Now that the word game Quordle is taking Glibertarians by storm, here’s my attempt to come up with just the right starting words. For those of you new to Quordle, a brief explanation can be found here. The basic idea is that there are four five-letter words, and you make guesses that apply to all four; the program tells you when a letter is in the word and if it is in the correct position. To succeed you must identify all four words in nine guesses or less.

Obviously you want your starting word or words to be more likely to match the four Quordle words. You can find letter frequencies in the English language, but they may not be the same for five-letter words. They also depend on what dictionary you are using; some are more complete than others. Taking a list of 69,903 English language words that I found on a University of Michigan website, I culled it down to 5,197 words with exactly five letters.

The position of a letter can also be important, since when you get an exact hit it reduces the possibilities considerably. Therefore determining where in the word different letters are likely to fall can also be helpful in choosing your starting words. The results for the 5,197 five-letter words (the last column shows frequencies with duplicate letters removed):

 

 

Note that the order changes in a few cases when duplicates are removed – A passes E, R passes S, I passes O, T passes L, H passes P, and J passes Z, but these pairs are very close in frequency anyway, so it doesn’t really matter.

For a starting set of words, we can calculate the total percentage of hits and the frequency of exact hits. As an example, Tundra’s standard starting words give the following total percentages and exact hits:

 

 

Note that the total percentages sum over all five positions, while the exact hits count only the position the letter is in.

RATED has the same letters as TRADE, but gets 45.6% for exact hits, as opposed to 44.3% for TRADE, so it looks like swapping out TRADE for RATED could improve your game a little by increasing the total exact hits to 112.3%.

But are there better starting words with different letters? Using exact hits as a guide, the letter A is the most likely 2nd letter, E the most likely 4th letter, S the second most likely 5th letter (after E), and R the third most likely 3rd letter (after A and I). They are also the top two vowels and consonants in overall hit percentage. Therefore a starting word ending in ARES would seem to be very good.

But what first letter to use? S is the most likely 1st letter, but you want to use a different letter to maximize your chance of finding letters. T and L are the next most likely consonants, even though they are not as likely to be a 1st letter as B or C. Using T, L, or C in front of ARES has some issues (see more on this below), and B is not nearly as likely overall. So I settled on D, giving DARES as a first word.

To form the second starting word, the remaining next most likely letters are, in order, O, I, L, T, and N. The only word with those five letters is Nilot (an inhabitant on the banks of the Nile River), which is capitalized and is not recognized by Quordle. (As an aside, Quordle does not allow you to enter a five-letter combination that it doesn’t think is a word.) So I decided to ditch the L and add a C, to get TONIC, since O and N are in their most likely place, I is in its second most likely, and T in its third most likely (not far behind the two most likely).

In some cases, the first two starting words are good enough that you don’t need a third word before trying for exact matches. If a third starting word is needed, the next most likely letters overall are L, U, M, P, and H, respectively, but there is no five-letter word with those letters. Dropping the H for the next most likely letter (Y), we conveniently can form the word LUMPY, with U in its most likely place, and Y as the third most likely letter to end a word. So we end up with starting words:

 

 

DARES has more hits and exact hits than RATED. The DARES/TONIC combo has about the same number of hits as RATED/SPOIL, but many more exact hits. LUMPY is only slightly worse than MUNCH. So, overall, DARES/TONIC/LUMPY looks like an improvement over RATED/SPOIL/MUNCH (and of course also over TRADE/SPOIL/MUNCH). DARES/TONIC/LUMPY has all five vowels and the vowel substitute Y, plus the nine most likely consonants.

After looking at more variations, another possibility is

 

 

This does better than DARES/TONIC/LUMPY on the first two words combined since it uses L instead of D, and has a better exact hit percentage on all three combined. To maximize just the first word using only E and A as vowels, there’s

 

 

although they are not as good through two or three words as the two previous triplets. Also, LARES comes from a proper name (Roman deities), and NICOL comes from the Nicol prism, named after William Nicol. Nevertheless, Quordle does recognize both Lares and Nicol.

Finally, Ownbestenemy tried using STOIC as a starter word. I think LEARN/STOIC/DUMPY is probably the best combo of that type, but only has 101.5% exact hits since a lot of its letters are not in a good position.

 

 

There are many caveats to this analysis. First, Quordle my use a different dictionary than I do; for example, they may only use a subset of words that are more common. I found a lot of weird words that I did not recognize among the 5,197 in the list, plus a number that are capitalized (like April) and/or are really acronyms (like ASCII); April and ASCII are not accepted by Quordle. On the other hand, some smaller dictionaries seemed to be missing some common words; one example I found with 3088 five-letter words did not have the words ABATE, ABHOR, or ABYSS, just within the words starting with AA or AB.

Second, Quordle may purposefully use words with less-likely letters, so using a likely hits table as a guideline may not be optimal. After doing a number of practice runs with DARES/TONIC/LUMPY and CARET/LOINS/DUMPY, it seemed to me to be missing more often than it should, but that could have just been an artifact of the small sample size. I very rarely “chump out,” i.e., not find all four words in nine guesses or less, using these two starting combinations.

If people give some of these a try, let me know how well they work for you, and feel free to use the data above to formulate your own strategy. What starting words are your favorites?