ABOUT

How I got started

I started these trees by asking, "can a player choose words so that they always win Wordle?" The answer was quickly, "yes." There seemed to be a lot of room, even in Hard Mode, to sort out the dictionary.

Then I wondered, can I ensure an answer in five turns or less? That took a little more computation, but it turned out to be possible.

Then I set myself a goal of winning in two turns. Winning in two turns, of course, requires some luck, but what is the best starting word to maximize the chances?

Then I started looking at other goals, like minimizing the expected number of turns.

Why Analyze Hard Mode?

All of these trees assume we are playing in Hard Mode. That is not due to a preference for Hard Mode, it is due to the practical fact that Normal Mode is hugely more complicated to analyze.

What are Pure and Open Play?

These are not terms from the game, just terms I invented.

The game uses a dictionary of 12972 words that are legal to guess, and a dictionary of 2315 words that can be the answer word.

I use "Pure Play" to mean only guessing from the smaller dictionary. This can be seen as "every guess can be an answer."

Open Play uses all the allowed guess words.As a rule, the Pure Play trees in this collection are the result of complete searches. The Open Play trees only search about 1000-4000 starting words, using a heuristic. The Open Play scripts haven't found any good starting words past the first 200 under this heuristic, but I can't say for sure these are the best results.

I separated Pure and Open Play because the list of Open words includes some weird ones. Restricting to Pure Play, however, is not realistic, because the smaller dictionary does not include a lot of common words, particularly plurals and present-tenses of four letter words. So Pure Play is too restrictive, and Open Play is too open. Neither is really a model of human play. Open Play has the advantage of being strictly the allowed set of guess words, but the disadvantage of making it much harder to do complete analysis.

Allowing Losses

All of the first trees assume, in addition to the stated goal, that you want to never lose. The second collection are for the case where you maximize/minimize your goal while allowing for some losses.

Purpose

As a math nerd, I really just wanted to see what could be done with the game, combinatorially. The underlying questions are about a specific graph with colorings based on the English language.

I suppose that one could use these trees to cheat, but is that really interesting? There are so many easier ways to cheat. You can just read the code to find tomorrows word, if you wnant.

Personally, I usually play the game myself, then, after I find the answer, I look at how various trees do in solving it. Sometimes, the trees inform me about words I might try, like COULD.

When I play, I often use one of these first words, but the rest of the words are just my guesses. I rarely play in Hard Mode.