I recently, like pretty much everyone else got into Wordle. One of the most important things in getting the correct answer is to find the best first word or two to start with which will help guide you to the correct answer. The ideal first word(s) should use one each of the most common letters so for example in the first 2 guesses you can test the top 10 characters.
My first (relatively uneducated) guesses based on what I vaguely remembered about letter frequency in English were ‘spear’ and ‘mount’ – 4 vowels and some of the most common consonants. However it’s pretty much a random guess so I was wondering if we could figure out a better approach.
It’s pretty straight forward to look at the source code of Wordle, which contains two word lists. The first one contains 2315 5-letter words which can be the answer, the second contains a further 10,000 of all possible 5 letter words in English.
So, I wrote a small script to analyse the frequency of letters in the list of possible answers, and then based on that filter the possible words to find the best starting (and subsequent) guesses which would work.
I’ve put the simple python script I used at the bottom of the article, but the output is:
Matching 5 new letters (39%) are: [‘arose’]
Matching 5 new letters (66%) are: [‘unlit’, ‘until’]
Matching 4 new letters (81%) are: [‘duchy’]
Matching 3 new letters (89%) are: [‘pygmy’]
What this means is that if you start with the word ‘arose’, and then ‘until’ (or ‘unlit’), even though it’s only 10 unique letters (38% of the alphabet) because they are the most frequent ones they will cover 2/3 (66%) of the possible words.
In terms of letter frequency overall we get the following ordered detail:
[(‘e’, 1233), (‘a’, 979), (‘r’, 899), (‘o’, 754), (‘t’, 729), (‘l’, 719), (‘i’, 671), (‘s’, 669), (‘n’, 575), (‘c’, 477), (‘u’, 467), (‘y’, 425), (‘d’, 393), (‘h’, 389),
(‘p’, 367), (‘m’, 316), (‘g’, 311), (‘b’, 281), (‘f’, 230), (‘k’, 210), (‘w’, 195), (‘v’, 153), (‘z’, 40), (‘x’, 37), (‘q’, 29), (‘j’, 27)]
The script I wrote is not perfect but it’s at least a start at finding some optimum words
import sys
with open(sys.argv[1]) as fh:
words = [l.strip() for l in fh]
chars = {}
for char in ''.join(words):
chars[char] = chars.get(char, 0) + 1
frequency = sorted(chars.keys(), key=lambda c: -chars[c])
print(sorted(chars.items(), key=lambda c: -c[1]))
total_freq = 0
while len(frequency) > 5:
matching = words
letters = []
for char in frequency:
new_matching = [w for w in matching if char in w]
if new_matching:
matching = new_matching
letters.append(char)
if len(letters) == 5:
break
total_freq += sum([chars[c] for c in letters])
print("Matching %d new letters (%d%%) are: %r" % (len(letters), total_freq / sum(chars.values()) * 100, matching))
frequency = [c for c in frequency if c not in letters]
