3Blue1Brown: The mathematically optimal Wordle strategy

(I recommend his videos to my students, who love them!)

I don't know anyone who has actually read the Wordle JavaScript, but there are two word lists. The first list consists of more familiar words, ordered by date to provide secret words for each day. The second list consists of other words in alphabetical order that are also accepted as guesses. One reverse-engineers this code by figuring this out; one can experiment by resetting the computer clock to a new day.

The standard assumption in any analysis of Wordle as actually played is that we don't know what day it is. Otherwise, the game is deterministic.

Various of us have written code that agrees that SOARE is the best first guess using Shannon entropy for how Wordle is actually played (RAISE is close and easier to remember), and TARES is the best first guess for the most common misunderstanding for how Wordle is played. I don't recognize his first guess, so I don't recognize what he's doing.

There isn't actually any proof that Shannon entropy is mathematically optimal here. I searched the literature for a relevant theorem after getting annoyed that so many online approaches were improvised. The trouble is that five letter words have a fixed, known, lumpy distribution, an artifact of human choice. If the game randomized both the secret word and the word lists themselves, and one could query an oracle to measure bin sizes for each candidate guess, ... but that's cooking the conclusion. If one took a limit as word length went to infinity, with a regular definition of what constitutes a word, there would likely be an optimality proof. On the other hand, after choosing an objective function one could entirely solve this finite game, as some have done, and entropy doesn't even come up.

A refined variant on entropy that would be computationally feasible in cases where one can't solve completely would be to look ahead several steps. For each possible response to each first guess word (in practice one need only consider the strongest, and a partial search is nearly optimal as my Dad noticed programming JOTTO on Kodak's computers in the 1960s), find the optimal next guess using Shannon entropy. Now measure the entropy of the bins after both guesses, to value the first guess.

In particular, max entropy heuristic + beam search will derive the optimal (now proven) strategy in terms of minimizing expected number of guesses

This site ranks CRANE 6th, & 8th in hard mode. Includes other parameters like PALET being optimal start if only 5 guesses were allowed