Scientists Used Math To Solve Wordle 99% Of The Time

This Entropy-Based Wordle Strategy Beat Human Instinct in Simulations

Most Wordle players trust their gut, cycling through vowels and common letters until something clicks. A team of researchers decided to treat the beloved word game as a math problem instead, and the results were hard to ignore. In simulated games covering every possible Wordle answer, their entropy-based strategy solved the puzzle correctly more than 99% of the time, compared to roughly 90% for a baseline strategy built around letter frequency, the kind of intuitive approach many casual players lean on.

That result does not mean any player can guarantee a win with one magic opening word. It means this strategy performed extremely well against the full list of possible answers. It is built around Shannon entropy, a way of measuring uncertainty named for a landmark 1948 paper by mathematician Claude Shannon. Applied to Wordle, entropy becomes a tool for asking which guess will teach the most, always choosing the word expected to reveal the greatest amount of information. The research was published in the Northeast Journal of Complex Systems.

Wordle, created by software engineer Josh Wardle, gives players six attempts to identify a secret five-letter word. After each guess, letters are flagged green for right letter and right spot, yellow for right letter and wrong spot, and gray for not in the word at all. That color-coded feedback is where the math gets interesting, because each response amounts to a small burst of data that either narrows the search or does not.

Wordle’s Winning Opening Word Was ‘Tares’

Researchers at Binghamton University in New York started with the full list of 12,972 valid five-letter words in Wordle’s dictionary. Of those, 2,315 are candidates for the actual daily puzzle answers.

Every guess in Wordle produces one of 243 possible color-pattern combinations, since there are five letter positions and each can turn green, yellow, or gray. They calculated the probability of each pattern for every word, then used those probabilities to compute an entropy score representing how much information a word is expected to reveal, on average, when played.

Words that produce a wide spread of outcomes carry more information than words that funnel most possibilities into just one or two patterns. Even a guess that comes back entirely gray can be valuable, since it confirms which letters do not belong in the answer. The goal was words that consistently deliver useful clues no matter what the secret word turns out to be.

After running the numbers, the top-ranked opening word across the entire list, ‘tares’, became the fixed first move for the entropy strategy in every simulated game.

Entropy Beat Letter Frequency in Every Simulated Wordle Game

To measure how well the strategy worked, researchers ran an exhaustive simulation. Every one of the 2,315 possible Wordle answer words was played twice, once using the entropy strategy and once using a baseline built around letter frequency.

That baseline approach is methodical in a familiar way. It starts with a word containing high-frequency letters like a, e, and r, then uses color feedback to rule out bad letters and zero in on words containing confirmed ones. It mirrors the logic many players apply without thinking too hard about it.

Entropy consistently won out. That gap held up across all 2,315 test words: the entropy strategy came out ahead in roughly 99 games out of 100, while the letter-frequency approach landed closer to 90. Researchers pointed to one specific weakness behind the shortfall: the frequency method can get stuck cycling through words that share the same letters, like ‘least’, ‘stale’, ‘slate’, and ‘steal’, without a clear way to choose between them. The entropy strategy sidestepped that trap and also tended to land on the right word in fewer total guesses on average.

Where the 99% Wordle Solver Still Falls Short

Researchers were candid about what the entropy strategy cannot do. It is “greedy,” meaning it only looks one step ahead rather than planning several moves in advance. More advanced strategies do plan ahead. Prior research cited in the paper showed that an optimal dynamic programming approach can guarantee solving any Wordle puzzle in at most five guesses, averaging about 3.42 guesses, a benchmark the entropy method does not reach.

This approach also depends on a pre-loaded word list and does not track which words have already served as past daily answers, something that could theoretically sharpen its edge. Researchers suggested one future improvement: weighting words by how often they appear in everyday English, rather than treating every valid five-letter word as equally likely to be the answer.

Beyond a Word Game

It might be tempting to file this study under interesting but trivial, since it is about a word game played for a few minutes a day. But the underlying math reaches well past morning puzzle routines. Shannon entropy and information theory are foundational tools in fields like data compression, medical testing, and cybersecurity, anywhere a system needs to make smart decisions under uncertainty with limited attempts.

This research frames Wordle as a simplified model of complex adaptive systems, environments where feedback shapes future decisions and order gradually emerges out of uncertainty. Wordle offers a small daily demonstration of a pattern that shows up across science and engineering. And in this particular test, letting the math lead won considerably more often than letting instinct lead.

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Disclaimer: This article summarizes findings from a peer-reviewed study for general informational purposes and does not constitute gameplay advice or a guarantee of results. Readers seeking full methodology and data should consult the original paper.

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