Strategy explained

The math behind Wordle

Why some guesses tell you more than others.

Every possible answer gives your guess a pattern of green, yellow and gray tiles. A useful guess divides the answers into lots of small groups, so whichever pattern appears, your next shortlist is manageable.

Information theory turns that idea into a score. You do not need the formula to use the solver, but it explains why a word with common letters is not automatically a good opener.

How a guess splits the answers

It's like sorting a deck of cards. "What suit?" splits a 52-card deck into four piles of 13. "Is your card the eight of clubs?" peels off one card and leaves you with 51. Both are valid questions; one is far more useful when you don't yet know the answer.

A Wordle row has 243 theoretical feedback patterns (five tiles × three colors = 35). For any guess, each possible answer belongs to the group that would produce its pattern.

1

Simulate

Pick a guess and work out the feedback it would receive from each possible answer.

2

Sort

Put answers with the same feedback together. Many of the 243 theoretical patterns will be empty; the useful ones form groups of different sizes.

3

Score

Information measures how balanced those groups are. Average remaining answers measures the shortlist you are likely to face next. The current bounded six-turn policy first minimizes answers the solver misses, then average guesses among wins. In endgames it scans every accepted guess against the current answers, so a low-frequency trap breaker is not discarded just because it falls outside a global word list. It uses the full board horizon in endgame ranges certified to fit the response ceiling, and an explicitly labelled, at-most-three-row lookahead in branch-heavy states. The measures can choose different winners. On the current possible-answer list, TARSE has the highest first-turn information score at 5.95 bits.

No guess makes every group small. The interactive chart in the next tab shows the actual split for any word you enter.

Three ways to compare openers

Information grades the first turn in bits. Average remaining answers grades the same turn by the likely size of your shortlist. The current six-turn ranking applies one solver to a bounded screen of strong openers, ranks exact misses first, and uses average guesses among wins as the tie-breaker. These measures choose different winners because they ask different questions.

What you optimizeWinnerScore
Fewest misses, then shortest winssite default SLANT 3.45 avg among wins
Most information per guess (entropy) TARSE 5.95 bits
Fewest answers left after one guess ROATE ~62 left

This page concentrates on entropy. For a practical comparison of all three measures, see the guide to Wordle starting words.

Compare the buckets

Enter a five-letter word to see how it divides the current possible-answer list. The chart highlights its worst result and overall information score.

Or try another opener:
? ? ? ? ?
Enter a word to visualize

The largest bucket shows the worst result for that guess. Entropy uses the full distribution, rewarding splits that spread probability across more balanced feedback groups.

Enter a word to see how it compares
Full feedback distribution (advanced)

All non-empty feedback patterns and their frequencies.

- Patterns
- Largest group
- Smallest group
Enter a word to see all feedback patterns
Your browser does not support canvas. The visualization shows how different feedback patterns reduce the pool of possible words.
For the mathematically curious: entropy

Entropy scores the information in a guess's feedback. It is useful, but it does not tell you which follow-up to play or guarantee the shortest route. The starting-word guide compares it with the six-turn ranking.

Entropy puts a single number on how evenly a guess sorts the pool. The formula:

H = −∑ p(x) log2 p(x)

Here, p(x) is the share of possible answers in feedback group x: group size ÷ 2360. Add the contribution from every non-empty group and the result is measured in bits. The current leader is TARSE at 5.95 bits.

With equally likely answers, halving the list removes one bit of uncertainty. The current 2,360-answer list begins at 11.2 bits; identifying one answer removes all of it.

Information and average remaining are related, but not interchangeable. Two guesses can have similar information scores yet different average group sizes because the measures weight large and small groups differently.

Shannon's 1948 paper, A Mathematical Theory of Communication, used this formula to measure uncertainty in an information source. In Wordle terms, each guess is a question and the colored tiles are the answer.

On the current possible-answer list, TARSE (5.95 bits) has the highest first-turn information score.

The solver rebuilds these feedback groups after every row. You can rank guesses by information or use the default ranking, which favors a smaller next shortlist and avoids bad worst cases.