Sunday, February 13, 2022

Seven Three-Word Sequences for Solving Wordle

Are you playing Wordle, the daily online game that gives you six chances to guess a five-letter word?

The big question is what word to use for your first guess. I've extended that idea to finding the first three words that provide a very good chance of solving the puzzle by choosimg the words based on the frequency of letters in English words in the table below.

The first three guesses will usually identify enough letters to make a good guess at the answer on the fourth guess, with two guesses still in reserve. Sometimes the first two words will identify enough letters to skip the third word in the sequence and make a good guess at the answer, as was successfully done in the game shown above.

STEIN / HOARD / CLUMP - Pick the low-hanging fruit. This sequence covers 87.51% of the letter frequencies, the highest percentage that can be covered with three guesses.

STONE / CHARD / IMPLY - Reach for the Y. This sequence trades the U for a Y. Stone can be played instead as notes or tones, if you prefer.

ATONE / CRISP / BULGY - Start with three vowels. Atone is often recommended as the first guess, its 40.43% covers the highest percentage of the seven sequences for the first guess, and the next two words in the sequence cover the remaining vowels.

ADIEU / STORY / CLAMP - Buy the vowels. This sequences covers all the vowels in the first two guesses. Adieu is also often recommended as the first guess. The third guess reuses the A that was guessed in the third word, so it can make sense to vary the third word based on what vowells the first two words turn up. For example, clamp, clomp, clump, chink, chunk, flack, fleck, flock.

ENTRY / AUDIO / CLAPS - Buy the vowels, version II. This sequence covers all the vowels in the first two guesses. Audio is often recommended as a first guess, but the frequencies suggest guessing entry before audio. Again, varying the third word based on the vowels already uncovered can make sense.

TREND / CLAMP / WHISK - Buy consonants. This sequence covers only three vowels in order to cover twelve consonants.

FRONT / BUCKS / LYMPH - Pitch a change-up for the most consonants. This covers the three less frequent vowels, and thirteen consonants (counting Y as both). But the low total frequency of 63.69% feels suboptimal when played in comparison to the other sequences above.

How well do these sequences work? I've got a 100% win rate at the offical Wordle site and a 99% win rate at the Wordle knockoff I play for practice. How well will they work for you?

The following table uses letter frequency percentages based on the main entries of the Concise Oxford Dictionary (9th edition, 1995):

E 11.16% Stein Stone Atone Adieu Entry Trend
A 8.50% Hoard Chard Atone Adieu Audio Clamp
R 7.58% Hoard Chard Crisp Story Entry Trend Front
I 7.54% Stein Imply Crisp Adieu Audio Whisk
O 7.16% Hoard Stone Atone Story Audio Front
T 6.95% Stein Stone Atone Story Entry Trend Front
N 6.65% Stein Stone Atone Entry Trend Front
S 5.74% Stein Stone Crisp Story Claps Whisk Bucks
L 5.49% Clump Imply Bulgy Clamp Claps Clamp Lymph
C 4.54% Clump Chard Crisp Clamp Claps Clamp Bucks
U 3.63% Clump   Bulgy Adieu Audio   Bucks
D 3.38% Hoard Chard   Adieu Audio Trend
P 3.17% Clump Imply Crisp Clamp Clamp Lymph
M 3.01% Clump Imply   Clamp Claps Clamp Lymph
H 3.00% Hoard Chard   Whisk Lymph
G 2.47%     Bulgy  
B 2.07%     Bulgy   Bucks
F 1.81%         Front
Y 1.78%   Imply Bulgy Story Entry   Lymph
W 1.29%       Whisk
K 1.10%         Bucks
V 1.01%        
X 0.29%        
Z 0.27%        
J 0.20%        
Q 0.20%        
1   38.05% 37.66% 40.43% 34.22% 34.12% 35.73% 30.16%
2   29.63% 27.00% 28.57% 29.21% 30.22% 24.70% 17.08%
3   19.84% 20.99% 15.44% 16.21% 18.93% 18.67% 16.45%
T 87.51% 85.66% 84.43% 79.63% 83.28% 79.11% 63.69%