Entropy-Driven Strategy Solves Wordle with Near-Perfect Accuracy

Wordle asks players to find a hidden five-letter word within six attempts, providing gray, yellow, and green feedback after each guess. The researchers modeled each round as a feedback system and quantified the remaining solution set’s uncertainty with entropy, choosing guesses that most sharply reduce that uncertainty.

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success RateScience DailySolving Wordle Using Information Theory

The work was led by Assistant Professor Congyu “Peter” Wu, with doctoral student Donald Stephens and co-author Talal Aladaileh, all members of Binghamton’s School of Systems Science and Industrial Engineering.

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• Success rate: 99 % of Wordle puzzles solved in simulations.

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

• Baseline comparison: Traditional heuristic based on frequent letters solved ~90 % of puzzles.

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

• Method: Entropy-maximizing guess selection evaluated after each feedback cycle.

Solving Wordle Using Information Theory

The study shows how a classic uncertainty measure can guide real-time decision making in a popular game, suggesting similar entropy-driven tactics could improve other combinatorial puzzles and serve as teaching examples in engineering curricula.

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

Wu noted the algorithm’s value lies in steering players toward guesses that accelerate information acquisition, even when those guesses are unlikely to be correct. Stephens emphasized the shift from probability-focused to uncertainty-reduction thinking, arguing that an “informative” guess can outweigh a high-probability one. Aladaileh highlighted the project’s transition from a classroom assignment to a peer-reviewed paper, reflecting the department’s focus on applying theory to practical outcomes.

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

• “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,” — Donald Stephens, Doctoral Student

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• “By applying Shannon entropy, the objective shifts to maximizing the expected reduction in uncertainty rather than the probability of being right.” — Research Team

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

• “The courses here don't just teach concepts; they push you to apply them in ways that have real, lasting impact,” — Talal Aladaileh, Co-author

Science Daily

• “The experimental results demonstrate that entropy-based word selection improves performance compared to a heuristic approach based on selecting words by letter distribution, providing a systematic framework for decision-making in Wordle,” — Researchers

Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate

To use the method in live play, a player would run a script that inputs the colored feedback after each guess and returns the next entropy-optimal word. The team plans to refine the algorithm for real-time use, test it on other word-based puzzles, and explore its relevance for adaptive learning tools.

Solving Wordle Using Information Theory