Wordle is all about the best starting word. We did the math on what wins.
How to boost your odds at Wordle: Experts in linguistics and computer science break it down.
The blank squares beckon.
There’s the easy temptation of the letter E. The solid punch of a well-placed L or T. Or the gambler’s delight of a J, X, or Z. Rare, but if there? Oh, so sweet.
We speak, of course, of Wordle, the online word-guessing game that has hooked millions in search of a new pandemic distraction.
Fans expressed concern this week when the New York Times purchased the game from its developer, who had been offering the daily challenge since late October at no charge. The media outlet says that for now, Wordle will continue to be free.
And the simple appeal of the game remains the same: easy to play, once a day, in a minute or two.
But that simplicity also is a source of peril: A player gets just six chances to guess a five-letter word. Any failures are recorded in the person’s cumulative statistics.
Time to up your game with some hard science. As a public service to the herd of word nerds, we consulted experts in linguistics and computer science about how to crack the code. We also crunched the numbers to fulfill that goal of Wordlers everywhere: finding the best starting word.
And along the way, we tuck in a bit of relevant Philadelphia history on a word-puzzler of long ago, better known today for his literary efforts: Edgar Allan Poe.
The basics of Wordle
The brains behind Wordle is Josh Wardle, a software engineer in Brooklyn. The name of the game plays on his last name.
Wardle created the game just for fun — at first sharing it just with his partner, then with family members, he told the Times. But when he released it to the public in late October, it took off. By early January, more than 300,000 people were playing, and the number is now well into the millions.
As many have noticed, it’s similar to the classic game Word Mastermind, which also comes in nonword versions that involve guessing sequences of colors or numbers.
In Wordle, every time the player guesses a word, the five squares change color to reflect the accuracy of the guess. A square turns gray if that particular letter is not contained in the answer word. Yellow means the letter is correct but in the wrong position. Green means it’s both correct and — ding ding! — in the right position.
Frequency and order
To boost the odds of guessing each day’s word, it makes sense to choose words with letters that occur frequently in the English language. No surprise there. (More later on the best words by this measure, and how we picked them.)
Also important is to keep in mind which letters typically combine with each other, and in what order — a set of rules that linguists refer to as phonotactic constraints. Even if they’ve never heard that term, skilled players grasp this concept intuitively, said Christiane Fellbaum, a Princeton University professor of linguistics and computer science.
For example, plenty of five-letter English words contain the sequence CK, usually at the end — as in CRACK or FLICK — but never at the beginning. Other rules govern how an S can be followed by a combination of “voiceless stops” and “liquid” sounds, as in the sequence STR-.
“There’s a kind of convergence among different factors,” Fellbaum said.
And because English is drawn from so many wellsprings, the language poses special challenges for the puzzle-solver, said Charles Yang, a University of Pennsylvania professor of linguistics and computer and information science. Germanic tongues and Latin are primary sources, but English also includes words from Arabic, Hebrew, and Native American languages, among others.
For example, Wardle’s list of allowable guesses includes QAJAQ: a more-authentic spelling of the Inuit word KAYAK.
“You really have a mixed bag of the different languages with different phonotactics,” Yang said. “Different letter combinations are more likely in some languages than others.”
The Poe and Philly connection
Secret codes and puzzles have been around almost as long as written language, though the emergence of a popular, Wordle-like phenomenon is relatively recent. In the United States, the epicenter for one of the first such crazes was Philadelphia in the 1840s, said Shawn Rosenheim, an English professor at Williams College.
The instigator was Edgar Allan Poe. In the July 1841 issue of a Philadelphia publication called Graham’s Magazine — a few years before his famous poem The Raven — he wrote “A Few Words on Secret Writing,” exploring how the frequency of letters could be used to decipher codes.
“It added to his reputation as this kind of analytic genius, which he was of course happy to reinforce whenever possible,” said Rosenheim, a Poe specialist.
In another Philly publication called Alexander’s Weekly Messenger, Poe invited readers to submit their own word ciphers, boasting he could solve them all. And code-cracking was a central element of his 1843 short story “The Gold-Bug.”
Rosenheim thinks Poe would’ve made short work of Wordle, and he would’ve instantly grasped its viral appeal.
How to pick the best starting word
Doing well at Wordle is all about picking the best starting word. It’s not as straightforward as taking the five most common letters in English — E, A, R, I, O — and making a word from them. (For one thing, there is no such word that we could find. And also, the letter frequencies are slightly different in the subset of words with just five letters.)
Among those to tackle this problem with analytics is the Cambridge-educated mathematician Alex Selby. He devised an algorithm to find the starting word that should, on average, require the fewest total guesses, assuming the player makes logical choices based on letter frequency and position.
His answer? SALET, a type of medieval helmet. With that as a starting word, Selby calculated that the player should arrive at the answer with a total of 3.4 guesses, on average.
Yang, the Penn linguist, took a stab at the problem, too, but limited himself to more common words. He started with E as a common last letter, then added A, the second-most frequent vowel, which often pops up in the middle of five-letter words when E is at the end.
He then looked at the consonant clusters that are used most often at the beginning of words, and arrived at TRACE. Somewhat surprising, as C is a relatively uncommon letter, but that word happened to rank high on Selby’s list, too.
The brute-force approach
We didn’t get that fancy. Instead, we crunched the numbers based purely on letter frequency. And here, there is good news.
To make it easier on players, Wardle limited his universe of answers to a set of 2,315 words, leaving out ones that he judged too unusual. Plurals ending in -S also are excluded.
But to give players flexibility, Wardle allows them to guess from among nearly 13,000 words.
We wrote a computer program to rank them all, by how many letters, on average, they would match in each of the 2,315 possible answer words.
Our 10 best starting words for Wordle
...and our 10 worst
By our brute-force method, the best starting word is ROATE.
No, we didn’t know what that meant, either. It is not found in some dictionaries, but it seems to be an alternate spelling of ROTE, as in learning by repetition. It matches 1.789 letters, on average, in all the answer words.
You’d get the same result by starting with the more common ORATE, as that contains the same letters. But ROATE might have the advantage, as R is a more common starting letter than O.
Others will have their own pet starting words. It’s fun to go with your gut, after all.
A common strategy is to use words with as many of the five vowels as possible (or six, if you count Y), as all five-letter words have at least one of them.
Yang admits he has played, though pronounces himself “terrible.” Fellbaum, the Princeton linguist, says the game also has a practical benefit.
“I play Wordle to wake up in the morning,” she said.
Happy hunting for the green squares.