Ultimate word in Wordle!

I wanted to find the strongest mathematical opening word in Wordle. The short version: a one-step heuristic picks ROATE, but a deeper two-step search picks SALET.

Wordle gives six guesses for a five-letter answer. Gray means absent letter, yellow means present but wrong spot, and green means correct letter in the correct spot.

S	A	L	E	T
R	O	U	T	H
T	H	R	O	B
T	H	O	R	N

Guesses: SALET → ROUTH → THROB → THORN

What I Tested

Approach 1: Greedy reduction Pick the first word that reduces the candidate set the most after one guess.

Approach 2: Two-step search Evaluate how good a first word is after one additional optimal guess.

Approach 1 Winner: ROATE

Using single-step entropy reduction, ROATE performed best, reducing the average search space to 60.42 words from 2315.

#	Word	Avg Remaining
1	ROATE	60.4246
2	RAISE	61.0009
3	RAILE	61.3309
4	SOARE	62.3011
5	ARISE	63.7257

Approach 2 Winner: SALET

A deeper tree search changes the ranking. SALET gives the best two-step result, reducing average remaining candidates to 3.37.

#	Word	Avg Remaining After 2
1	SALET	3.3706
2	TOILE	3.4009
3	SLATE	3.4147
4	SLANE	3.4242
5	ROATE	3.4406

This aligns with independent analyses from MIT, 3Blue1Brown, and others.

Takeaway

Computer-optimal and human-optimal openings are not always the same. SALET is excellent for exhaustive search, but human play may benefit more from words that reveal clear positional clues quickly.

Math Notes (Short Version)

Wordle has two sets: an answer set (2315 words in the original list) and a larger valid-guess set. I scored words by expected remaining candidates over color outcomes and then expanded to a two-step search.

\[ N(\text{WORD}) = \sum_{i=1}^{n} P(\text{Color}(X_i)) \cdot N(\text{Color}(X_i)) \]

Code is available on GitHub.