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This question assumes a knowledge of Wordle's innards including a review of its source code. This blog is useful background reading.

Is it possible to fail (six unsuccessful guesses) at original Wordle without making mistakes? In other words, is there a Wordle word (from the solutions list) for which there is a valid (from the guesses list) and efficient (always using every clue perfectly) sequence of six guesses that fail? Consider easy and hard mode to be two versions of the challenge.

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    $\begingroup$ Looks like a valid question to me. Basically asking "in the solution tree for Wordle using optimal strategy, is there a word located at distance more than 6 from the root?" $\endgroup$
    – justhalf
    Jan 16 at 18:46
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    $\begingroup$ @justhalf exactly. Thank you for transporting me back 35 years to 3rd year information theory class. $\endgroup$
    – jay613
    Jan 16 at 19:53
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    $\begingroup$ Btw for completeness, can you put in the question as well what is the difference between easy and hard mode? I don't play Wordle, so not familiar with those. $\endgroup$
    – justhalf
    Jan 17 at 8:26
  • $\begingroup$ @justhalf This question assumes an exhaustive understanding of the game and its implementation, so I don't think adding basic descriptions of how to play it would enhance the question. Easy mode allows you to ignore prior clues to some extent. This allows certain strategies including guessing (which I think is why it's called easy) and strategies that sacrifice occasional very high scores in favor of a better average score. Hard mode requires each guess to be consistent with prior clues. $\endgroup$
    – jay613
    Jan 17 at 12:20
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    $\begingroup$ What is the play optimizing for? Lowest score, or just getting the word? They may have different strategies, leading to different results (and hence, different answers to your question). $\endgroup$
    – Abigail
    Jan 17 at 16:54

1 Answer 1

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For 'easy' mode:

No, it is not possible to fail with optimal play. Using some of the strategies outlined in answers to What's the optimal strategy for Wordle?, I found several decision trees that will successfully identify any given solution word in five or fewer guesses.

For 'hard' mode:

There might be a few. For example, if the solution word is one of {bound, found, hound, mound, pound, round, sound, wound}, you might run out of luck. You would need to guess something like PRISM or SHARP early in order narrow down that list.

After modifying my code, I have found a few decision trees that miss only two words. The search was nowhere near exhaustive, so these are not necessarily optimal. I have not ruled out the possibility of a 100% successful decision tree.

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  • $\begingroup$ I feel like the hard decision tree would have to look at the cases where you have a lot of words off by 1 letter and try to take as many out as possible right away, then hope to keep everything to 6 guesses $\endgroup$ Jan 16 at 21:42
  • $\begingroup$ I don't understand "trees that miss only two words" when your example provides a list of 8 words that might be ambiguous at step 5. $\endgroup$
    – jay613
    Jan 17 at 12:37
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    $\begingroup$ @jay613 then in his decision tree it must be the case that the earlier guesses can split them apart on different branches, except for two. $\endgroup$
    – justhalf
    Jan 17 at 13:43
  • $\begingroup$ @Daniel, do you have the decision tree that you mentioned for easy mode somewhere? I would like to see it. $\endgroup$
    – justhalf
    Jan 18 at 9:35
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    $\begingroup$ My code has only shown that such trees exist. I have again modified my code to search multiple branches at each guess in order to find more optimal trees. An overnight run, checking each possible solution word as first guess, has identified over 900 that have 100% successful trees in hard mode. Next, I'll work on saving some of those trees so that I can share. $\endgroup$ Jan 18 at 10:17

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