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The Mathematics of Word Elimination: Filters and Decision Boundaries
How each guess filters the list of possible answers, and why different strategies choose different guesses.
Key Research Takeaways
- Each guess acts as a filter. After each result, only the words that could have produced that pattern remain.
- A guess that is best on average is not always best in the worst case, so the two strategies can choose different words.
- Consonants often remove more candidates than vowels, because vowels appear in so many words.
Article Sections
Guesses as filters
Each guess produces a pattern of feedback. Every candidate word that would have produced a different pattern is eliminated. The set of remaining candidates gets smaller with each turn, and the game is won when one candidate is left.
Average versus worst case
A guess that does well on average can leave a large group of candidates in an unlucky case. A cautious strategy looks at the worst-case group size instead. Choosing between the two depends on whether you want the fewest guesses on average or the lowest risk of a bad result.
Why consonants help
Vowels such as E and A appear in many words, so a guess containing them often confirms only a little. Common consonants in useful positions can rule out larger groups. Mixing both is usually a good balance.
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