Comment on Wordle No. 943
January 19, 2024
Some of you may recall that I wrote software that can play
Wordle, the online game owned by and housed at The
New York Times. At the outset such software must know what
words are accepted by Wordle as guesses and what words might
be used as the solution in a game. Thus, the software must
employ two word lists.
There is one game every day. The first game in history (before
acquisition by The New York Times) was conducted online
June 19, 2021. Yesterday (January 18, 2024) was the day of game
no. 943. As that game is over, I may reveal its solution, which
was "stole". My favorite first guess is the word "roate". After
making that guess yesterday, I saw this:
It's relative rare for me to determine three of the five
letters with my first guess. My software, using a list of
what I think are words that might reasonably appear as
solutions, reported that the possible solutions among the
words on my list were "stoke", "stole", "stone", "stove",
and "those". At first glance it appears that I have a 20%
chance of guessing correctly on my second guess by picking
one of those 5 words at random. But I can dig deeper. For
each of those words I can hypothesize that that word is the
solution, use any one of the words as a guess for that
solution, and find the number of words that would still be
in play. In this way I can determine for each of those
words as a guess the number of words still in play following
that word as a guess, and select for my next guess a word
for which the number of words still in play is minimum.
With this example -- and using my word lists -- each of the
four words beginning with 's' is a better second guess than
the word "those".
There are two further wrinkles, one helpful and one not
helpful. The unhelpful wrinkle is that the solution may not
be on the list of words that I imagine as possible
solutions. For that list I had a good start because the
early game of Wordle had semi-public lists of allowed
guesses and possible solutions. As time went by, the list
of allowed guesses was significantly expanded but remained
semi-public. But the list of possible solutions dropped out
of semi-public sight, and, more to the point, there have
been four solutions over time -- in games 646 (guano), 659 (snafu),
720 (balsa), and 730 (kazoo) -- that were not on the early list
of possible solutions.
The helpful wrinkle is that up through today -- game 944 -- no
word has been used as a solution more than once. Quite
obviously, unless Wordle is discontinued before, say, its
10th anniversary in 2031, sole use solutions cannot continue
forever.
Why do I call that a helpful wrinkle? I expect that the Wordle
editor at the New York Times is aware of the history of sole use
and is aware that at some point sole use must be discontinued.
But for the meanwhile a player can gain advantage by assuming that
sole use is still in effect. With game 943 the assumption of sole
use narrows the list of 5 words in play to 2, "stoke" and "stole",
which means that a random second guess among those has a 50% chance
of being correct.
One more example. Suppose the first guess is "least".
Then
That is a remarkably lucky guess yielding 4 letters. The words in play --
using my list of possible solutions -- are "steel", "stole", and "style".
The "deeper dig" procedure flags "stole" and "style" as optimal second guesses,
but assuming sole use, there is only one optimal second guess, which is
"stole".
