Often the authors of these plays theorize that the word should be one that uses as many vowels as possible, contains letters that occur frequently in English, or has features that occur regularly in the language.
Well, my finance students and I decided to tackle this question in the most definitive way possible by determining the optimal first word to play in Wordle.
Our analysis actually ran through all possible combinations of five-letter words and ran simulations on all possible iterations – over a million of them – to determine the best starting strategy.
A “tried” and true approach
In Wordle, players have six attempts to guess a five-letter word. Each time the player makes a guess, they learn if each letter is correct and in the right place, appears in the word in another place, or is not in the word at all.
Players may have different approaches. Some might just want to solve the word, even if it takes six tries. Others try to do it with as few guesses as possible.
From our analysis, if you’re trying to win with as few guesses as possible, the top three words to use are “slice”, “tried” and “grue”. Using any of these three words will produce an average number of word attempts of 3.90, 3.92, and 3.92, respectively, if you’re using an optimal strategy to play (more on that later).
If, on the other hand, you’re just trying to win within the allotted six guesses, the first three words to play are “follower”, “clamp”, and “plaid”. Using any of these three words will give an average success rate to win the game of 98.79%, 98.75%, and 98.75%, respectively, if you play the optimal strategy.
And therein lies the first interesting distinction between playing to win and playing to win with as few guesses as possible.
If you’re playing to win in all six assigned guesses, it seems best to play a word that only has one vowel and four consonants, because six of the first 10 words only have one vowel. But if you’re playing to win with as few guesses as possible, it’s best to play a word that has two vowels and three consonants: All top 10 have two vowels.
Inside the simulations
Other researchers, such as David Sidhu of University College London, have tried to determine the “best first word” from a linguistic point of view. In these efforts, the best selection is decided by the frequency with which certain letters appear in the English language, or the frequency of the location of these letters in five-letter words.
While these approaches are noble, our analysis goes beyond that by performing simulations on all possible word options to find the best type of word to play first.
To perform this analysis, two of my students, Tao Wei and Kanwal Ahmad, built a program that reviewed the 2,315 official five-letter words from the Wordle dictionary. The program attempted every possible word as a first guess and ran simulations on all possible final word solutions, checking how long each attempt would take to guess the correct final word – 1,692,265 simulations in total.
We then averaged all attempts for each word to see how many guesses we could expect to make to arrive at the final correct word.
To perform this massive simulation, a method is needed to choose the optimal word on the second guess, the third guess and so on.
To give you the best odds on each ensuing guess, it is important to select the letters most likely to appear in each position. So the program used the list of 2,315 words in total to determine how often each letter appears.
After receiving the results of the previous guess, the program filtered the possible words to those that meet the criteria. Suppose the first guess was “dude”, and L and E were in the correct position, while B, O and K did not appear in the solution. The program would then narrow down the list of possible words to those like “channel” and “slate”.
The program then assigns a score to each word in this list, where the score is the sum of the frequency of its letters. The word “slate”, for example, has a score of 37% because the letter “S” appears 5% of the time in the complete list, while the letter “A” appears 8% of the time, and so on. The word with the highest score is then submitted as the next guess.
Running this simulation on all the first possible hypotheses and on all the possible solutions yielded the results.
But maybe you don’t want to start with the same word every time you play. In this case – and if you want to win with the fewest guesses – try to make sure your first guess has two vowels, with one of them at the end of the word.
If you’re just looking to win in the allotted six guesses, you might want to consider a word with fewer vowels – and definitely a word that ends in a consonant.
Hopefully our mathematical approach to Wordle hasn’t sucked all the joy out of the game. At the very least, it will give you a head start should you decide to bet friendly on tomorrow’s game.
This article is republished from The Conversation under a Creative Commons license.