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Deduction

Wordle

Selby’s proven-optimal minimax solver.

1 player2 solversSolved
MinimaxHeuristicImport stateBest moveProbabilities
Your guesses
Type letters with your keyboard. Click a tile to cycle its colour: grey → yellow → green → grey. Press Enter to advance to the next row.

Tip: type to fill, click a filled tile to cycle its colour.

Suggestion
Selby's minimax solver — partitions remaining answers by feedback and picks the guess with the smallest worst-case bucket. Provably optimal: average 3.4212 guesses, max 5, opener salet.

Tap Analyse to compute the optimal next guess.

Status
Guesses recorded0 / 6
Candidates left2315
Mode
SolverMinimax (Selby 2022)
About

The solver uses Alex Selby's 2022 proof: brute-force over the 2315-word original answer list, opener salet and minimax partition-size selection guarantee a solve in at most 5 guesses, averaging 3.4212.

Hard mode. Each subsequent guess must respect every revealed hint (greens locked at position, yellow letters required to appear). With this extra constraint no strategy can solve 100% of words in 6 guesses — published results (Poirrier 2022) report ~98% solve rate and ~3.51 average using the same SALET opener with minimax follow-ups restricted to the legal pool, which is what this solver does when the toggle is on.

Guess pool restricted to the 2315 answer words for speed and clarity. After the opener, the optimal guess is almost always itself a possible answer, so this restriction loses very little versus the full 12 972-word allowed list.

Deep dive

How BoardSolve plays Wordle

In 2022 Alex Selby proved that Wordle is solvable in at most 5 guesses from the opener SALET, with a minimum average of 3.4212 guesses over the official 2 315-word answer list. BoardSolve ships the same minimax partition algorithm.

Minimax partition

Each candidate guess partitions the remaining answer set by the 3^5 = 243 possible colour patterns Wordle can return. The minimax score of a guess is the size of its largest partition class — and at the root, the guess minimising the total expected depth (with the largest partition as a tiebreak) is optimal.

BoardSolve precomputes the colour pattern for every (guess, answer) pair in the official lists so the inner loop is a single table lookup, then searches with iterative deepening and pruning by the proven-optimal depth bound.

Hard mode and custom dictionaries

The same engine handles 'hard mode' (every guess must be consistent with previous clues) by restricting the candidate guesses to the current answer set. You can also paste a different answer list — the algorithm is independent of the specific words.

References & further reading

  1. Selby, A. (2022) . sonorouschocolate.comProof of optimality and the SALET opener used by BoardSolve.
  2. Sanderson, G. (3Blue1Brown) (2022) . YouTube / 3blue1brown.comAccessible derivation of the entropy-based scoring used in the explanatory tooltips.
  3. Bertsimas, D. & Paskov, A. (2022) . MIT preprint