the letters that fit into six interlocking words. You don’t have to type a thing, you simply drag the letters around until all of them light up green to show all words are correct. Every Waffle can be solved in ten moves, but the game allows you fifteen moves if you need that many.
The games given above were able to incorporate the Wordle word lists, and I assume that’s just what they did (their websites do not say). The following games use unique answer lists that relate to their subject matter:
- FOODLE: This resembles Wordle, except that the five-letter answer words have something to do with food. I managed to solve this puzzle, but only after I looked up the definition of UGALI. Yes, it’s a food. If you already knew that, you might be ready to play Foodle.
- MEDDLE: This is a game to guess a six letter word on a medical topic. You have seven tries to find the word.
Wordle also inspired other variations, using arithmetic formulas, countries, songs, movies, a dungeon and a multi-player high-pressure scramble. In addition, there are Wordle-like games in other languages (149 at last count).
IMO, wait until you’re bored with Wordle before you go searching the above list of games. And when you do, I suggest trying the options in the order I listed them.
Wordle Strategies and Tactics
Every game invented to entertain or challenge humans also becomes a target for programmers, who compose software that will find the best or fastest solution. There are competing robot solvers which search out the most efficient way of obtaining the solution.
However, robots have immediate access to every possible answer and every acceptable guess word. In addition, there are various ways to define a best solution. (Most certain to win within six moves? Most likely to win in three moves? Likely to win in the fewest average number of moves?)
The human solver is best advised to ignore robotic ideals. Better to focus on what will best help a human being, given a normal breadth of knowledge.
Google lists many articles that claim to give the best Wordle starting words. However, since they use different metrics of “goodness,” the articles come to different conclusions! Rather than giving you one more detailed study, I’ll show you how I think about the game, add some analysis of my own, and wish you great fun!
One way of approaching a word guessing game is to be aware of how often different letters are likely to appear. If E’s and T’s appear in more words than Z’s and Q’s do, we might want to include those more common letters in our guesses.
You can’t determine the frequency with which letters appear in English words until you first specify the domain, that is, the source of the text. Wikipedia has a good discussion of letter frequency that gives several versions.
I personally like the word frequency that was used in the Linotype machine invented by Ottmar Mergenthaler in 1884. On the Linotype keyboard, the keys were arranged in order of expected letter frequency, which was chosen to be:
ETAOIN SHRDLU CMFWYP VBGKQJ XZ
This letter sequence has the virtue that the first 12 letters are almost pronounceable, which helps us remember them. And for that reason, “Etaoin Shrdlu” has made appearances in software, literature and music.
However, if we’re looking for a possible Wordle answer, we’re not confined to a letter frequency surmised almost 140 years ago! I’ve computed the letter frequency in Wordle’s answer set for you, and here the letters are in descending order of occurrence:
EAROTL ISNCUY DHPMGB FKWVZX QJ
Now let’s talk about some top-level strategies for approaching Wordle, and some specific tactics within those.
Strategy 1: Finding the Vowels
The English language has many pitfalls for a foreign speaker, but it has some welcome regularities too. For one thing, most words contain a vowel.
In Wordle’s list of 12,946 allowed guesses, only 53 have none of the vowels A E I O U. Words like cysts, gypsy, myths, nymph, pygmy, shyly, synch and tryst. And only 12 of those appear on the list of 2,308 answer words. So if you assume that the answer word contains an A E I O U vowel, you will be wrong only 0.5% of the time.
Given this information, one possible strategy is to, as quickly as possible, find out which vowels are present, and where they are. There are only 9 allowed guesses that contain four different AEIOU vowels:
ADIEU AUDIO AULOI AUREI LOUIE MIAOU OUIJA OURIE UAREI
Of these, only AUDIO is one of the possible answer words.
If we use any of these words as our first guess, we learn a great deal about the answer. However, it’s hard to choose between them:
- Do we want the highest chance of getting one or more letters exactly right? (green boxes) With LOUIE we have a 40% chance to get at least one letter exactly right, with OURIE 36%, and progressively less with the others.
- Do we just want to learn as many as possible of the letters that appear somewhere in the answer? (yellow plus green boxes) With AUREI and UAREI we’ll get about 1.4 yellow or green boxes; with AULOI and OURIE about 1.2.
