Mathematic

How to Win At Wordle Using Math

You have probably heard of Wordle, the popular new game in which you have six chances to guess a word. The goal of the game is for you to guess what the word might be. After that, you will tell whether the letters you have chosen are in the word and if they are in the appropriate place. Green letters are in the right place, whereas yellow characters are in the right place but in the wrong spot. The letters turn gray if they are incorrect.

The game’s core rules are similar to those of the board game Mastermind, in which you must guess the colors of pins chosen by an opponent. Similarly, the ideal strategy for beating the game is to maximize the amount of knowledge you gain with each turn. In Mastermind, for example, it is ideal to use colors you did not use on your first turn on your second turn to figure out which colors are in play.

Unlike Mastermind, there are 26 possible letters in each slot in Wordle (thanks to the alphabet for the added difficulty), but the premise stays the same: if you want to win, you should try to learn as much knowledge as possible in each turn. It is possible to figure out which letters are more likely to appear because there are a limited number of five-letter words that can be used (they are not arranged in any particular order). You can increase your chances of gaining information for your next guess by using letters that are more likely to appear.

The word list that Wordle uses has not been revealed (perhaps to prevent people from cheating by using math). People have not stopped trying to figure out the best opening moves, though. For their analysis, Redditor adeadhead looked at the occurrences of letters in the Stanford Graphbase five-letter words list and calculated how many times each letter appears in all possible five-letter words, resulting in the following:

S : 3033, E : 3009, A : 2348, O : 1915, R : 1910, I : 1592, L : 1586, T : 1585, N : 1285, D : 1181, U : 1089, C : 964, P : 955, Y : 886, M : 843, H : 814, B : 715, G : 679, K : 596, F : 561, W : 505, V : 318, X : 139, Z : 135, J : 89, Q : 53

As you can see, starting your game with the letters J or Q would be a bit of a wild maverick. They went on to construct a list of the best terms to use as an opener because the letters are more likely to include more information due to their frequency. Other Wordle users have done their own analysis with different dictionaries and discovered considerable overlaps.

The ideal words to employ, according to one on GitHub, are arose, soare, aeros, serai, reais, raise, arise, aesir, aloes, and seral. “Fuffy” and “xylyl” are the worst. On your second attempt, instead of guessing at the word directly (unless you think you have cracked it), try to maximize the information gathered. Try to use letters you haven’t seen before; you’ll gain a lot more information that way than if you use letters you’ve seen before. Also, try to select letters that are more likely to appear, with vowels being especially useful.