The popular daily puzzle game Wordle requires one to identify an unknown five-letter word selected from a pool of around 2,300 common words. One tries to guess the word in as few tries as possible, with a maximum set at six. After each guess, you get three kinds of feedback: a letter is highlighted green if it is the right letter in the right location; yellow if it is a letter that is used in the word but appears in the wrong location, and grey if the letter is not used at all. I wrote about this a few weeks ago.
Some enthusiasts were not happy about the recent news that the word of the day, rather than being randomly selected, had begun to be curated by a human. (This may have been prompted by the fuss that occurred when the word of the day during the abortion crisis was FETUS.) This had resulted in some recent words being connected to a current event, so that the word last Thursday (Thanksgiving day) was FEAST and the day before that (the busiest driving day of the year) had been DRIVE. As a result, some people who were aware of this change had managed to guess the word on the first try. But it did not make them happy. I can understand why, because it shifts the puzzle from one involving logic to one in which you try to guess what is in the mind of the editor based on some current event, which is much less interesting. I had not been aware of this change, and there is some ambiguity as to whether, due to the criticisms, the puzzle has gone back to being random. I hope it has.
There have been various strategies suggested as to what is the best word to start with to try and get the lowest score. I always use as my starting word SALET, after I read this article that some researchers had found that it was the best choice, based on the frequency of letters.
A pair of MIT researchers recently set out to find the optimal starting word for the popular online puzzle, discovering that the statistically superior first guess is SALET, which is a 15th century helmet.
The peer-reviewed paper, titled “An Exact and Interpretable Solution to Wordle”, puts an end to the ongoing debate over what five-letter word constitutes the best opening move in the game.
“If you play SALET and you play intelligently you can assuredly win the game within five guesses,” researcher and MIT Ph.D. student Alex Paskov tells CNBC Make It. “You don’t even need that last guess.”
While WordleBot — an AI from Wordle owner New York Times which analyzes your strategy — recommends SLATE, CRANE, SLANT, CRATE and CARTE as the strongest openings, Paskov says the issue is that analysis wasn’t done using MIT’s computational capabilities.
“What the New York Times actually did to determine CRANE is they focused on a small subset of possibilities that they can solve on a basic computer,” he said. “But at MIT, we have a lot of resources, we have very fast computers, very big supercomputers. So we weren’t too afraid to face this bigger, more difficult task of exhaustively enumerating every possibility.”
Once I use SALET as the first word, based on the feedback, I use a table of letter frequencies to replace the wrong letters with other letters, using the more common ones first. There are different ways of finding letter frequencies. One is to take a large body of English language text and calculate it from there. But that gives extra weight to those letters that appear in words that occur more frequently, like THE. Another is to take the words in a dictionary and find the frequency from those words.
The letter frequency in English language text is:
E T A O I N S R H L D C U M F P G W Y B V K X J Q Z
The frequency based on the dictionary approach (using the Oxford English Dictionary) is:
E A R I O T N S L C U D P M H G B F Y W K V X Z J Q
Notice how the letters T and H are more frequent in the English language set, while R gets demoted.
I use the dictionary frequency table. So if on my first try of SALET, I get the feedback that none of the letters in SALET are correct, then since the remaining letters are R I O N C U D P M H G B F Y W K V X Z J Q, my next try is CURIO. If on the first try, the only correct letter is E and it is in the wrong place, I try OUNCE for my second attempt. And so on for the next try.
With SALET as the starting word, and using the frequency table to select replacements, I can usually get the word within three or four tries, only rarely needing to go to five, one short of the maximum of six.
The catch with starting with SALET is that since it is such an esoteric word, it will never be the word to be guessed and so my chance for guessing the word on the first try is zero. However, on one occasion I got that ALET were the correct letters in the correct locations so I got the correct word VALET on the very next try.