Information Theory Finds the Best Wordle Starting Words
wordleinformation-theoryentropypuzzle-optimization
Abstraction: Using Shannon entropy to optimize Wordle opening word selection
Key points:
- Shannon entropy measures information gain: one bit halves the solution space; "soare" achieves 5.89 expected bits, reducing 2,309 solutions to ~22 on average
- Grant Sanderson (3Blue1Brown) computed expected entropy for all ~10,000 possible input words against the 2,309 solution words
- Two-word opening strategy: "slane" + optimal second word yields 10.04 total bits, reducing possibilities to ~2.19 words on average — slightly better than "soare"
- Key tradeoff: high entropy starting words sacrifice hit rate (e.g., rare letter X gives huge info if present but low probability of being present)
- Wordle was created by Josh Wardle in 2013/2021, acquired by NYT for low seven figures in January 2022; grew from 90 users (Nov 1, 2021) to 300,000 by Jan 1, 2022
Connections: Wordle · New York Times · Information Theory · Entropy · Combinatorics
Source: https://www.scientificamerican.com/article/information-theory-finds-the-best-wordle-starting-words/