Oh, wait, actually the best Wordle opener is not “crane”…
Audio Brief
Show transcript
This episode revisits an analysis of optimal Wordle strategy, correcting a crucial coding error and revealing new insights.
This discussion presents three key takeaways: the impact of a crucial bug on prior analysis, the identification of SALET as the new algorithmic optimum, and the distinction between mathematical optimality and practical human strategy.
The original code contained a bug related to handling duplicate letters, which skewed results for the optimal first guess. Correcting this error revealed a new top-performing word.
After re-analysis, the mathematically optimal starting word for a computer algorithm, based on lowest average score, is SALET. However, for humans, intuitive choices like TRACE or CRATE often prove more effective due to their ease of follow-up.
The analysis highlights that a greedy approach optimizing only the first step is less effective than a two-step optimization. Considering information gain from the second guess leads to a more globally optimal solution.
Ultimately, even minor coding errors can significantly alter analytical conclusions, especially in complex systems like Wordle's optimal strategy.
Episode Overview
- This episode is a follow-up and correction to a previous video about solving Wordle using information theory.
- The creator admits to a bug in his original code that incorrectly handled the logic for words with duplicate letters, which skewed the initial results.
- After fixing the bug, he re-runs the analysis to determine the new, truly optimal starting word based on different metrics like one-step information gain, two-step information gain, and lowest average score.
- The video contrasts the technically "best" word for a computer algorithm with what might be a more practical or intuitive choice for a human player.
Key Concepts
- Bug Correction: The central theme is acknowledging and correcting a coding error. The bug specifically related to how Wordle assigns colors (yellow/gray) when a guess contains a duplicate letter that appears fewer times in the answer.
- Information Theory: The concept of entropy, or expected information gain, is revisited as the primary metric for evaluating the quality of a guess. A good guess is one that, on average, provides the most information to narrow down the remaining possibilities.
- One-Step vs. Two-Step Optimization: The video distinguishes between a "greedy" approach (choosing the word with the highest information gain for the first guess only) and a deeper, two-step analysis that considers the expected information gain after the second guess as well.
- Optimal Algorithm vs. Human Strategy: The speaker highlights that the word an algorithm finds to be mathematically optimal (like "SALET") may not be the best choice for a human, who relies on different heuristics and may not know the optimal follow-up moves.
Quotes
- At 0:14 - "It turns out there was a very slight bug in the code that I was running to recreate Wordle and then run all of the algorithms to solve it..." - The creator begins the episode by confessing to the error in his previous analysis that led to the incorrect conclusion.
- At 2:30 - "But one of the very few things of substance that does change and that arguably does matter a fair bit, was the final conclusion around how if we want to find the optimal possible score for the Wordle answer list, what opening guess does such an algorithm use." - He explains that while many core concepts remain the same, the bug significantly impacted the most-cited result of the original video: the best starting word.
- At 9:10 - "But the thing is, I don't actually think this is the best opener for a human playing the game." - After revealing "SALET" as the new optimal word for the algorithm, he emphasizes that a technically perfect solution for a computer isn't necessarily a practical or enjoyable strategy for a person.
Takeaways
- The theoretically best starting word for Wordle, when optimized for the lowest average score over all possible games, is "SALET".
- Small bugs in logic, especially for edge cases (like duplicate letters), can lead to completely different conclusions in a complex analysis.
- Optimizing for a single step (a "greedy" approach) is not always the best long-term strategy; looking multiple steps ahead can yield a more globally optimal solution.
- For human players, a good starting word is not just about mathematical optimality but also about intuition and the ability to easily formulate subsequent guesses. Words like "TRACE" or "CRATE" are excellent practical choices.
