The University of Toronto’s Student Newspaper Since 1880

# How to beat Wordle at its own game

Using information theory to optimize your guesses

There’s something very seductive about a game like Wordle.

When it comes down to it, Wordle is very simple. There are a limited number of recognizable five-letter words in the English language. The list of words that Wordle will accept numbers almost 13,000. Out of those, there are only about 2,300 individual five-letter words, handpicked by the creator’s girlfriend to be guessable to the average player, that Wordle might use as puzzle answers — slightly fewer, now that The New York Times has pruned down the list for obscenity and Canadian spelling.

If you’re anything like me — that is to say, insufferable — you probably had a hard time playing through a full game of Wordle without starting to wonder how, theoretically, you could solve Wordle in such a way that you wouldn’t ever have to play through it again.

It seems like it should be easy, right? You get six guesses to find the final word, and every time you guess, it feels like you cut down the possibilities significantly. After all, Wordle has three different responses for each letter of your guess. If your guess starts with an ‘a,’ it might tell you that you’re right, and the word starts with an ‘a’; that you’re wrong, and the word doesn’t have an ‘a’; or that you’re kind of sort of on the right track, and there is an ‘a’ in the word, but it’s located somewhere completely different.

So every time you make a guess, Wordle could theoretically give 35 possible answers. Those responses are not all equally likely — if they were, you’d regularly be solving the Wordle in two guesses — but that should still give you enough information to narrow the possible solutions down pretty far with the right guess.

So how do you find the right guess?

One of the most common strategies that you’ll see people talking about online involves choosing an initial word that’s high in vowels. It’s intuitive — a five-letter word is going to have to have a vowel somewhere, and knowing which vowels you’re looking for gives you a concrete path to start down. Throw in a couple of common English consonants, and you’ve got what feels like a very sensible Wordle guess strategy!

And maybe that’s enough for you, if you’re a reasonable person who wants to continue playing Wordle and actually having fun doing so. But if you’re willing to dive a little deeper into the workings of Wordle, there’s definitely more to explore.

To start with, we need to define what it would mean to optimize a Wordle guess. Ideally, you want something that gives you a lot of information about the final word. More precisely, you want Wordle to give you a response that will narrow your possible guesses significantly. That’s probably one reason people use common consonants — you’re more likely to get a hit, and if you don’t, that eliminates a lot of possible final words.

Popular math YouTuber 3Blue1Brown uses the terminology of information theory to explain the idea of optimization more precisely. Every time you cut your field of possibilities in half, you eliminate one ‘bit’ of uncertainty. Based on the number of possible Wordle solutions, when you start the game, you’ve got approximately 11.17 bits of uncertainty. You want to get that number down to zero.

If you’re trying to optimize the amount of uncertainty you’re eliminating, they explain, the best way to do so is to choose an initial guess that gives you the highest average number of bits of information, no matter what Wordle’s response is.

That means that ‘zygon’ is probably not a great first guess. If you’re right about one of the letters, that’ll teach you a lot, but if you’re wrong about all of them, you won’t have much to work off of.

Many of their suggestions — words like ‘soare,’ ‘slate,’ and ‘reais’ — do actually contain a lot of common letters. According to Laura Tilton, an educator who’s mapped the frequency of Wordle letters on Twitter, ‘e,’ ‘r,’ ‘a,’ ‘o,’ ‘t,’ and ‘l’ are the six most common letters among valid Wordle solutions.

But positioning is important, too. Eight out of 3Blue1Brown’s initial top 10 words end in an ‘e,’ and seven contain ‘a’ as their third letter.

Many of those initial suggestions hold up under further refinement as well. Jonathan Olsen, a researcher at the University of Colorado, has complained that many Wordle solution lists suggest suboptimal strategies because they focus too heavily on the information from the first guess. But many of his suggested starting words, like ‘reast,’ ‘salet,’ and ‘trace,’ also appear on 3Blue1Brown’s top 10.

On his website, Olsen has created a tool where you can try out multistep Wordle strategies that he’s found by building decision trees — models of how a Wordle game could look after every decision the player makes.

Even the top strategies aren’t going to always net you a good game — a lot depends on luck. Some of 3Blue1Brown’s best opening words, which maximized information according to projections of all possible game scenarios two guesses in, only won the game in about 3.4 guesses, on average. They theorized that it doesn’t seem possible to create a strategy that wins you the game in three guesses or fewer on average.

This set of strategies also isn’t exhaustive — there are other factors to consider. If you play on hard mode, where you have to reuse your previous correct guesses, your strategy will have to change slightly. If you really want to make all of your friends absolutely furious, you can make sure you’ll get it in one try every time — the original list of future Wordle solutions in chronological order was accessible from the website’s source code, and you can find people who have compiled records online of all the daily solutions for the foreseeable future.

If you want to set yourself higher challenges, you could use a less-than-ideal first word, just to make it a little more difficult. According to Alex Selby, a mathematician from Cambridge, UK, you’ll usually get very little information from ‘jazzy.’ You could play Absurdle, which works in much the same way as Wordle, but actively tries to sabotage you at every step.

On my part, I haven’t played Wordle regularly for a while. It’s fun, but it feels simple and gameable enough that I can’t concentrate on trying to solve one game without trying to solve them all.

These days, I’m a lot more interested in Semantle, where you have unlimited guesses to guess a word based on similarity scores from word2vec — a technology from the field of computational linguistics that tries to represent the semantic meaning of a word based on the contexts in which it usually appears. It relies a lot more on how news stories of the recent past have been written, so it feels like it requires a lot more guesswork. And if I really feel like leaning into the guesswork side of things, there’s always Letterle.

But you don’t have to stop playing Wordle for the sake of playing Wordle. You could forget all of this and choose some other strategy entirely. Learning about information theory is fun in its own right, but it doesn’t have to affect your actual day-to-day gameplay.

Sometimes, there are more important reasons to play a game than to win it, and many people feel sentimental about their original guesses. The top commenter on 3Blue1Brown’s original video may have hit on something very fundamentally human when they wrote, “Interesting video, real good stuff. Gonna keep using PENIS but this was really cool and informative!”