Binghamton Researchers Use Information Theory to Solve 99% of Wordle Puzzles in Simulations

Anyone who has stared at a half-filled Wordle grid knows the temptation: pick a word that looks like the answer and hope. Researchers at Binghamton University say a better approach is to guess words that teach you the most, even if they are unlikely to be right.

The team, led by Assistant Professor Congyu "Peter" Wu, built a strategy using Shannon entropy, a measure from information theory. In simulations, the method solved 99% of Wordle puzzles. A more conventional strategy built around common letters such as "A," "E" and "R" solved 90%.

Wordle gives players six attempts to find a hidden five-letter word. The first guess can be any valid word, and after each attempt the game returns color-coded clues showing how close the guess was. Players use that feedback to narrow the possibilities. The game ends when all five squares turn green or the six attempts run out. Because each guess shrinks the pool of candidate answers, the researchers say, the game is a natural fit for information theory, the branch of mathematics concerned with measuring and communicating information.

Shannon entropy is a way of measuring uncertainty. In Wordle terms, it helps estimate how much useful information a given guess is expected to reveal. Rather than asking which word is most likely to be correct, the researchers asked which guess would eliminate the greatest number of possibilities.

"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 Wu, who is a faculty member in the Thomas J. Watson College of Engineering and Applied Science's School of Systems Science and Industrial Engineering.

That can make the recommended guesses look odd. A word that has little chance of being the solution can still be valuable if its letters split the remaining candidates 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. He added that the objective shifts to maximizing the expected reduction in uncertainty rather than the probability of being right, which in practice can lead to solving the puzzle in fewer guesses.

The method also adapts as the game goes on. Common letters can be useful, the researchers note, but the mathematical approach continually adjusts its choices based on what has already been learned.

For everyday players, using the strategy during a real game would take some extra work. According to the source, a player would need to run a separate script or program, enter Wordle's color-coded feedback after each guess, and let the software calculate the next guess expected to provide the most information. In other words, it is less a trick to memorize than a tool to run alongside the puzzle.

The work began as a class assignment in which Wu challenged students to show how information theory could solve a real problem. The students chose Wordle. Co-author Talal Aladaileh said the project's growth from a classroom exercise into a published paper reflects the rigor, depth and quality of the school's program. Wu said it shows how information theory can move beyond describing uncertainty to become a tool for making better decisions, turning a static measurement into a dynamic solution.

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

The source material does not detail the simulation setup, such as the word lists used or the average number of guesses needed, so those specifics remain unclear. The 99% and 90% figures come from simulations rather than from human players in live games, and the source does not describe any tests with people. Still, the result is a lively example of how a mathematical idea can reshape a familiar internet pastime: sometimes the smartest move in Wordle is a guess you do not expect to be right.