Oh, wait, actually the best Wordle opener is not “crane”…

Summary

In this video, the creator discusses a minor bug in their Wordle-solving algorithm, which affected only a small number of cases involving multiple instances of the same letter. They explain how fixing the bug slightly changed the optimal opening guess in Wordle from 'crane' to 'salé,' an obscure medieval term. Despite this, the main focus of the video remains on understanding information theory and entropy. The creator emphasizes that while algorithms can optimize Wordle guesses, the joy of playing the game lies in human intuition rather than technical perfection.

Takeaways

• 🤖 There was a slight bug in the code used to simulate and analyze Wordle gameplay, affecting only a small percentage of cases.
• 🟨 The bug related to how Wordle colors repeated letters, like the difference between yellow and gray when guessing words with multiple instances of the same letter.
• ⏳ The mistake was introduced while trying to speed up computations, but precomputing all patterns would've been a better approach.
• 🎓 The main lessons about information theory and entropy remain intact, despite the coding error.
• 📊 One significant change is the conclusion about the best possible opening guess for Wordle, shifting from 'crane' to another word after fixing the bug.
• 🔄 An exhaustive two-step search shows that while 'soar' ranks highly in information gained, the best first guess in practice is 'slain'.
• 🔍 After running simulations, the best performing starting word is 'Salé,' with real words like 'trace' and 'crate' performing almost as well.
• 📖 The video emphasizes the educational value of understanding information theory and how greedy algorithms can fall short compared to more thorough searches.
• 👨‍💻 Human players use intuition and experience when playing Wordle, which is different from the algorithmic approach overfitting to a known word list.
• 🎯 The goal of the video wasn't just to find the optimal opener for Wordle, but to sneakily teach information theory through an engaging and trendy topic.

Q & A

What was the bug in the code related to Wordle solving mentioned in the video?

The bug was related to how colors were assigned to guesses with multiple instances of the same letter, such as 'e' in 'speed' when the true answer was 'abide'. The issue affected a small percentage of cases where the wrong pattern was produced for these guesses.

How did this bug affect the final results in the video?

The bug had a minor effect on most cases, but the key change was that the optimal opening guess changed from 'crane' to 'salé' after the bug was fixed. However, the main concepts of information theory discussed in the video remained unaffected.

What is the significance of using the Wordle answer list in the final analysis?

By using the official Wordle answer list, the analysis overfitted to the test set, allowing for optimal performance calculations. This means the algorithm knew for certain whether a word was included as an answer and could assign probabilities accordingly.

What was the theoretical best opening word after fixing the bug?

After fixing the bug, the optimal opening word for Wordle was found to be 'salé', which is an alternate spelling for a medieval helmet. 'Crate' and 'trace' also performed almost identically.

Why was the best opening guess initially thought to be 'crane'?

Due to the bug in the code, the algorithm was playing a slightly different version of the game, which led to 'crane' being identified as the best opener. After fixing the bug, this changed.

What did the algorithm use to quantify information for a Wordle guess?

The algorithm used a formula based on entropy, which calculated how much information would be gained from a guess by estimating how many times the possible answers would be reduced by half after seeing a certain pattern of colors.

How did the bug affect the distribution of patterns in the game?

The bug caused some distributions to be slightly off in cases where words had multiple letters that matched letters in the answer. This could result in either more or fewer answers being included in certain buckets for pattern analysis.

Why is overanalyzing the game considered 'dirty' by some?

Some people feel that overanalyzing the game to find the best opening guess ruins the fun of Wordle. It can feel like cheating if you use the optimal guess but inefficient if you don’t, as it detracts from the intuitive enjoyment of the game.

What is the lesson the video creator wants viewers to take away?

The main takeaway should not be the optimal Wordle opening guess, but rather the principles of information theory, such as how to quantify information and understanding the limitations of greedy algorithms compared to deeper search methods.

Why does the creator recommend forgetting the optimal opening guess?

The creator suggests forgetting the optimal guess because Wordle is meant to be played intuitively. The optimal guess is highly tailored to a specific list of answers, and if that list changes, the strategy becomes irrelevant. The focus should be on understanding information theory instead.