In the 1960's my dad programmed Jotto (a simpler five letter secret word game) on Kodak's computers. Entropy became the first interesting mathematical concept that I learned.
Log base 2 of the remaining words is a measure of how many yes/no questions it would take to identify the word. An entropy strategy looks for a clue word that minimizes the expected value of this measure. One optimizes sum p log p over the pile sizes.
Pure mathematicians prefer certain concepts with a religious fervor. Often this has been informed by a reasonable number of problems where a concept has been proven optimal. The best applied mathematicians understand pure math but prefer practical work. To a pure mathematician, the rest are just guessing.
Here, one needs a clearly stated objective function for measuring success. Entropy strategies are often optimal for simple objective functions.
A critical detail for this game: The secret words come from a shorter list than the valid guess words. One wants a guess word that best partitions the shorter list of secret word candidates, not the full list of valid guess words.
Hah funny to see other people strategizing like this..
I did some research and (from what I found) the most common letters in English are:
E, O, T, A, I, R, N, H, S (not in any order)
So I came up with TRAIN and SHOVE as 2 starting words that use all those letters without repeats, plus V.
WORLD is also a good one because it uses one of the most common starting letters (W, T, A, O, D) and one of the most common ending letters (E, D, S, T).
Some other good starting words for me have been RIVET, CANDY, PLUCK and BASTE.
I do not. According to the original article, Wordle uses[1] 2,500 common words out of the 12,000 5-letter words in the english language[2]. I use the 5 letter words in the collins scrabble dictionary (which is about 12,000 words).
The assumption you need to make for my analysis to be correct is that the letter patterns in the 2,500 possible answers is statistically similar to the distribution of letter patterns in the original 12,000. There are probably some differences between the distributions, and I'd love to rerun my code with the actual word list Wordle uses, but in the absence of that list, I think that my code does about as good as possible.
[1] uses for the answers; I assume it allows all 12,000 for guesses.
[2] NYTimes does not specify which source they used
I did some analysis on this last week [https://noxville.medium.com/raising-the-wordle-first-guess-b...], ROATE left the lowest average valid answers (60.424) but 195 in the worst case. RAISE was the second best average (61.0) but a much better worst case of 168 words. Both are just heuristics, there might be a better word than either if the game were solved.
Yes, it's in the list of guessable words - however it's not a valid answer word. You need to use the WORDLE word list in order to evaluate how good or bad your initial guess is, using another word list will provide distorted results.
That's what I was clarifying with 'Yes, it's in the list of guessable words - however it's not a valid answer word'.
They have two lists of words: one is a list of possible answers, and another is a list of extra (valid) words which can be guessed (in addition to the words in the answer list). Sometimes it might be better to use a non-answer word as a guess: the best case gets worse (since you cannot win immediately) but the average case and worst case both get better.
> You are trying to use the word that once you get the match result back, it discards the most number of words.
This isn't strictly true either. Two N-sized subsets of words from a common initial set might have completely different difficulty in reducing further, because in the worst case there might not be a valid guess which nicely spreads the remaining words out among the 243 possible outcomes for that guess.
Set-size is a good heuristic, but it's just that - a heuristic.
Yes, as you'll see in the readme that I have numbers for both approaches. The first section is the average number of remaining words after getting the match result back, and the second section is the average number of yellow and green squares.
You might also try maximum instead of average. This is minimax and represents worst case scenarios for each guess.
This is mostly useful for optimal play against an opponent (which is not the case here). Imagine an adversarial version where the opponent doesn't have to commit to a word at the beginning but must reveal one matching all clues if you can't get it in 6 guesses (basically, they can change their word when you guess and you are trying to make that impossible).
I think it's an archaic spelling of the verb "steer". I remember the edition of Treasure Island I had as a boy has Long John Silver use it in the line "We can stear a course, but who's to set one?" when they are discussing whether to mutiny.
Though when I google that phrase, Silver uses the modern spelling.