DeWordled Months

Published Monday, February 28, 2022 by Bryan

It has been a month since my last DeWordle post. In that time, I've given DeWordle a near-complete rewrite and redesign. I've refocused it on being a tool to think about Wordle games, instead of trying to be a game in itself. Like any tool, you can make up your own games to play with it, but using it as a tool to analyse gameplay is where I've had the most fun with it, and is what I'm going to do in the rest of this post.

I've played Wordle for two months now, and I've used two very different strategies in each of those months. While the internet is now full of endless posts telling you which word is the best one to start with to get the lowest score, what my experience seems to show is that there is no bad startword if your only goal is to guess the secret word before your guesses run out. Put another way, I think that a person with a large enough vocabulary should never lose at Wordle.

I'm making this assertion after trying two different starting word strategies, and never failing to guess the secret word. My strategy for the first month was to use the same start word every day: FOCUS. My strategy for the second month was to allow a program to chose a random start word for me.

Number of games (Y axis) won after N guesses (X axis)

My scores, as shown above, match what many have posited to be the "expected" distribution: mostly 4/6, with a few 3/6 and 5/6 mixed in. Of the other scores: 1/6 is obvious luck; 2/6 seems like half luck; 6/6 seems like a flaw in strategy.

Let's see if I can show why I think that via DeWordle. The following table is sorted by ascending score, with month 1's games on the left, and month 2's games on the right. The links in the "first word" columns will take you to a DeWordle showing the state after just that guess - most notably the number of secret answer words that match. The links in "score" columns will take you to a DeWordle showing the "full" game, with start and end words set, and all of the intermediate words I might have used to get the patterns in between.

Month 1: same start Month 2: random start
game # first word score (N/6) game # first word score (N/6)
228 STOOD 🟨🟨🟨⬜️⬜️ 2 1
246 EDICT ⬜️⬜️🟨🟨🟩 2
207 FOCUS  🟩🟨⬜️⬜️⬜️ 3 234 MAFIA 🟨🟨🟨⬜️⬜️ 3
211 FOCUS ⬜️🟩⬜️⬜️🟨 3 235 CLOAK ⬜️⬜️🟨⬜️⬜️ 3
214 FOCUS ⬜️🟩⬜️⬜️⬜️ 3 238 ELATE ⬜️🟩🟨🟨⬜️ 3
215 FOCUS ⬜️🟩⬜️⬜️⬜️ 3 239 BRISK 🟨🟨🟨⬜️⬜️ 3
220 FOCUS ⬜️⬜️⬜️🟨🟨 3 251 MOVIE ⬜️⬜️🟩🟩⬜️ 3
221 FOCUS ⬜️⬜️🟨⬜️⬜️ 3 253 SCREE ⬜️🟨⬜️⬜️⬜️ 3
222 FOCUS ⬜️🟩⬜️🟨⬜️ 3
226 FOCUS ⬜️⬜️⬜️⬜️⬜️ 3
203 FOCUS ⬜️⬜️🟨⬜️⬜️ 4 227 SIEVE 🟨⬜️⬜️⬜️🟩 4
205 FOCUS ⬜️⬜️⬜️🟨⬜️ 4 230 CHAIN ⬜️⬜️🟨⬜️⬜️ 4
206 FOCUS ⬜️⬜️⬜️⬜️⬜️ 4 231 MUNCH ⬜️⬜️⬜️⬜️⬜️ 4
209 FOCUS ⬜️⬜️⬜️⬜️⬜️ 4 232 SWAMP 🟩⬜️⬜️⬜️⬜️ 4
210 FOCUS ⬜️⬜️🟨⬜️⬜️ 4 233 DUKSY 🟨⬜️⬜️⬜️⬜️ 4
216 FOCUS ⬜️⬜️🟨⬜️⬜️ 4 236 GRAVY ⬜️⬜️🟨⬜️⬜️ 4
218 FOCUS ⬜️⬜️🟨⬜️⬜️ 4 237 BRING ⬜️🟨⬜️⬜️⬜️ 4
219 SPIEL ⬜️⬜️⬜️⬜️🟩 4 241 MOTTO 🟨🟨⬜️⬜️⬜️ 4
224 FOCUS ⬜️🟩🟨🟨⬜️ 4 242 DROWN ⬜️⬜️⬜️⬜️⬜️ 4
225 FOCUS ⬜️⬜️⬜️🟨⬜️ 4 244 UNCUT ⬜️⬜️⬜️⬜️⬜️ 4
247 SCENE ⬜️⬜️🟨⬜️⬜️ 4
249 SADLY ⬜️⬜️⬜️⬜️⬜️ 4
252 LOGIN 🟨⬜️⬜️🟨⬜️ 4
254 GRUNT ⬜️⬜️⬜️⬜️⬜️ 4
200 FOCUS ⬜️⬜️⬜️⬜️⬜️ 5 229 KNACK ⬜️⬜️🟩⬜️⬜️ 5
201 FOCUS ⬜️⬜️⬜️⬜️⬜️ 5 240 GENIE ⬜️⬜️🟩🟩⬜️ 5
202 FOCUS ⬜️⬜️⬜️🟨🟨 5 243 TODDY ⬜️⬜️⬜️⬜️⬜️ 5
204 FOCUS ⬜️🟩⬜️⬜️⬜️ 5 2 245 CHAMP ⬜️⬜️⬜️⬜️⬜️ 5
208 FOCUS ⬜️⬜️⬜️⬜️⬜️ 5 248 VINYL ⬜️⬜️🟨⬜️⬜️ 5
212 FOCUS ⬜️⬜️⬜️⬜️🟨 5 250 SWORD ⬜️⬜️🟩⬜️⬜️ 5
217 FOCUS ⬜️⬜️🟨⬜️⬜️ 5
223 FOCUS ⬜️⬜️⬜️⬜️⬜️ 5
213 FOCUS ⬜️🟨⬜️⬜️⬜️ 6

I think the favorable interpretation of this data is that my February games were on average better than my January games. Mathematically, that's certainly the case, with a mean score of 3.86 in February, vs. 4.07 in January. I think it's pretty easy to see that I had a couple of score-3 games bump up to score-2 games, and several score-5 games bump up to score-4 (with no score-6 games).

Looking at the differences between the score-2 and score-3 games, it also seems like FOCUS was not a great start word. I hesitate to say this, because while it's easy to write of "not included" squares as useless, that's not actually the case. A considerable part of my final guesses is figuring out what word I could make, given what's left. It's also obvious from game 224, that even when I did get a bunch of letters initially, I didn't always convert that information to a great score.

A hint if you're trying to guess which of the possibilities I guessed between the first word and the answer: I've always played on hard mode, keeping letters in place as soon as they turn green. In the last week or two, I have started playing Dordle and Quordle, where this mode of play does not work (for me, at least) at all. I'm still not sure if I'll change my Wordle playing to do the same.

Footnotes

  1. 228/MOIST was spoiled for me by reading Twitter before playing, and seeing references to a commonly hated word.
  2. 204/GORGE is from memory, and could therefor be incorrect. Apparently I didn't tweet it. I sort of remember being annoyed at an early game, though, and the patterns I've punched into DeWordle for it fit that theme.

Categories: Development