Surdle: Satisfiability Modulo Wordle
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Surdle: Satisfiability Modulo Wordle
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Re: Surdle: Satisfiability Modulo Wordle
#2For 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.
Re: Surdle: Satisfiability Modulo Wordle
#3Does anybody know good resources for learning z3. I find the docs hard and material is pretty scarce on the topic.
Re: Surdle: Satisfiability Modulo Wordle
#4Does 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.
Re: Surdle: Satisfiability Modulo Wordle
#5For 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, o…
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.
Re: Surdle: Satisfiability Modulo Wordle
#6For 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, o…
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...
Re: Surdle: Satisfiability Modulo Wordle
#7For 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, o…
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 nu…
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.
Re: Surdle: Satisfiability Modulo Wordle
#8Does anybody know good resources for learning z3. I find the docs hard and material is pretty scarce on the topic.
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...
Re: Surdle: Satisfiability Modulo Wordle
#9Earlier quoted context omitted.
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 nu…
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.
Re: Surdle: Satisfiability Modulo Wordle
#10is this game the new flappy bird? Why are dozens of posts made every day?