How Entropy Helps You Solve Wordle Faster

What Is Entropy?

In information theory, entropy measures the "surprise" or "information content" of an event. Named after Claude Shannon, it quantifies how much uncertainty exists in a system. For Wordle, entropy tells us: how much does a particular guess reduce our uncertainty about the answer?

Mathematically, Shannon entropy is calculated as:

Where p(x) is the probability of each outcome. A higher entropy value means more information gained on average.

How Wordle Analyzer Calculates Entropy

For each candidate guess word, Wordle Analyzer simulates all 243 possible color patterns (3⁵ = 243 combinations of green/yellow/gray across 5 positions). For each pattern, it calculates how many of the remaining answers would produce that pattern.

The steps are:

1. For each candidate word, iterate through every possible answer still remaining
2. Compute the color pattern that would result from this guess-answer pair
3. Group answers by pattern — how many remaining words produce each of the 243 patterns
4. Calculate probability for each pattern: p = (words producing this pattern) / (total remaining words)
5. Apply Shannon's formula to get entropy in bits

Why CRANE Beats ADIEU

ADIEU is a popular choice because it tests 4 vowels. But entropy analysis reveals it's suboptimal:

CRANE produces 150 distinct patterns compared to ADIEU's 112. This means CRANE creates more "buckets" of possible answers, and each bucket is smaller on average. The result: after one guess with CRANE, you typically have 40 words left vs. 57 with ADIEU — a 30% improvement.

Entropy in Action: A Real Example

Suppose the answer is TIGER. Let's trace how entropy guides us:

1. Guess 1: CRANE → 🟨⬜⬜⬜🟨 (C is yellow, E is yellow) → ~35 words remain
2. Guess 2: OPTIC (highest entropy for remaining words) → ⬜⬜🟨🟩🟨 → ~3 words remain
3. Guess 3: TIGER → 🟩🟩🟩🟩🟩 → Solved in 3!

Beyond Entropy: Wordle Analyzer's Composite Score

While entropy is the most powerful single metric, Wordle Analyzer combines it with three additional dimensions for a complete scoring formula:

• Entropy (40%) — Information gain from the guess
• Letter Frequency (30%) — Position-weighted scoring for common letters
• Unique Letters (15%) — Bonus for testing as many distinct letters as possible
• Solution Bonus (15%) — Slight preference for words that could also be the answer

Try It Yourself

The best way to understand entropy is to see it in action. Enter any Wordle game state into Wordle Analyzer and observe how entropy scores change as you provide more information. The efficiency meter shows how much of the possibility space you're eliminating with each guess.