81–90 of 159 posts
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This does not quite work. For today's word (abbey): - input "arise" (match "a", wrong position "e") - solver says there are 10 possible words, one of them is "apnea" - input "apnea" (match "a", match "e") EDIT: fixed - solver says there are 0 possible words (it assumes last "a" should appear yellow, but the wordle page has the last "a" as grey because there is only one "a" in the word)
Apnea would be match for “a” and “e”
One is to try to maximize the expected information gain of your guess. If we have an initial set of 128 possible words, we begin with log2(128) = 7 bits of entropy. When we make a guess and receive a response, we narrow down the list of words to the set compatible with that response. If, for example, there are 32 words compatible with our response, then we now have log2(32) = 5 bits of entropy, and our guess was worth 2 bits. For a given guess, there are many possible replies each with its own information gain - in the best case, we get all greens, and are left with 0 bits of uncertainty (for a gain of 7), while in other cases we may get all greys, and learn comparatively little. Further, each reply has its own probability of occurring - all greens is only 1/128, but other replies might be more likely if there are several possible targets that would generate the same reply. Thus, we weight the information gain of each reply by its probability to arrive at the expected information gain for that guess. For the word list provided in the article, I get TARES as the best first guess by this metric.
The second strategy is to continue down the game tree, and find the guess with the lowest number of expected (or alternatively the lowest worst-case) number of guesses. In principle, we might find that while TARES gains us a lot of information as a first guess, it leaves us without a good second guess (since we are restricted to guessing real words, and those words might all be redundant in some way), and thus our total expected number of guesses is larger than if we had taken a slightly less informative first guess. My hunch is that in practice this sort of situation is unlikely to occur, and the best first guess by this metric is probably similar to that of the first metric, although I haven't tried.
Earlier quoted context omitted.
This does not quite work. For today's word (abbey): - input "arise" (match "a", wrong position "e") - solver says there are 10 possible words, one of them is "apnea" - input "apnea" (match "a", match "e") EDIT: fixed - solver says there are 0 possible words (it assumes last "a" should appear yellow, but the wordle page has the last "a" as grey because there is only one "a" in the word)
Apnea would be match for “a” and “e”
- least time - fewest moves - fewest unique letters - etc.
Most interesting to me was solving in the least time and having fixed words to maximize letter coverage, which theoretically was 25/26 letters during first five guesses. Access to such a list would make it such that the goal is given those words, can we find the answer in less than some fixed time, e.g., one minute from start to finish.
Further interesting was attempting to find such a list without computer assistance, short of having access to word lists and filters, which ultimately led to a near optimal list of words for the first five moves with 24/26 letters:
** spoiler -> the (5) seed words are located at https://pastebin.com/D1DkzXA4 -- the password is gTgRCFrLYL
The 'a' is notably repeated, and worse, is in the same position; was planning to run a computer search to (1) explore if a perfect solution of five dictionary words with entirely unique letters exists &/or failing (1), then (2) is there a list with 24/25 unique letters or 1-2 repeated letters s.t. all letters are in different positions.
There are of course places where such a set of words with fairly maximal coverage still falls short -- a nearly so example is the word pair UNLIT and UNTIL. Determining how many such combos that might be nondeterministic with such a fixed set of starting words exist in the dictionary would be good if someone wanted to dig deeper, e.g., {ARISE, RAISE, AESIR, REAIS, SERAI} which was cited in another comment.
5.291 soare 5.294 roate 5.299 raise 5.311 raile 5.311 reast 5.321 slate 5.342 crate 5.342 salet 5.345 irate 5.346 trace 5.356 arise 5.360 orate 5.370 stare 5.382 carte 5.390 raine 5.400 caret 5.402 ariel 5.406 taler 5.406 carle 5.407 slane Shown are the twenty best initial guesses using Claude Shannon's definition of information entropy. Each number is the expected number of yes/no questions needed to resolve the rem…
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What was your source for "English words"? This is an interesting problem, itself.
Googling will give you countless lists. The internet solved that problem decades ago. The biggest problem is when your guessing dictionary contains words that aren’t in the acceptable word list in Wordle. For that, I generate 10 guesses on each turn. At least one of them should show up. I didn’t want to use Wordle’s dictionary because that felt like cheating.
A dictionary is not interesting, but for the selection of the contents.
> Googling will give you countless lists. The internet solved that problem decades ago.
That's not a solution when the definitive lists all differ. English is a high context language, so the existence of words is both a function of frequency and locality (this includes time periods). Deciding on what's the canonical list isn't "look up what Wordle uses" anymore than Webster or Oxford. That's the problem I'm referencing.
Earlier quoted context omitted.
This does not quite work. For today's word (abbey): - input "arise" (match "a", wrong position "e") - solver says there are 10 possible words, one of them is "apnea" - input "apnea" (match "a", match "e") EDIT: fixed - solver says there are 0 possible words (it assumes last "a" should appear yellow, but the wordle page has the last "a" as grey because there is only one "a" in the word)
SPOILER!!!!
Yesterday was the first time I played, after reading about some monetization thing on HN related to wordle. For me, my first guess was ABIDE, and was able to get AB in the correct location, with e in there as well.
Thinking that e was the second last letter, I was convinced it was ABLED, since it was the only word I could think of with an e in that position, but I didn't realize that I already tried D in the first word.
Using guesses 3-4, I wasn't able to narrow it down further than AB_E_. But I was able to eliminate some characters, leaving only ~ Q, X, Z, Y, J, K, F. In my mind, I couldn't figure out what 5 letter word could be made using just these letters, so I systematically tried swapping all combinations (wordle doesn't accept fake words).
It was only after that that I realized I could repeat letters, so I tried until I figured out duplicating B would give abbey, which seemed probably enough to be a real word.
“A strange game. The only winning move is not to play.”