- We achieve a bit of both results by using OURIE as a first guess.
Vowel Approach: The Second Guess
The first guess has given you a good idea of the vowels in the answer word. If you get one or two green boxes you can keep those in your next guess. And if you have a total of three green and yellow boxes, you can usually assume you have found all the vowels.
What if you get only one or zero colored boxes? Then a good bet for your next guess would be a word that includes Y and the vowel you haven’t yet tested. Fill in with most likely consonants from the EAROTL ISNCUY sequence above.
I have used the starting words ADIEU, AUDIO and OURIE with reasonable success. However, all these vowel-heavy words are burdened by containing the letter U, which as we saw above is only the 11th most common letter. It’s not necessarily a good idea to use a valuable guess spot for a U if we can find a more productive approach. So let’s keep considering the alternatives.
Strategy 2: Searching for Colored Boxes
Another approach is to ignore the vowels and focus on words with high-probability letters. There are many almost-equally-good choices, so I decided to confine the first guess to one of the possible answer words. That’s because there’s a small chance of hitting the word right on the very first guess, which is so exciting a prospect that we don’t want to exclude it.
I eliminated words with repeated letters, because they don’t yield as much information about the answer. This left a list of 1,566 words. Here’s an analysis of candidates on that list:
- Once again, do we want the highest chance of getting one or more letters exactly right? (green boxes) With SLATE we have a 49% of getting at least one green box, with SAUCE and SLICE more than 48%, and progressively less with others.
- Do we just want to learn the maximum number of letters that appear somewhere in the answer? (yellow plus green boxes) With ALERT, ALTER and LATER we can expect 1.7 or more yellow or green boxes; and 1.6 colored boxes with any of the next 20 candidates.
How can we maximize both the likelihood of green boxes and yellow boxes in our first guess? I made two columns of words, the first in descending number of green boxes, the second in descending number of yellow boxes:
- 1% of the top of both lists had no words in common.
- 2% of the top had only the word STARE on both lists.
- 3% of the top also included SNARE and SANER.
- 4% of the top added ARISE, RAISE, STALE, STORE.
- 5% of the top added CRATE, SCARE and TRACE.
All of these nine words are strong first guesses. You’ll note that several of them are anagrams of each other.
Strategy 3: Build On What You Know
We’ll now focus on how to choose your second guess and beyond. There’s not much internet discussion in this area.
One obvious approach is to use information that you discovered from your first guess. In fact, if you select the setting “hard mode,” Wordle requires you to do this.
If you get one or more green boxes, keep those letters just as they are. If you get one or more yellow boxes, keep those letters but put them into other positions. Then fill in letters that you haven’t previously used to make a word that will be your second guess. Obviously, you should try to choose relatively common letters for these added letters. Depending on how many hits you got with your first guess, you might even find the answer word with this second guess!
Strategy 4: Devote 2 Turns To Discovery
Another second-play strategy is to purposely devote the first two or three guesses simply to learning as much as you can about the all letters in the answer.
If you plan to commit two guesses simply to exploration, here are some combinations to consider:
- CRATE or TRACE, followed by LIONS or LOINS: There’s a 98.42% chance that you will discover at least one letter that lies somewhere in the answer word.
- STORE, then INLAY, has a 98.37% chance.
- ARISE or RAISE, then CLOUT, has a 98.32% chance.
- SANER or SNARE, then CLOUT, has a 98.22% chance.
You may think, once a number is as high as 98%, what do I care how high it is? Well, the highest probabilities here are also the guesses that give you the largest number of green and yellow boxes. So, yes, bigger is better, even when it’s this close to 100%.
If your first guess yields you no colored boxes, you really need that second guess to narrow the universe of possible solutions.
Strategy 5: Devote 3 Guesses To Discovery
If we want to use three guesses to learn the letters used, the following sequences have a 99.38% chance of discovering at least one letter in the answer word:
- CRATE, LIONS, DUMPY
- CRATE, LIONS, HUMPY
- STORE, INLAY, CHUMP
In Wordle, three guesses consume one-half of all your allowed guesses. You may not want to use all three of these guesses unless you found no green and only a couple of yellow boxes in the first two guesses.
