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Is Wordle always beatable under optimal play?
Is Wordle always beatable under optimal play on easy mode (where you can guess any valid word)?
To put the question more formally, does there exist a deterministic computer program that can play Wordle successfully, without cheating, for every target word? Wordle is a deterministic game besides the hidden target word, and there is a known, finite list of target words, so this question should be decidable. An examination of Wordle's source code shows that there are 2,315 possible target words and 10,657 additional allowed guess words (12,972 total allowed guess words).
Bonus questions.
(These are included in case an answer happens to have them; they are not necessary to answer the question.).
Is the answer different for easy mode (where you can guess any valid word) vs hard mode (where your guess has both be a valid word and match the clues you've been given so far)?
If there is such a program, what is the word it uses for it's first guess? (If the program is deterministic, it should always use the same opener).
What is the worst case performance of an optimal program (ignoring the 6 guess limit if there is no optimal program that always wins)?
Question from user Zags at stackexchange.
Answer:
Wordle is always beatable under optimal play, on both easy and hard modes. This is doable using Knuth's minmax algorithm for mastermind with a curated starting guess tree.
Here is an example program that does so on easy: https://codegolf.stackexchange/a/242412/73123.
This program wins in at most 5 moves despite being suboptimal (at a minimum, the codegolf challenge restricts the guess space to the 2,315 word list when actual Wordle has 12,972 allowed guesses). It uses the starting word "LANCE", along with a curated list for some of the 2nd and 3rd round guesses, and the word that creates the smallest max split for the rest of it's guesses. Its win distribution is:.
Turn 1: 1.
Turn 2: 49.
Turn 3: 871.
Turn 4: 1354.
Turn 5: 40.
Here is an example that wins every game on hard mode: https://gist.github/zags/a093467ee6e71fd35ff849a5b76f22e5.
It's worst case performance is 6 moves, and uses the starting word "CALMS" and if it's a total miss, uses "BENTO"; otherwise, it uses the word that creates the smallest max split, with a small weight for guessing valid answer words over non-answer words. Its win distribution is:.
Turn 2: 94.
Turn 3: 834.
Turn 4: 1120.
Turn 5: 253.
Turn 6: 14.
Answer from user Zags at stackexchange.
Is Wordle always beatable under optimal play on easy mode (where you can guess any valid word)?
To put the question more formally, does there exist a deterministic computer program that can play Wordle successfully, without cheating, for every target word? Wordle is a deterministic game besides the hidden target word, and there is a known, finite list of target words, so this question should be decidable. An examination of Wordle's source code shows that there are 2,315 possible target words and 10,657 additional allowed guess words (12,972 total allowed guess words).
Bonus questions.
(These are included in case an answer happens to have them; they are not necessary to answer the question.).
Is the answer different for easy mode (where you can guess any valid word) vs hard mode (where your guess has both be a valid word and match the clues you've been given so far)?
If there is such a program, what is the word it uses for it's first guess? (If the program is deterministic, it should always use the same opener).
What is the worst case performance of an optimal program (ignoring the 6 guess limit if there is no optimal program that always wins)?
Question from user Zags at stackexchange.
Answer:
Wordle is always beatable under optimal play, on both easy and hard modes. This is doable using Knuth's minmax algorithm for mastermind with a curated starting guess tree.
Here is an example program that does so on easy: https://codegolf.stackexchange/a/242412/73123.
This program wins in at most 5 moves despite being suboptimal (at a minimum, the codegolf challenge restricts the guess space to the 2,315 word list when actual Wordle has 12,972 allowed guesses). It uses the starting word "LANCE", along with a curated list for some of the 2nd and 3rd round guesses, and the word that creates the smallest max split for the rest of it's guesses. Its win distribution is:.
Turn 1: 1.
Turn 2: 49.
Turn 3: 871.
Turn 4: 1354.
Turn 5: 40.
Here is an example that wins every game on hard mode: https://gist.github/zags/a093467ee6e71fd35ff849a5b76f22e5.
It's worst case performance is 6 moves, and uses the starting word "CALMS" and if it's a total miss, uses "BENTO"; otherwise, it uses the word that creates the smallest max split, with a small weight for guessing valid answer words over non-answer words. Its win distribution is:.
Turn 2: 94.
Turn 3: 834.
Turn 4: 1120.
Turn 5: 253.
Turn 6: 14.
Answer from user Zags at stackexchange.
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