For anyone who has stared at a stubborn Wordle grid and run out of ideas, researchers at Binghamton University say the better move is not a lucky guess. It is a math-based one.

A team at Binghamton University, State University of New York, said it developed a strategy that solved 99 percent of Wordle puzzles in simulations by applying information theory.

Wordle gives players six attempts to identify a hidden five-letter word. After each guess, the game marks letters in grey, yellow, or green to show if a letter is absent, present in the wrong spot, or correct and in the correct position.

The researchers built their approach around Shannon entropy, a measure of uncertainty in information theory. Instead of picking the word most likely to be correct, the strategy picks words expected to reveal the most useful information and cut down the remaining possibilities fastest.

“Let’s say you’re at a certain guess. The previous guesses will eliminate a whole bunch of options, and based on the remaining options, guessing some words will send you into a trajectory where information gain is speedier,” said Congyu “Peter” Wu, an assistant professor at the Thomas J. Watson College of Engineering and Applied Science’s School of Systems Science and Industrial Engineering.

That means a word can be useful even if it is unlikely to be the final answer, as long as it helps sort the remaining options into smaller groups.

“A subtle but important insight from the paper is that a guess doesn’t have to be the most likely answer; it simply has to be informative,” said Donald Stephens, a doctoral student at Binghamton University. “By applying Shannon entropy, the objective shifts to maximizing the expected reduction in uncertainty rather than the probability of being right. In practice, this approach can lead to solving the puzzle in fewer guesses.”

The team compared the method with a more conventional strategy based on frequently used letters such as A, E and R. In simulations, the information theory method solved 99 percent of Wordle puzzles, while the common-letter strategy solved 90 percent.

Using the strategy in a real game would require a separate script or program. After each guess, a player would enter Wordle’s color-coded feedback, and the software would calculate the next guess expected to provide the most information.

The work began as a class assignment, when Wu asked students to show how information theory could solve a real problem. The students chose Wordle, and the project later became a published paper.

Co-author Talal Aladaileh said the project showed the strength of the program at Binghamton’s School of Systems Science and Industrial Engineering.

“The courses here don’t just teach concepts; they push you to apply them in ways that have real, lasting impact,” Aladaileh said.

Wu said the project showed how information theory can be used as a decision-making tool.

“What is especially creative and valuable about the team’s intellectual contribution,” Wu said, “is that it transformed a static measurement (Shannon entropy) in a scientific domain into a dynamic solution that helps accomplish a popular task better, which showcases the team’s deep understanding of class material and their talent as engineers.”

The paper, “Solving Wordle Using Information Theory,” was published in the Northeast Journal of Complex Systems.

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