If you use all three just to explore in Wordle, you’ll have to think carefully from here on, using all the information you have picked up from the first three guesses. However, if you’re playing a Wordle cousin game with more allowed guesses, three discovery guesses may be a reasonable way to start out.
Strategy 6: The Discovery Approach to Quordle or Squareword
What about using four guesses just for exploration? You probably don’t want to do this with the regular Wordle game because you would consume most of your allowed six guesses. However, four guesses of discovery might be useful in a game that gives you more total guesses, such as Quordle or Squareword. As noted above, I assume that these games use the same answer list as Wordle.
There are quite a few four-word sequences that give a 99.6% chance of identifying letters in a single answer word. Of course, if the game presents multiple unknown words the chance of success (and the expected number of colored boxes) is even higher.
Here are a few good four-word sequences:
- CRATE, LIONS, HUMPY, BADGE
- STORE, INLAY, CHUMP, BUDGE
Note added 6/16/2022: The following sequences are also useful and are accepted by the New York Times version of Wordle. However, word lists in some other Wordle-like games don’t accept “culty”, “dimbo” and “uncoy”:
- SNARE, CULTY, DIMBO, PHAGE
- STARE, UNCOY, BLIMP, FUDGE
There’s something special about the first two of these sequences: each of them is a high-probability sequence if you use only the first one, two or three words of the four. Thus you can start the sequence of guesses and see how many colored boxes you obtain. Once you have found enough of them you can abandon this sequence and instead start guessing words that fit the green and yellow boxes that have appeared.
I’ve used the first two of these four-word sequences to solve Quordle and Squareword and they seem to work well.
I recommend Wordle and its cousins for enjoyable, nonaddictive fun. Think of it as interval training for the brain: a couple of push-ups each day to keep your mind working.
– Featured image by Art Chester
– Linotype keyboard by DavidWBrooks on Wikipedia
– Cube and tile patterns from Creative Magic on pixabay, Keistutis on openclipart, Mart Production on pexels
Great column, Art. Wordl is my lunchtime treat. I’ve missed 2 out of about 50 so far. My go-to first word is CANOE, and if only one vowel shows, then BUILT to flush out the rest. If I get 2 or 3 vowels at first, then I try to flush out S H R L on my second choice. I like that my first word catches trickier words ending in E. So my question to you is: How sub-optimal are my choices compared with your besties? Thanks again for your great writings?
Hi Bob! As a scientist, you know that a simple question can have a complex answer. However, as a scientist you also can tolerate complexity!
CANOE as a first guess yields 0.425 probable green boxes. It’s #136 of 1566 answer words without repeated letters, so it’s in the top 9% of that list. It yields a probable 1.079 yellow boxes, so on that list it’s #325, within the top 21%. If you add these numbers together as a measure, CANOE is in the top 14%.
The combination CANOE, BUILT has a 97.45% chance of giving you at least one colored box. But its value to you is higher than that, because you choose your second word based on the yield of the first guess. Which is a smart strategy.
If you like having three vowels in your first guess, RAISE yields you 0.445 green boxes and 1.22 yellow boxes. If you prefer to include AEO, AROSE gives the most green boxes, 0.438, plus 1.26 yellow boxes. But CANOE is almost as good, we’re talking very small differences here.
It’s ironic, because I was dissing words containing U, but the 3-vowel guess word that yields the very most green boxes is SAUCE with 0.482. It’s higher than SAUTE with 0.479, which seems surprising. That happens because in the fourth position of the word, C is more common than T, even though T is overall a more frequent letter. However, these only yield 0.9 and 1.0 yellow boxes.
So I say, you’ve got great words already, but you could also try a few more. – Art
Wow. I knew my query would make you rise to the challenge! Thanks; I’ll be trying your suggestions.
Art, the amount of information in your article is staggering. Did you write it all? Are you locked in a room with your computer all day?
I have not done a deep dive for myself. I play the game each day without searching anything from outside. For me, it’s a simple test of strategy and vocabulary. As you noted, the scores for this method are not real high, but at least I have the pleasure of doing it myself.
Marvin, I applaud any approach that keeps the game “fun” rather than “work”, and yours clearly works for you. I did the analysis in bits of spare time to satisfy my curiosity, then decided to share the results for those who want to know a little bit more. Personally, I find it interesting to sample different Wordle-like games depending on my mood. – Art