We’ve all been there. You open Wordle, stare blankly at the glowing green and yellow grid, and type in a random five-letter word just to get the ball rolling.
“CHOKE.”
The result? Three gray tiles. C, H, and E are out. But wait—did you actually learn anything useful, or did you just waste a crucial turn?
If you want to stop guessing and start solving Wordle like a machine, you need to stop relying on “gut feelings” and start applying mathematics. Specifically, you need to master the art of letter elimination.
Here is how to use math, probability, and information theory to strip away inappropriate letters and narrow down the English dictionary in record time.
Stop Guessing Words, Start Gathering “Information”
In 2020, computer scientist 3Blue1Brown (Grant Sanderson) applied information theory to Wordle to find the absolute best starting words. His conclusion shocked many casual players: the best starting word isn’t necessarily trying to win on turn one. It’s trying to gather the maximum amount of information.
In math terms, this is measured in bits of entropy.
When you guess a word, you want to split the remaining possible solution space as evenly as possible, regardless of whether the letters turn green, yellow, or gray. Gray letters are actually incredibly powerful because they instantly eliminate roughly 40% to 60% of the remaining vocabulary.
To eliminate inappropriate letters efficiently, your first two words should ideally contain 10 completely unique, high-frequency letters.
Play the Odds: Frequency Analysis
Not all letters are created equal. In the English language, certain letters appear with vastly superior frequency. If you eliminate rare letters (like Q, Z, X, and J) too early, you aren’t doing much mathematical heavy lifting. But if you eliminate high-frequency letters, the puzzle collapses inward.
According to linguistic frequency analysis, the most common vowels and consonants in 5-letter English words are:
- Vowels: E, A, O, I, U
- Consonants: S, R, T, L, N, C
If your first two guesses are SLATE and ROIND (or a variation like CRANE and STOUT), you have tested the top 10 most common letters in the English language.
By the end of turn two, you will likely have eliminated 6 to 8 inappropriate letters. You haven’t just made a guess; you’ve built a statistical net.
The “Information Theory” Trap: Avoid Duplicate Letters Early
A common beginner mistake is guessing a word with double letters early in the game (words like BLOOM or TENT).
Mathematically, this is inefficient. If you guess a word with a double ‘O’ and it turns gray, you’ve only eliminated one unique letter concept. If instead, you tested two distinct letters, you double your chances of hitting a green or yellow tile and drastically slash the number of valid remaining words.
Rule of thumb: Never repeat a letter in your first two guesses unless forced to by previous clues. Maximize unique letter exposure to maximize inappropriate letter elimination.
The Killer Strategy: The “Eliminator” Board
If you want to put this into practice, try designing a two-guess opening strategy that systematically wipes out standard consonants and vowels.
Consider this pairing:
- CRANE (Tests C, R, A, N, E)
- STOUT (Tests S, T, O, U… wait, T is repeated, let’s fix that) -> SPOIL (Tests S, P, O, I, L)
Combined, CRANE and SPOIL test: C, R, A, N, E, S, P, O, I, L. That is five vowels and five of the most common consonants.
After just two turns, you will have aggressively pruned the English dictionary. Whatever letters are left gray are officially “inappropriate” for today’s puzzle, and your brain is freed from considering them.
Summary Checklist for Mathematical Wordle:
- Treat gray tiles as victories: Every dead letter exponentially shrinks the pool of remaining answers.
- Prioritize high-frequency letters: Target E, A, R, O, T, L, N, and S in your opening moves.
- Avoid duplicates early: Keep your first two guesses unique to maximize your mathematical reach.
- Trust the process: Don’t chase a win on turn two. Build an airtight foundation of eliminated letters, and the solution will practically reveal itself on turn three or four.
Next time you fire up Wordle, leave the intuition at the door. Let math do the heavy lifting, and watch your average score plummet.
