The Mathematics Behind Wordle
Wordle is fundamentally an information problem. Each guess either confirms or eliminates letters and positions. The player who extracts maximum information from each guess wins in the fewest tries. Understanding this transforms Wordle from a vocabulary quiz into a logic puzzle.
The English-language Wordle draws from a pool of roughly 2,300 common five-letter words. Your job is to narrow that pool to one word using a maximum of six guesses — but the real benchmark is three.
Information theory gives us a framework: a "perfect" first guess should eliminate the most possible words regardless of the answer. This means choosing letters that appear frequently across the Wordle word list.
The Best Opening Words
Letter frequency analysis of the Wordle answer list shows that E, A, R, O, T, L, I, S, N, and C appear most often. An ideal opening word uses five distinct, high-frequency letters.
CRANE — C, R, A, N, E covers five of the top ten letters. In testing across the full Wordle answer list, CRANE solves the puzzle in an average of 3.45 guesses — above average for an opener.
SLATE — S, L, A, T, E. The S is particularly valuable because many Wordle answers end in S (though the original NYT list excluded plurals, more recent versions include them). Average solve: 3.37 guesses.
RAISE — R, A, I, S, E. Hits four vowels indirectly (A, I, E plus the implied O coverage in guess 2). Solve average: 3.32 guesses.
STARE — S, T, A, R, E. Widely regarded as one of the top three openers mathematically. Average: 3.31 guesses.
CRANE, SLATE, and STARE form the holy trinity of Wordle openers according to most computational analyses.
Interpreting Yellow vs Green Clues
This is where most players lose time. A green tile means correct letter, correct position. A yellow tile means correct letter, wrong position. A gray tile means the letter doesn't appear in the answer (or you've already accounted for all instances of it).
Green tiles: Lock this position. Every subsequent guess must have this letter here.
Yellow tiles: The letter is in the word, just not there. Move it. But don't just move it randomly — think about which positions it can't be. If A is yellow in position 2, it can't be in position 2. But it could be in 1, 3, 4, or 5.
Multiple instances: If you play two E's and one turns green and one turns gray, the word has exactly one E. If both turn yellow or green, the word has two or more E's.
The Decision Tree for Guess 2
Your second guess should do two things simultaneously: it should test the information you received, and it should introduce new letters not yet probed.
If your opener gave you two greens, your second guess can afford to focus those locked positions while testing four entirely new letters in the remaining slots.
If your opener gave you three yellows, your second guess should avoid all five positions where those letters appeared (they're confirmed in the word, just misplaced) while still probing new high-frequency letters.
The "never repeat" rule for guess 2: Unless you're extremely confident about the answer, never include letters already confirmed gray. Every gray letter you replay is wasted information capacity.
A useful second-word pairing with CRANE is LOUSY (L, O, U, S, Y — all new letters that cover remaining high-frequency slots). This two-word combo together covers 10 of the most common Wordle letters.
Guess 3: Close the Loop
By guess 3, you should have 3-5 confirmed letters and a clear sense of the word's structure. Now you're solving, not probing. The goal is to apply all constraints and produce a word that fits.
Work through it systematically:
If two candidates remain (say, SHORE and STORE), your guess 3 should distinguish them — play STORE if you need to. But if you're feeling confident and SHORE matches all constraints, take the shot.
Common Letter Frequency Data
The ten most common letters in Wordle answers, in order: E, A, R, O, T, L, I, S, N, C. The least common: Q, Z, X, J, V.
The most common starting letters in Wordle answers: S, C, B, T, P, A, F. The most common ending letters: E, Y, T, R, L, H, N.
This means words ending in -LY, -ER, -ED, -EN, and -NT are excellent coverage targets for your second guess.
Mistakes Most Players Make
Using the same opener every day: Adaptive openers based on what you learned yesterday are strictly worse than a fixed optimal opener. Stick with STARE or CRANE every day.
Playing words they "feel" are right: Gut instinct narrows your options unnecessarily. Trust the constraints.
Forgetting yellow letter positions: Yellow means "somewhere else." Players often re-test the same position. Track it.
Playing plurals and past tenses without evidence: -ED and -S endings are common but not certain. Don't assume.
Use our Wordle Solver to see all valid candidates after each guess — it makes the logic transparent and helps you learn the decision-making process.