39 ms·

It seems clear to me that there is an optimal starting word, but that the best second word has to depend on the info you gain from the first. Case in point: If

It seems clear to me that there is an optimal starting word, but that the best second word has to depend on the info you gain from the first. Case in point: If you get 3 green 2 yellow in the first word, you can solve on the next guess. Of course, you can constrain your strategies to "I always use the same two/three starting words", and in many cases that will be fine. But it's quite obviously not optimal. Also, the optimal strategy must depend on your goal metric. Do you go for "least average guesses", "least maximum guesses", or "least average guesses while never losing"? There's lots of unstated assumptions in all the analyses thrown around...

pyrale 5y ago
> Case in point: If you get 3 green 2 yellow in the first word, you can solve on the next guess. That's a very specific edge case, though. I agree with you that the second word should vary depending on the first result, but picking the best first and second words require lots of analysis. The first word should be picked in order to open up the best options for second word, and while I believe the second word should not contain letters from the first, unless you got extremely lucky, the distribution of letters of remaining available words probably changes which letters you want to cover. Failing to do the required analysis, my current strategy is to pick two words that cover the 10 most common letters in english, ETAOINSHRD. Sometimes it's "ethos" and "nadir", sometimes "thine" and "roads", etc. So far, it's worked well.
nwiswell 5y ago
> It seems clear to me that there is an optimal starting word I took one step further and calculated the optimal starting word for obtaining green matches (I assume that this also makes it likely to produce yellow matches, although I did not explicitly optimize for that). Beginning with the full list of 5-letter words, I calculated the frequency of each letter of the alphabet in each of the 5 possible positions for a 5 letter word. Then I iterated through the list a second time, this time assigning a score for each word equal to the sum of frequencies for each letter in its respective position. By a significant margin, the highest score is SLATE (over 1400). Runners up (over 1300) are SAUTE, SHIRE, and CRATE. Caveat: this approach assumes that all possible words are equally likely to be the answer.
- codefined 5y ago
  Interestingly, doing a similar analysis where we bucketed each word into 243 (3^5) buckets based on the possible result, we found "RAISE" as the best word. Source[0] [0] https://gist.github.com/popey456963/a654e98d0180566b897b70ee54c400e2 https://gist.github.com/popey456963/a654e98d0180566b897b70ee...
  - nwiswell 5y ago
    RAISE also sounds pretty plausible. How is the score calculated? What is the trade-off between expectation greens / expectation yellows? Intuitively I expect that greens are significantly more "valuable" than yellows, since they reduce the search space much more... Maybe this is all the wrong approach and the right metric is how many legal answers remain after the first guess?
    - PennRobotics 5y ago
      I would say that the distribution of yellow letters in the remaining word determines the value. If you have a yellow "X" or "Q" or one yellow vowel after testing all 5 vowels, that is a lot more meaningful than a yellow "T", which could really go anywhere. A yellow "G" but grey "I" tells me (at least intuitively, not quantitatively) a bit more than a green "I" and grey "G". A recent word had a single vowel. This made it reasonably easy to guess where those vowels could go and to also choose a consonant-heavy next word that would really tear apart the search space if even one consonant was valid. I think I'll switch to using RAISE or SLATE as a first choice. It was ADIEU before, but there's almost never an A in slot 1, U in slot 5, or D in slot 2, and I don't feel like any of these letters has a significantly most common position with just the info from these 5 letters. The yellow/grey letters are helpful after ADIEU, but I still need to explore at least 4 more letters (including O, and usually N or C) to even get a good idea of where any matches might go. In the moments that letter 4 is "E" while guessing ADIEU on round 1, that actually doesn't help me much with round 2. In fact, then I'm faced with the decision to explore unguessed letters in general, words with two "E"s, and/or words with "E" in 4th position. (same with "I" in 3rd)
    - EveYoung 5y ago
eightails 5y ago
> It seems clear to me that there is an optimal starting word, but that the best second word has to depend on the info you gain from the first. Definitely. The likelihood of a letter appearing in a given place changes depending on the letters around it. A Q will almost always be followed with a U, for example. I wrote a script yesterday which spits out the relative probabilities of possible letters in each unknown position, given the current known/excluded letters -- it was interesting to see the effect in action.

