My (Ashok Gupta’s) strategy

I am not a computer or data scientist.  I don’t have access to super computers.  The strategy I am presenting here is based on empirical data.

In-a-nutshell
Wordle is a game of skill and luck.  Skill alone will take you only so far. In my experience, skillful use of analytical approach seldom yields scores of 3 or less. For that you need some luck or ESP.

Preamble
I have analyzed the characteristics of Wordle words beginning with the very first Wordle on June 17, 2021, to-date.  I keep this data base current.  The metrics I will be quoting here include 400 Wordle words (through July 24, 2022).  I have watched that as the number of entries in the database has grown, some of the metrics have undergone some shifts.  This is especially true with letter frequency by position.  It is my expectation that once there are “large enough” entries in the database, shifts will be minimal.  In my analysis, I treat the letter Y as one of the 6 vowels.

Objective
Primary objective: Average score of 3.5 (actual thru 400 Wordles 3.7)
Sub-objectives: 100% solve rate in 6 tries, 95% solve rate in 4 tries or less, 6 tries less than 1%
Actual Performance through 400 Wordles:

  • Average score: 3.7 vs the target of 3.5
  • Solve Rate: 99% against the target of 100% s
  • % Of 6 guesses required to solve: 3% against the target of less than 1%.

Strategy
There is no shortage of strategies.   The one I use can be characterized as start with “Maximizing hits” followed by “maximizing elimination” (either 2nd word or the 3rd word, depending upon what is revealed by the first word.)  Let’s call it the primary strategy.

There is a range of possible secondary strategies under the primary strategy. The two bookends for the secondary strategy, per my judgement, are:

  • Fixed first word strategy: start with the same word, day in and day out
  • Random first word strategy: start with whatever word comes to mind at the time (may be the same or different from one day to another, no constraint of any kind).

In my household, I use the first method and my wife uses the later.  Mostly, she does better than/equal to me.  I say that she has ESP when selecting the first and often the second word.  One of my neighbors has the same ESP skill.  One example – the word of the day was TRITE.  The first guess she chose gave her hits of the first three letters (TRI).  With these hits, possible answers were many, including TRIBE, TRICE, TRIKE, TRINE, TRIPE, and TRITE.  She solved it in two guesses by picking TRITE out of the 6. Go figure!

First word: I have used SOARE as the first word since the beginning thru July 22, 2022.  I chose this word based on frequency of use by position (i.e., 1st, 2nd, 3rd, 4th, 5th).  The rankings/frequency of the 5 letters (as of July 22, 2022) are shown below:

 

A different approach is to use a word whose letters have the highest frequency anywhere in the word.  The word I chose is ROATE.  The rankings/frequency of the 5 letters (as of July 22, 2022) are shown on the next page.

As you should have noticed ROATE has a slight edge over SOARE (about 2 pts – 42.2% vs 40.7%) in terms of getting a hit (green or yellow).

However, if both SOARE and ROATE reveal the presence of only one vowel, and you want to explore what other vowels may be present, SOARE offers a better option for the second word than ROATE.  There are only three five letter words that contain U, I and Y in any position – JUICY, UNITY and UNIFY.

The four most frequent consonants anywhere are R, T, L, and S (8.6%,6.9%,5.9%, and 5.4% respectively). So, in the case of SOARE, it would be nice to look for the letter T along with the three vowels (U, I and Y). Luckily, UNITY is that word.  There is no overlap of letters between SOARE and UNITY.

In the case of ROATE, we need to find a word that contains the letters S along with three vowels (U, I and Y).  Regretfully, there is no such word.  The word UNITY is a sub-optimal option since the letter T is repeated. The next best option is UNIFY, since there are no overlaps, but the letter F is not one of the top 10 most frequent letters.

Therefore, if the objective with the 2nd word is to discover the presence of U, I, and Y, SOARE offers a better option.

The frequencies of the six vowels (anywhere) in the descending order are – E, A, O, I, U and Y (10.1%, 8.9%, 7.7%, 5.5%, 3.5% and 3.1% respectively).  Since Y is the least frequent vowel, if you are willing drop Y in favor of another consonant from the 2nd word, the universe of possibilities increases tremendously.

If the objective is to test for I and U only with the second word (i.e., drop Y for now), the viable words to go with SOARE and ROATE are CULTI and SULCI respectively.  With these pairings we are able to cover the five highest frequency consonants (any of the five positions in the word) – R, T, L, S, and C.

In either case, the third word I use that looks for Y is NYMPH.  As stated earlier, whether to use NYMPH or not will depend on what is discovered by the first two guesses.  The frequency rankings of the four consonants in NYMPH, i.e., N, M, P, and H are #6, #11, #9 and #7 respectively.  If we consider the coverage of the 9 consonants covered by the three words (SOARE/CULTI/NYMPH, and ROATE/SULCI/NYMPH), the only missing letter from the 9 most frequent consonants are D (#8) and G (#10).

The 5-letter words that include only Y as the vowel are crypt, dryly, glyph, gypsy, lymph, lynch, myrrh, nymph, pygmy, shyly, slyly, tryst, and wryly – 13 in total. If we exclude the letters S, R and T (since there are covered by the first two words) we are left with glyph, lymph, lynch, nymph, and pygmy.  A further culling of the words to remove duplicate Ys leaves us with only 4 words, i.e., glyph, lymph, lynch, and nymph.  Since the letter L is already covered by CULTI/SULCI, NYMPH is the only 5-letter word left that does not repeat the consonants covered by SOARE/ROATE and CULTI/SULCI.

Key elements of the strategy I employ

  • Start with the same word
  • Choose the second word, based on the discoveries from the first word
  • Use “eliminate, not enumerate” (EnE) strategy for the third (and fourth if after the third guess, 3 or more possibilities still exist). Sometimes, based on the exact hits with the first guess, EnE may be applied to the second guess also. The EnE strategy is especially effective if the selection involves one of several (3 or more) words where only one letter is different. An example is Right, Sight, Tight, Light, Fight, Night, and Might.  It is obvious that enumeration (trying one word at a time) may go past the 6 guesses allowed.

 

EnE strategy
I will explain this strategy with examples in a separate post.  I will provide an intro here.

Let’s assume we are at the third guess and, based on the first and second guesses, there are 3 possible answers.  If we follow the “enumerate” path (i.e., try the possible solutions one at a time), the apriori probabilities for the scores of 3, 4 or 5 are 1/3, 1/3 and 1/3.   That says there is a 1 in 3 chance of scoring a 5 and 2 in 3 chances of scoring 4 or less.   Under the “eliminate” path we identify a word that would eliminate 2 out of 3 possibilities thereby narrowing the choice to just 1.  This means that the score will be a 4 100% of the time. As you can see under the “eliminate” strategy, we don’t have the risk of scoring a 5.

In some cases, the elimination word happens to be one of the viable answers.  In such a case there is a 1 out of “n” chance of scoring a 3. (“n” is the number of possible solutions).

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