I've been playing Wordle for the last few weeks now, and have been enjoying it quite a bit. Pretty quickly, the goal becomes to find the wordle with as few guesses as possible. So I was inspired to implement my own version and find out what the best possible starting word is.

I started by making my own implementation of Wordle. This wasn't trivial, as there are quite a few edge cases to consider. You can run wordle_game.py for the full experience.

My implementation allows three levels of assistance:

1. No help at all.
2. A reminder of which letters are absent and required.
3. A list of all possible words it could be, given the clues you have.

There is also an offshoot of this that allows you to get the level 2 assistance even when playing on another website. You just have to input which guesses you used and the color for each letter.

The way it works is actually really simple. I take the list of all the words accepted by the program (accepted words) and all the words the program might choose as a wordle (wordles). Note that there are about 5x more accepted words than wordles.

I then go through every accepted word and give it a score, based on how much information it gives you.

Scoring Algorithm (against a single wordle):

Score(S: start word, W: wordle):
1. Compute the information S provides about W
2. Compute [W*] = set of all wordles that would have provided the same exact information as W
3. return {score = number of wordles - size of [W*]}

Score (S: start word, [W]: all wordles):
1. Let W be a wordle in [W]
2. Compute Score(S, W)
3. Repeat 1-2 for all W in [W]
4. Return the average score

The best* starting words can be found in scores_linear.txt and scores_invsqrt.txt.

Top 5 linear scores:
roate 2254.575
raise 2253.999
raile 2253.669
soare 2252.699
arise 2251.274

Top 5 inverse sqrt scores:
reast 457.179
slate 455.365
trace 455.291
crate 453.671
salet 452.58

* best as measured by the metric discussed above, these scores do not account for subsequent guesses, which is quite significant

• I actually scored words using two slightly different algorithms. One is exactly as I describe above, while the other actually measures the score as the proportion by which the number of possible wordles is reduced.

  • It actually takes the square root of this proportion so as not to weight high scores too heavily.

• Scoring a word against a single wordle runs in time O(n), since it needs to iterate through every other possible wordle. Scoring a word against all wordles (what we want to do) takes time O(n^2), hopefully that's clear enough. This takes about 2 seconds.
  Scoring every word against every wordle takes time O(n^3), or around 20,000 seconds. I could have left my laptop running over night, but I decided to make a basic heuristic to find good words more easily.
  Before taking the time to score a word, I would first check if (1) 4 of its letters are in the 7 most common letters and (2) it has all unique letters. I was then able to score around 850 words in less than 30 minutes.
  Interestingly, we can sort of invert this heuristic to try to score the worst possible words.

  Bottom 5 linear scores:
  xylyl 1446.953
  susus 1440.54
  fuffy 1432.276
  jujus 1409.61
  immix 1330.736