Analyzing the most strategic words to guess on Wordle, based on letter frequency distributions

Overview

wordle-analysis

Evaluating different heuristics to determine the most effective solving strategy and building an AI-powered assistant tool to help you win.

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The Data

12972 guessable words
2315 mystery words*

* = These words comprise a word bank that is hard-coded into the
Wordle source code and used to randomly pick the daily puzzle each day

Exploratory Analysis

Most common letters

In the words of Pat Sajak, "R, S, T, L, N, E". These are the most frequently appearing letters in the English language and are, as such, used in the Bonus Round of the game Wheel of Fortune. But I wanted to start this project by verifying if they are, in fact, the most frequent letters when we limit our scope to only 5-letter English words.

As it turns out, E, A, R, O, T, L, I, S are the most frequent letters that appear in 5-letter words. Now, quick, think of a 5-letter word using these letters!

Heatmap to analyze letter frequency by positions

Simple Scoring Heuristics

Suppose today's Wordle solution is CRIMP. Let's walk through some example guesses and unpack how to make sense of the resulting colored tiles.

Guess 1: RAISE => 🟨 🟩 => R is present in the word, but not in the right place
Guess 2: MOUNT => 🟨 => M is present in the word, but not in the right place
Guess 3: GRIME => 🟩 🟩 🟩 => R, I, and M are all correct and locked in
Guess 4: CRIMP => 🟩 🟩 🟩 🟩 🟩 => 🎉 yay, you solved the Wordle! 🎉

If you take each guessable word and use it to try to guess each of the 2,315 mystery words, we can get a sense of how much valuable information we obtain using the scoring system above. For each guess, let's count up the number of greens we get, the number of yellows, blacks. Then, using a weighted average to maximize greens and yellows, we can sort our list of guessable words to find the words that yield us, on average, the highest heuristic score. A list of the 5 top words using this approach is provided below! Try starting your Wordle with any one of these words next time and see how you do!

Guess Average Correct 🟩 Average Present 🟨 Average Absent Weighted Average Tile Score 🟩 🟨
SOARE 0.660043 1.107991 3.231965 2.428078
STARE 0.572786 1.192657 3.234557 2.338229
ROATE 0.541685 1.247516 3.210799 2.330886
RAILE 0.544708 1.225054 3.230238 2.314471
AROSE 0.538661 1.229374 3.231965 2.306695

Simulation Results

Approach Best Initial Guess
Max-size Prioritization RAISE
Max-entropy Prioritization SOARE
Max-splits Prioritization TRACE
Owner
Sejal Dua
Data Scientist & Software Engineer
Sejal Dua
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