pyrale 5y ago

> Case in point: If you get 3 green 2 yellow in the first word, you can solve on the next guess. That's a very specific edge case, though. I agree with you that the second word should vary depending on the first result, but picking the best first and second words require lots of analysis. The first word should be picked in order to open up the best options for second word, and while I believe the second word should not contain letters from the first, unless you got extremely lucky, the distribution of letters of remaining available words probably changes which letters you want to cover. Failing to do the required analysis, my current strategy is to pick two words that cover the 10 most common letters in english, ETAOINSHRD. Sometimes it's "ethos" and "nadir", sometimes "thine" and "roads", etc. So far, it's worked well.

nwiswell 5y ago

> It seems clear to me that there is an optimal starting word I took one step further and calculated the optimal starting word for obtaining green matches (I assume that this also makes it likely to produce yellow matches, although I did not explicitly optimize for that). Beginning with the full list of 5-letter words, I calculated the frequency of each letter of the alphabet in each of the 5 possible positions for a 5 letter word. Then I iterated through the list a second time, this time assigning a score for each word equal to the sum of frequencies for each letter in its respective position. By a significant margin, the highest score is SLATE (over 1400). Runners up (over 1300) are SAUTE, SHIRE, and CRATE. Caveat: this approach assumes that all possible words are equally likely to be the answer.

codefined 5y ago
Interestingly, doing a similar analysis where we bucketed each word into 243 (3^5) buckets based on the possible result, we found "RAISE" as the best word. Source[0] [0] https://gist.github.com/popey456963/a654e98d0180566b897b70ee54c400e2 https://gist.github.com/popey456963/a654e98d0180566b897b70ee...
- nwiswell 5y ago
  RAISE also sounds pretty plausible. How is the score calculated? What is the trade-off between expectation greens / expectation yellows? Intuitively I expect that greens are significantly more "valuable" than yellows, since they reduce the search space much more... Maybe this is all the wrong approach and the right metric is how many legal answers remain after the first guess?
  - PennRobotics 5y ago
    I would say that the distribution of yellow letters in the remaining word determines the value. If you have a yellow "X" or "Q" or one yellow vowel after testing all 5 vowels, that is a lot more meaningful than a yellow "T", which could really go anywhere. A yellow "G" but grey "I" tells me (at least intuitively, not quantitatively) a bit more than a green "I" and grey "G". A recent word had a single vowel. This made it reasonably easy to guess where those vowels could go and to also choose a consonant-heavy next word that would really tear apart the search space if even one consonant was valid. I think I'll switch to using RAISE or SLATE as a first choice. It was ADIEU before, but there's almost never an A in slot 1, U in slot 5, or D in slot 2, and I don't feel like any of these letters has a significantly most common position with just the info from these 5 letters. The yellow/grey letters are helpful after ADIEU, but I still need to explore at least 4 more letters (including O, and usually N or C) to even get a good idea of where any matches might go. In the moments that letter 4 is "E" while guessing ADIEU on round 1, that actually doesn't help me much with round 2. In fact, then I'm faced with the decision to explore unguessed letters in general, words with two "E"s, and/or words with "E" in 4th position. (same with "I" in 3rd)
  - EveYoung 5y ago

eightails 5y ago

> It seems clear to me that there is an optimal starting word, but that the best second word has to depend on the info you gain from the first. Definitely. The likelihood of a letter appearing in a given place changes depending on the letters around it. A Q will almost always be followed with a U, for example. I wrote a script yesterday which spits out the relative probabilities of possible letters in each unknown position, given the current known/excluded letters -- it was interesting to see the effect in action.