The Information Theory Behind Wordle

Wordle is a five-letter guessing game and, more interestingly, a Shannon-style information puzzle. Every guess gives you back a colored pattern — green, yellow, gray — that carries a specific number of bits of information. The information theory of Wordle is the mathematics of choosing guesses that maximize the expected information bits returned. The 3Blue1Brown video on this topic ran the math publicly in 2022 and produced the canonical optimal opener.

Shannon entropy in 90 seconds

Claude Shannon defined information entropy in 1948 as the expected number of bits needed to encode a message drawn from a probability distribution. A coin flip with two equally likely outcomes is 1 bit. A six-sided die is log2(6) ≈ 2.58 bits. A perfectly predictable event is 0 bits.

In Wordle, “the message” is which target word the game has chosen. At the start, there are 2,309 possible solutions in the original NYT solver list (the curated answer list). The starting entropy is log2(2309) ≈ 11.17 bits. Each guess returns a feedback pattern that narrows the candidates — and reduces the remaining entropy. The optimal guess is the one that reduces entropy the most on average.

How a Wordle guess carries information

A Wordle guess produces a 5-character pattern from the alphabet {green, yellow, gray}. That’s 3^5 = 243 possible patterns. Each pattern partitions the remaining candidate words into a subset that would produce that pattern given the guess and the target.

If a guess perfectly bisects the candidate pool — half the words produce pattern A and half produce pattern B — that guess returns 1 bit of information. If a guess always returns the same pattern regardless of target (because it’s a guaranteed-gray word like XYLOP), it returns 0 bits.

The expected information from a guess is the sum over all 243 patterns of (probability of pattern) × (information gained from pattern). The optimal first guess maximizes this expected value.

3Blue1Brown’s analysis

Grant Sanderson’s 3Blue1Brown channel posted “Solving Wordle using information theory” in February 2022. The video walks through the entropy calculation in detail, computes the expected information for every legal first guess, and identifies SOARE as the top opener on the original Wordle solver list.

The follow-up video revised the analysis to incorporate the answer-list curation (not all 2,309 words are equally likely; the NYT only uses common solutions). The revised top opener is SALET on the answer-only list, with the optimal solver averaging 3.42 guesses per game.

The candidate list distinction

Wordle has two word lists. The “allowed guess” list has roughly 12,000 valid five-letter words you can type. The “answer” list has roughly 2,300 curated common words that can actually be the day’s solution. The NYT has revised both lists since launch, but the structure is unchanged.

The information theory calculation depends on which list you assume. Against the full 12K guess list, the optimal opener is one set of words; against the curated answer list, the top opener shifts. Most solvers use the answer list for the entropy denominator since the target is always from that list.

The top-bit openers

The highest-information openers from public solver analyses (slightly different results depending on lists and assumptions):

• SALET: ~5.88 bits expected against the NYT answer list. The canonical optimal opener from 3Blue1Brown’s revised analysis.
• REAST / TRACE / CRATE: ~5.85 bits. Common choices among top solvers.
• SLATE / CRANE: ~5.82 bits. CRANE is the human favorite in this band.
• SOARE: top of the original full-list analysis.

The popular human openers — ADIEU (4 vowels), AUDIO (5 vowels), STARE — return 4.0 to 5.5 bits, not bad but measurably below the optimum.

Information-greedy vs. depth-search solvers

The simplest Wordle solver picks the highest-information guess at every step. This is the “greedy” approach and averages around 3.6 guesses per game.

The optimal solver does multi-step depth search — it doesn’t just pick the highest immediate-information guess, it picks the guess whose follow-up search tree minimizes the average total guesses. This pushes the average down to 3.42 guesses (the proven optimal for the NYT answer list, computed by Alex Selby and others).

The difference between greedy and optimal is one of the great minor results of recreational mathematics. The optimal solver occasionally sacrifices immediate information for a better positional setup — the same kind of long-game thinking that distinguishes good chess engines from greedy ones.

Hard mode and information

Wordle’s hard mode requires every subsequent guess to use all confirmed greens and yellows. This restricts the candidate guesses dramatically — many high-information probe words become illegal because they don’t use the constraint.

Hard mode raises the optimal solver’s average from 3.42 to roughly 3.51 guesses. The cost is small because most useful probes are also constraint-respecting. For details on configuring hard mode, see our guide to the Wordle algorithm.

The connection to probability and expected value

Information theory in Wordle is conceptually related to the expected value calculations in our mathematics of poker piece. Both use the same idea: a decision is good if its expected outcome under uncertainty is positive. The unit changes — money in poker, bits in Wordle — but the framework is identical. Shannon’s entropy is poker’s variance for puzzle games.

Why ADIEU isn’t optimal

The intuition behind ADIEU is “lots of vowels, lots of information.” But vowel density isn’t the same as information density. A word with five different vowels can still leave you in a 600-word candidate pool because the consonants of the answer aren’t yet probed. SALET (with one vowel and four common consonants) reduces the candidate pool faster on average because the consonant frequencies do more partitioning work.

The math is counterintuitive only because human intuition reads “more vowels = more information about vowels.” The actual question is “more partition power across all possible patterns,” and consonant-heavy openers do that better.

What does an optimal Wordle game look like?

An optimal solver opening with SALET typically reveals 1-3 greens or yellows in the first guess. The second guess narrows to under 20 candidates. The third guess often solves. The fourth guess is for the cases where the answer has unusual letter patterns. Beyond four guesses is rare on the answer list with optimal play.

A human player with knowledge of the math can get to 3.6 guesses average. Pure intuition averages closer to 4.0. The gap is real but small, which is part of why Wordle has stayed engaging — even non-mathematicians get within striking distance of optimal play.

Frequently asked questions

What’s the best Wordle opener according to information theory?

SALET against the NYT answer list (3Blue1Brown’s revised analysis). SOARE is the optimal pick against the full guess list. Top human-friendly alternatives include CRANE and SLATE, all returning roughly 5.8 bits of expected information.

How many guesses should an optimal Wordle solver average?

3.42 guesses per game against the curated NYT answer list. This is the proven optimum computed with full depth-search. Greedy solvers (picking the highest-info guess each turn) average about 3.6.

Why isn’t ADIEU the best opener?

ADIEU has four vowels but does less consonant partitioning. Information theory cares about how evenly a guess splits the remaining candidate pool, not how many vowels it contains. Consonant-rich openers like SALET split better on average.

What is entropy in Wordle terms?

Entropy is the average number of bits of information left to discover before you’ve solved the puzzle. Starting entropy is log2(2309) ≈ 11.17 bits. Each guess returns a feedback pattern that reduces remaining entropy. Solving the puzzle means reducing remaining entropy to 0.

Does the information theory approach work in hard mode?

Yes, with adjustments. Hard mode forbids guesses that don’t use confirmed greens and yellows, which removes some high-info probes from your allowed set. The optimal solver’s average rises from 3.42 to roughly 3.51 in hard mode — a small cost.

The bottom line

The information theory of Wordle is Shannon entropy applied to a five-letter puzzle. SALET is the canonical optimal opener; 3.42 guesses is the proven optimum; consonant density beats vowel density for partition power. Most human players hit 3.8-4.2 guesses on average and don’t need the math to enjoy the game. For a one-button alternative with no entropy to calculate, the Chrome Dino game at the top of this page swaps letters for cacti.