How Wordle Works: Optimal Guess Math

The rules, exactly

Wordle picks a 5-letter word from a curated list. You have 6 guesses. After each guess, every letter in your guess gets one of three colors:

GREEN — right letter, right position.
YELLOW — right letter, wrong position.
GRAY — letter not in the word.

Sounds simple. Then someone guesses ALLOY against the answer ALPHA, and gets confused when the second L comes back gray.

The duplicate-letter rule everyone gets wrong

Wordle's hidden constraint: colored highlights "consume" each letter in the answer. If the answer is ALPHA (one L) and you guess ALLOY (two Ls), only ONE of your Ls can be green-or-yellow. The other one must be gray — there isn't another L in the answer to match it against.

The algorithm runs in two passes:

Pass 1: greens. For every position where guess[i] === answer[i], mark green AND remove that letter from the answer-pool used for yellows.
Pass 2: yellows. For each remaining un-greened letter in the guess, check whether the answer-pool still has that letter. If yes, yellow; remove from pool. If no, gray.

This is the edge case our Daily Word game and our Wordle Solver both implement correctly. Most clones don't — they treat each letter independently, which gives wrong feedback on duplicates.

Worked example: ALLOY guessed against ALPHA

Answer:  A L P H A
Guess:   A L L O Y

Pass 1 (greens):
  Pos 0: A === A → GREEN. Pool now: _ L P H A → "LPHA"
  Pos 1: L === L → GREEN. Pool now: _ _ P H A → "PHA"
  Pos 2: L vs P → no match
  Pos 3: O vs H → no match
  Pos 4: Y vs A → no match

Pass 2 (yellows):
  Pos 2: L. Pool "PHA" has no L → GRAY.
  Pos 3: O. Pool "PHA" has no O → GRAY.
  Pos 4: Y. Pool "PHA" has no Y → GRAY.

Result:  🟩 🟩 ⬛ ⬛ ⬛

Notice the THIRD letter (L) comes back GRAY even though L is in the answer — the green L already used up the only L. That's correct Wordle behavior. If a Wordle clone shows your third L as yellow, it's buggy.

The information-theoretic optimal first guess

In late 2022, Grant Sanderson (3Blue1Brown) published an entropy-based analysis: which first guess gives you the most information on average? The answer:

SOARE • SLATE • CRANE • TRACE

These are tied at the top of the entropy table. The math: each color pattern (e.g. 🟩⬛🟨⬛⬛) is one of 3⁵ = 243 possible outcomes. A "good" first guess is one where the outcomes are spread evenly across the 243 buckets — high entropy, maximum information.

SOARE achieves the most-even split because it covers the 5 most common letters (S, O, A, R, E) in typical 5-letter English answer words. Each of those letters appears in roughly 25-50% of the answer pool, so each color outcome is approximately equally likely.

Optimal play across all 6 guesses

Computer scientists have brute-force-solved the original NYT Wordle answer pool (~2,300 words). The optimal strategy:

SALET as opener — average win in 3.421 guesses, never fails in 6. (Tracy MacSweeney, 2022.)
Best opener if you must include common letters and a Y/H/W: CLOTHE.
Best 2nd guess (no greens/yellows): CHIRP (covers letters not in SALET).
Best 2nd guess (1+ green from opener): depends entirely on the green — a lookup table from MIT Press's published 2023 solver.

With optimal play, average solve time is 3.42 guesses. Most human players average around 4.0–4.5. The gap is mostly the duplicate-letter edge case (sigh) and choosing emotionally-appealing words like ADIEU instead of mathematically-optimal SALET.

Why we still lose

Even with optimal play, ~0.4% of NYT Wordle words have ambiguous final guesses where you have to pick one of two indistinguishable candidates. Common examples: BATCH vs CATCH vs HATCH vs LATCH vs MATCH vs PATCH vs WATCH (7 candidates after _ATCH). If you've used 5 guesses to narrow down, your 6th is a 1-in-7 coin flip.

These are called "Wordle traps." The Wordle editor at NYT explicitly tries to avoid them on consecutive days, but they happen — and they're why even the best players lose 1-2 games a year.

Practical takeaways

Open with one of: SOARE, SLATE, CRANE, TRACE, SALET. They're roughly equivalent.
If you got 1+ green, your 2nd guess should test new letters, not lean on the green.
Watch for duplicate-letter situations — if your gray L is suspicious, double-check the algorithm.
Stuck on guess 5 with multiple candidates? Use our Wordle Solver to enumerate them.

Want to play with the math?

Try our Daily Word with SOARE as your opener for a week — track your average guesses-per-win. You'll see the improvement.