Information Gain in Wordle: The Core Mental Model

Guesses as questions

Imagine you have 200 possible answers left. A guess that, no matter the result, leaves you with roughly the same large group is a weak question. A guess whose different possible results each point to a small, distinct group is a strong question. The strongest guess is the one that, on average, leaves you with the smallest remaining group.

This is exactly what information theory measures with entropy: the expected reduction in uncertainty. You do not need the formula. You need the instinct that a guess testing letters you are unsure about — across many candidates — is worth more than a guess confirming something you already suspect.

Why a non-answer can be the best guess

Beginners often refuse to 'waste' a guess on a word that cannot be the answer. But if a known non-answer splits the candidate list far more evenly than any possible answer, it is the better play — especially early, when you have guesses to spare. This is the sacrifice or probe guess, and it is a hallmark of advanced solving.

The exception is late in the puzzle or in hard mode, where the cost of not guessing the answer rises. Information value must always be weighed against the guesses you have left.

Estimating gain at the table

A practical heuristic: a guess is high-information when its letters appear in many remaining candidates and are roughly 50/50 to be present. Letters that are almost certainly in or almost certainly out carry little information. So after a couple of guesses, look at your candidate list, find the letters that divide it most evenly, and build a word around them.