Advanced Entropy Optimization: Squeezing Every Bit From a Guess
Entropy is the single most powerful idea in competitive Wordle, yet most players use it only as a vague slogan — 'pick the word that tells you the most.' This article turns that slogan into a working method you can apply without a calculator, covering how to estimate the information content of a guess at the board, how to balance expected gain against the chance of a direct hit, and how the best solvers shift their entropy strategy as a game progresses.
What entropy actually measures
Entropy measures uncertainty. When 200 candidate answers remain and each is roughly equally likely, your uncertainty is high. A guess is valuable to the precise extent that its result is expected to collapse that uncertainty — to split the candidate field into many small, distinct groups rather than leaving one large lump intact.
The crucial mental model is the partition. Every guess sorts the remaining candidates into buckets keyed by the color pattern they would produce. A guess that creates many evenly sized buckets is high-entropy: whatever pattern you see, you land in a small bucket. A guess that dumps most candidates into one giant bucket is low-entropy, because the most likely result barely narrows your field.
Estimating information at the board
You will never compute logarithms mid-game, and you do not need to. Use three proxies. First, distinct common letters: a guess testing five untested high-frequency letters almost always partitions well. Second, positional novelty: testing a letter in a position you have not yet probed reveals more than re-testing a known slot. Third, bucket evenness: glance at your candidate list and ask whether the guess would obviously cleave it roughly in half or leave it nearly whole.
With practice these proxies converge on the same ranking a solver would compute exactly. The skill is not arithmetic; it is learning to see the candidate field as a set that a guess slices.
When to stop maximizing entropy
Pure entropy maximization is correct only while the cost of not guessing the answer is low. Early in a puzzle, with four or five guesses in hand, the optimal play is almost always the highest-information word even if it cannot itself be the answer. But as guesses run out, the calculus flips: a guess that is slightly lower-entropy but could actually be the answer becomes preferable, because winning this turn is worth more than perfect information you may never use.
Expert play is therefore a glide path. You start as an information maximizer and gradually become a probability maximizer, with the crossover usually arriving around guess four when a handful of plausible answers remain.
Two-move entropy planning
The strongest solvers think two guesses ahead. Rather than choosing the single best word now, they choose the word that leaves the best expected position after the next result. This matters when two candidate openers have similar immediate entropy but very different follow-up structure — one strands you with awkward greens, the other leaves a clean field.
You can approximate this without computation by favoring guesses whose letters recombine well. A word whose tested letters can reshuffle into many common follow-ups keeps your second move flexible, which is the practical meaning of 'good expected position.'
Key takeaways
- Think of every guess as a partition of the candidate field into buckets.
- Estimate information with distinct common letters, positional novelty, and bucket evenness.
- Shift from maximizing information to maximizing answer probability as guesses run out.