Wordle has now joined Spelling Bee, which I posted about two years ago, as part of my top of the morning mental fitness routine. My go-to place for Wordle is New York Times Games. For those who haven’t played, Wordle gives you six chances to guess the day’s five-letter word. The Times maintains a list of approximately 5000 acceptable words. Each guess has three possible outcomes: letters that don’t appear in the word in grey, letters that appear in the word but in a different place in gold, and letters that appear in the word in the correct place in green. There are hard and easy versions of Wordle, with the former requiring you to use green or gold letters in subsequent guesses, and the latter not making that stipulation. The Times uses the easy version.
Developing a Strategy
Most wordlers develop a strategy they consistently employ. Observing that every word contains one or more vowels, some wordlers will load as many vowels as possible into the first guess, examples being AUDIO or ADIEU. Other wordlers will go with the most frequently appearing letters, whether consonants or vowels. Wikipedia presents the frequency of letters in all English words and Bakhtiari’s recent article presents the frequency of letters in five-letter English words. The two distributions are similar, but not identical.
A strategy might involve the first two guesses, for example including the five most frequent letters in the first guess, and the sixth to tenth most frequent letters in the second guess. A wordler could go a step farther and use the eleventh to sixteenth most frequent letters in the third guess. For example, the 11 most frequent letters in five-letter words, in order of frequency are A,E,S,O,R,I,L,T,N,U, and D. The words STOLE and NADIR include 10 of the 11. I haven’t found two five-letter words that include the first ten letters. If you are lucky enough to guess three of the five letters in the first word, you might opportunistically try to guess the day’s word on your second guess, rather than slavishly following the strategy.
Competing with the WordleBot
The Times has a WordleBot, essentially artificial intelligence. The WordleBot plays the game itself and tells you how well you did in comparison to it and to the average player. The WordleBot has two huge advantages over us. First, it knows all the words in the Wordle dictionary. And, after each guess it can determine how many and which words haven’t been eliminated as possible solutions. Based on its experience, WordleBot has selected its own starting word, which is now SLATE. After the first round it can select a word that, based on its experience, it thinks will eliminate as many words as possible. WordleBot can keep doing this until it gets down to the word of the day, almost always on the third or fourth round.
I have noticed that WordleBot always eliminates all but a handful of words by the third round. I’ve also noticed that WordleBot doesn’t use a frequentist strategy like the one I’ve described above, but often its second guess includes letters identified as gold or green in the first round. I would dearly like to find out WordleBot’s algorithm for the second round.
It seems to me that, in the long run, because of the information it has gathered and analyzed, WordleBot will do better than any human player. In any game, a human might beat WordleBot by virtue of luck. The human could choose a better set of letters in the first round. At the end of the game, the human could be lucky in choosing from a handful of possible, rather than attempting to eliminate all but one word, as WordleBot does.
Competing with the Average Wordler
WordleBot tells every player how much their results were due to skill (defined as effectiveness at eliminating words) and due to luck and it compares the number of guesses they required with the average for other players. When I have a high skill score and have found the answer in fewer rounds than the average, I feel a fleeting sense of accomplishment in beating the average wordler. Maybe STOLE and NADIR consistently are better words to start with than theirs.
For what it’s worth, I’ve played 86 games, won all but 2, and for the 85 I’ve won my average is 4 guesses. As I’ve gained experience, more of my wins are in three or four guesses, and I now have as many wins in three guesses as in four.
Mind the Dialect
I also must remind myself that New York Times Wordle uses American English, so words like labor, ardor, armor, and favor are in the dictionary. But odor isn’t. And some of the selected words have a particularly New York flavo(u)r. For example, stein: here we say mug. Or this weekend, spiel: here we say megillah (just kidding).
Human Mind vs. AI
Like much of life, Wordle presents a competition between the human mind and artificial intelligence. AI uses search and algorithms. Human minds use heuristics and intuition. Maybe we humans can sometimes do better because we have a better intuition about the words the human minds at The New York Times will select than does a bot.
I’m also fascinated by the research about Wordle being conducted by Professor Bakhtiari, at nearby McMaster University. He and I have been in touch, and I look forward to commenting on his next paper. Maybe he will be exploring algorithms for the second guess. I think that represents the frontier in the world or Wordle research. And perhaps his research will help human minds like mine improve their heuristics.