The best first word in Wordle…according to maths

Comments

1. Please see

   https://medium.com/@tglaiel/the-mathematically-optimal-first-guess-in-wordle-cbcb03c19b0a

   Tyler Glaiel
   (Tyler and Glair are both words)
   Dec 30, 2021

   With RAISE as the first guess, you will average 3.49546 guesses to solve but have that sweet, sweet chance of landing that hole-in-one (1:2315)

   This version of the bot finds a solution in 3.49417 guesses on average, and has a worst-case of 5 guesses (meaning, it *always* finds a solution). The ideal first guess using this method is ROATE.

   Please review the algorithm you “hacked mercilessly”, you should be able to reproduce or refute the above. And have a look at why you have RAISE in both feasible and unfeasible test words.

   easy mode
   ROATE 3.638 – not solution set
   RAISE 3.641 – not solution set
   RAISE 3.669 – potential solution

   hard mode
   ROATE 3.850 – not solution set
   RAISE 3.889 – not solution set
   RAISE 3.928 – potential solution

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   1. Hi Nick! Thanks for your comment. I think the difference here is that Tyler’s algorithm works slightly differently to this one—the first version scores words based on yellow and green squares, and the second looks just at the size of the solution set and not the entropy, hence they give slightly different results. 🙂

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   2. Interesting. Raise has been my typical opening wordle for a while now, and I was unclear why it wasn’t in the top 100. Now I see that these are two different methods. Which one is best? 3.49 does sound marginally better than 3.6something for the various versions of the entropy bassed model. Guess I’ll stick with Raise…

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2. Nick presents ROATE. I’ve been starting with ORATE and doing pretty well…mostly 3’s and 4’s. Same letters. Different order. Does order make a difference?
   Also… although you mention S as one of the most commonly used letters, I haven’t seen it come up that frequently in a winning word. Could it be that its membership in most common letters is connected to its use creating plurals? So far it seems that winning words don’t appear to be plurals.

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   1. Order does make a bit of difference because of the patterns created, but without looking into specific cases it’s a bit hard to work out exactly why! However, it could well be that R is a more common starting letter than O, meaning finding out whether there is an R in first place or not narrows down the search space more rapidly.

      The reason for the lack of plurals is that as I understand it the creator of Wordle excluded them when he designed the game!

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3. I’m surprised haole didn’t make it on the top 100 list? I’m not a math wizard or computer programmer, tho. 🙂

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4. I usually use “TRASH” and have found this works well most times. I was surprised this was not in your listing. Where would this rank?

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5. great

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6. I’m a little surprised by the paucity of d’s and h’s in the list. These are very common as far as consonants go. I have had good luck with “death” as an opener, but have also used others such as “crate” or “stare.”

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7. If the goal is guessing in the least amount of times, don’t you also have factor in not playing a word that has been played. I was under the impression they are not repeating words.

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   1. You could do that if you liked, but it feels a bit like cheating! 🙂

      Reply

      1. One problem with Steve’s idea is remembering all the answers. Writing them down would absolutely be cheating, since we’re doing this not, as he claims, to guess the answer in the least number of times, but rather to improve/maintain our mental alertness.
         Second problem, and even worse, possibly existentially so, is that at number 605 today, we’re well past one quarter of the possible words. What would we do without Wordle in 1710 days? Perhaps your computer could calculate the rate of anxiety increment as the last day approaches.
         Finally, I certainly don’t remember all the answers, usually can’t even remember today’s, but I’m pretty sure there have been repetitions. So there may yet be hope for us after the 2315 mark.

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