Surdle: Satisfiability Modulo Wordle | Hacker News Reader

Surdle: Satisfiability Modulo Wordle

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31 pointsmrry10 comments

For this problem, an enumerative solver may be more optimal (and faster); where optimality is finding the word with the least number of guesses: There are ~158k 5-letter words. Start with a word containing letters with the highest frequency of occurrence amongst 5 letter words (this prob distr is likely to be close to the distr in the english language). Make that guess. Eliminate any words containing black letters, or not having green letters in the right place, or missing a yellow letter. Pick the highest probability word from the remaining. Repeat.

This should almost always get you the answer in 3 guesses. [Edit: Realized after writing that 3 is too optimistic given you might not have enough constraints after the 2nd guess, and agree with dzdt's comment. 4 might be where we end up at.]

I would be curious to see the distribution of #guesses needed across the 158k words.

Not an expert (I've played thrice) but I think I read somewhere that the game has a much smaller list. Something like 2,500 or so, at least orders of magnitude from 158k.

Your numbers are not right.

I don't know which dictionary Wordle uses, but for scrabble competition (SOWPODS) there are 12478 valid 5 letter words. [1] By my experience the Wordle dictionary is similarly complete.

But while you overestimate the dictionary size you underestimate the number of moves required. I don't play optimally but have done 150+ rounds keeping all constraints satisfied with each play. The modal number of moves to win is 4 (about 50% of games); I get about 20% in 3 moves, 20% in 5 moves.

Over 75% of the time I find 4 or more constraint satisfying moves, even trying to favor eliminating common letters. It is implausible that an optimal strategy would decrease this to 3 moves.

Also to keep in mind: Wordle's dictionary of possible solutions is much smaller than the dictionary of allowable guesses. I have never seen an unfamiliar word as a solution, though I am far from knowing all 5 letter dictionary words.

[1] http://scrabbleguru-sowpods.blogspot.com/2013/01/words-by-le...

If I've understood the minified source correctly, Wordle has 2,315 words it can pick for the word of the day and 10,657 additional words that it'll let you enter.

Yes, I believe this is correct. I also noticed this in the source. A choice seems to have been made to use a curated list of more friendly-ish solution words.

Does anybody know good resources for learning z3. I find the docs hard and material is pretty scarce on the topic.

https://ericpony.github.io/z3py-tutorial/guide-examples.htm should be a quick start.

I have some links up here, including a video and a google colab notebook https://www.philipzucker.com/z3-rise4fun/ http://colab.research.google.com/github/philzook58/z3_tutori...

is this game the new flappy bird? Why are dozens of posts made every day?

A whole case study can be done on this game, because it’s unusually compelling in an organic way. It’s a nice, short activity that happens once a day, much like drinking a cup of coffee. It’s social in the sense that everybody is trying to guess the same word and you can share the results with emoji’s without spoiling it for others. It requires some minor deductive skills and since everybody is familiar with the English language, you have a decent starting point for what it might be.

The fact that it only happens once a day is interesting because it adds a sense of scarcity and accomplishment. I’m not saying it should or that such an emotion is a good thing, but just how most human brains respond to the game, the same way one’s heart tends to quicken near a cliff.

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