Wordle’s Best Starting Word Has Been Calculated With Math

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YouTuber 3Blue1Brown has used math and programming to conclude the ideal starting letter for the best chance of solving the daily Wordle.

A YouTuber has solved the riddle of the best first word to use in Wordle using math. Wordle is a widely popular word game that has recently seen a meteoric rise in prominence. Wordle’s popularity has spawned copycats including Moxle, a Magic: The Gathering themed rendition of the game.

Wordle’s ability to let players casually compete with their friends without being a head-on contest by tracking players’ scores and letting them share easily on social media where they can compare with others is part of the game’s popularity. The best way to get an edge in this friendly competition is to have a reliable starting word that gives you as much information as possible about what the word you are trying to find might be. Players have all kinds of different approaches, but one Wordle player has taken it into their own hands to solve the puzzle once and for all.

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A recent article by Polygon discussed a video by YouTuber Grant Sanderson, or 3Blue1Brown, in which he demonstrates the mathematically best starting word for Wordle. Sanderson found his interest piqued by the puzzle game and realized it was an excellent opportunity for an exemplification of certain aspects of information theory, in particular, entropy. To do this 3Blue1Brown built a program that would play the game for him, based on the most common letters in English words. That alone, however, does not fully answer the question as there is still the matter of letter order, which is handled differently.


There are just shy of 13,000 words that Wordle will permit players to guess, but only about 2,500 that will ever actually be correct answers. The larger list contains many words that are at best extremely uncommon and at worst debatably not words at all. But the game wants to let players guess using most things that they might think of to fit the allocated space, which is fair enough. The answer that Sanderson eventually comes up with through his program is that « crane » is generally the best word to start with, but only if followed by the correct subsequent word as well. While the next word will change based on what letters are revealed by « crane, » the next step is simple. All players have to do is follow « crane » with a word that uses letters that are commonly used in English words that are not in crane. Such letters include the other vowels, as well as consonants like H, S, and T, among others.


Because of the nature of the words players are given to work with, Sanderson ultimately comes to the conclusion that he can’t get his algorithm to reduce uncertainty below a threshold that would guarantee a correct answer before the third guess, even with optimal play. The closest his program gets, when using the shorter list of words as the program’s only possible answers, is an average of 3.43 guesses per word. Ultimately, Wordle is a game that lends itself quite well to being permutated out, but it still requires luck to get the answer quickly.


Sources: 3Blue1Brown/Youtube (via Polygon)

 

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