These are my thoughts about an online word game hosted by the New York Times called Wordle. The game picks a 5-letter word and the player tries to guess it. After each guess (up to 6) the game reveals for each letter of the guess whether the letter is correct, in the word but somewhere else, or not in the word at all. Results look like this:
Wordle 593 3/6
⬜🟨⬜⬜⬜
🟨⬜⬜⬜🟨
🟩🟩🟩🟩🟩
Blank (sometimes black) is for the letter not appearing anywhere in the word. Yellow means that the letter in that guess position is in the word, but somewhere else, and green indicates the right letter in the right place. Each row evaluates one guess.
For example, if the solution was “STRIPE” and the player guessed “PARTS” the game would respond:
🟨⬜🟩🟨🟨
There is a “P” but it’s not in the first position. There is no “A” at all. The “R” is correct and in the correct position “T” and “S” are in the word, but not in those locations.
Having a mathematics and computer science background, I immediately thought that the game is best played using information theory, maximizing the amount of information obtained by each guess. Information is maximized when the game’s possible responses are equally (or as close to equally) likely.
It was relatively straightforward to write a computer program I named “WOBOT” to play the game; however, there might be more to winning than just the pure math. One obvious requirement to play the game optimally is to know all the possible solutions. The NY Times wrote in August 2022 that there were 2,309 of them. That original list is available on Github: it came from the original Wordle game before the Times bought the rights, but includes 6 additional words that the Times considered too obscure or offensive. In other places, the Times says that there are 2,309 and here is that official list.
Continue reading
