The Best Analysis of the Best First Guess in Wordle

February 11, 2022

I take on the entire Internet. Some words are meaningless. You learn a lesson that will serve you well far beyond Wordle. I get to use the word "heuristic" in a sentence.

#math

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There has been much ado across the Internet lately about the best first guess for Wordle. I can’t review all the proposed words, but a few include roate, arose, soare, later, and adieu.

Unfortunately, none of them are the best initial guess.

Instead, I would like to propose that the best initial guess for Wordle is, unequivocally, …

… complicated.

Wait, don’t leave, I’ll explain. The whole question hinges on a critically important word but not a five-letter word. It’s the word “best”—a word that is straight-up dangerous at worst and absurdly ambiguous and unhelpful at bes—wait, uh, nevermind.

For Wordle, “best” could mean any number of things. The best starting word could be:

  • The word that sets you up to solve the puzzle in the fewest number of guesses, on average,
  • The word that gives you the best chance at solving the puzzle within six guesses (“winning the game”),
  • The word that sets you up to minimize the worst-case number of guesses, or
  • The word that sets you up to solve the puzzle as fast as possible (but risks not solving it at all)

This is not an exhaustive list, either. The point is that it doesn’t make sense to claim that a word is the “best” without carefully defining the problem you are solving. With a clear definition, you will be able to tell whether a particular solution is truly the best you can do. To make matters even worse, even if you can define the problem, that doesn’t mean you can practically find the solution. If that’s the case, you have to make simplying assumptions so the problem becomes “tractable.”

Of course, the usefulness of your solution depends on how realistic your assumptions are. For example, in the case of Wordle, a reasonable assumption might be that solving the puzzle is nearly equivalent to finding the five letters in the word (regardless of order) since there aren’t many anagrams of the same five letters. Once you know the letters, you can quickly figure out the solution. This rule of thumb that simplifies the problem is known as a heuristic.

To be fair, most of the in-depth articles about Wordle starting guesses do recognize that there isn’t just one way to approach the question, and it’s possible that a word could be “best” for multiple objectives. Personally, I like starting with arose or soare and the following it up with unity. Those words cover the vowels + y and some more common consonants.

Obviously, the lesson here isn’t limited to Wordle. We encounter claims of “best” all the time, whether in advertising or decision making. Properly evaluating these claims requires that we ask the question, “Best for what?” or “Best in what sense?” Discerning the answer is critical for understanding the significance of the claims and the action steps that should follow.

Like what word you should guess first in a viral online word game.

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Written by Matthew Russell who follows Jesus, studies machine learning at the University of Kentucky, and interns at NASA. Get to know him or check out his projects on GitHub.