Solving Wordle using information theory

Solving Wordle using information theory

🎙 3Blue1Brown (Grant Sanderson) 👥 8.6M 📅 February 6, 2022 ⏱ 30 min 👁 11.8M 📄 science communication 🧭 2026-08-28
Available in: English (current) Français

Keywords

entropyinformation theoryWordlealgorithmShannon

Summary

The video presents a method to solve the popular word game Wordle using information theory, specifically the concept of entropy. The creator, Grant Sanderson, explains the rules of Wordle and then introduces the idea of measuring the information gained from each guess in bits. He defines entropy as the expected information of a guess, calculated from the probability distribution of possible color patterns. The video walks through the process of building a bot that maximizes entropy at each step, using a list of about 13,000 valid words. The initial version achieves an average score of 4.124, which is improved by incorporating word frequency data from Google Books Ngram via a sigmoid function to weight the likelihood of each word being the answer. The final bot achieves an average score of 3.421, demonstrating the effectiveness of the entropy-based approach. The video also includes a brief historical anecdote about the naming of entropy by von Neumann and discusses the trade-off between information gain and word commonness.

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Critical Evaluation

Value of the Information & Strength of the Argument

The video provides a clear and compelling argument for using entropy as a measure of information in a decision-making process. The value lies in its pedagogical approach: it starts with intuitive examples (reducing possibilities by half) and builds up to the formal definition of entropy. The argumentation is solid, as each step is justified with examples and the logic is transparent. The creator also addresses potential limitations, such as the assumption of equal probability for all words, and then refines the model to incorporate word frequencies, showing a thoughtful and iterative approach to problem-solving.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high. The video is based on established information theory concepts, and the creator provides the code used for the analysis, allowing for reproducibility. The sources cited include the original Wordle site, the GitHub repository with the code, and the Manim library used for animations. The title accurately reflects the content, and the video fulfills its promise of teaching information theory through a practical example. The creator also acknowledges the use of word frequency data from Google Books Ngram, which adds credibility to the methodology.

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Title / Content Match

The title accurately reflects the content: the video uses information theory to solve Wordle, and the approach is thoroughly explained.

Quality & Reliability

9/10

The video is a rigorous, well-structured explanation of information theory applied to a concrete problem. The methodology is transparent, the code is provided, and the mathematical derivations are clear. The presentation is consistent with established information theory concepts (Shannon entropy) and the results are reproducible.

Chapters

Cited Sources

  • Wordle — The original Wordle game, used as the subject of the analysis.
  • Code for this video — The code used to implement the Wordle solver and generate the animations.
  • Manim (3Blue1Brown's animation library) — The custom Python library used to create the video animations.
  • Manim Community Edition — A community-maintained version of the Manim library.
  • 3Blue1Brown FAQ — FAQ page with information about the Manim library.
  • 3Blue1Brown website — The official website of the channel.
  • 3Blue1Brown Reddit — The subreddit for the channel, where discussions and additional resources are shared.
  • Vincent Rubinetti — The composer of the music used in the video.

Concurring Sources

  • Information theory — The video's approach aligns with the principles of information theory, particularly the use of entropy to quantify information.
  • Shannon entropy — The video's definition of entropy matches the standard definition in information theory.

External References

Contribution & Novelties

The video’s original contribution is its clear and accessible explanation of how information theory, specifically entropy, can be applied to a real-world puzzle like Wordle. It provides a step-by-step methodology for building an optimal solver, from the basic entropy maximization to the incorporation of word frequency data. The video also offers a novel perspective on the trade-off between information gain and word commonness, which is a key insight for algorithm design.

Pour aller plus loin :

120 words

Radar Profile

The radar profile shows high scores in information quantity, quality, and reliability, with a slightly lower score in technical level. This indicates that the video is highly informative and reliable, but may require a moderate level of mathematical background to fully grasp the technical details.

Reliability 9/10

💬 Très positif. Sur les 30 commentaires analysés, le climat est extrêmement favorable, avec des éloges pour la pédagogie, l'humour et la qualité de l'explication, ainsi que des anecdotes personnelles sur l'utilisation du bot.