Lessons from Wordle?

A game of wordle

The online game Wordle has got very popular lately, and resulted in several conversations about strategy – particularly the starting word. Some people pick a word with a lot of vowels (observing that most words have vowels) and some pick words with a lot of consonants (observing that words written without vowels are much more recognisable than words written without consonants.

Some people have realised that some letters are more common in English than others, and they pick a starting word with as many of those as they can. You might get even smarter about it and look particularly at the letter frequencies in 5 letter words viable in the game – even perhaps the different frequencies at the different positions in the word. You may get smarter still and update the frequencies once you have excluded words with information gathered from previous goes.

Check out the videos at the bottom of the page for an interesting look at this with a very nice explanation of information theory.

Some have suggested training an AI to play, but I don’t think that you need to do that because you can figure it out with logic and that is a) more fun and b) you actually get to know why the strategy is good (rather than just have a computer tell you it is good).

And yes, you can work out clever strategies aimed at fast wins – getting as many clues as fast as possible, and playing to maximise your chances of green or yellow squares.

But the problem is – you will lose. Quite often in fact. The reason for this is that there are simply too many similar words. No matter how clever you are with your starting word and your follow up plays, eventually you will encounter a situation where there are just too many possible words and not enough rows to narrow them down. Unless you are very lucky (or cheat) you will* lose from time to time.

In hard mode (in which you have to use the letters you’ve found in subsequent guesses), even playing like a machine, I think you will lose at least 1 in 50 games – winning on the 4th play on average.

No big deal if you are having fun – and in fact knowing that it is not possible to win every time – no matter how clever you are – is quite comforting.

But what if we want to avoid losing at all costs? This is another way at looking at optimisation – sometimes we are not concerned about the very best (the fast wins) but about the very worst (the losses). That’s a bit like structural timber grading (yes we got there!) because for construction timber it is not the good pieces that you need to pay most attention to – it is mostly about focussing on the bad ones.

If we want to optimise for avoiding loses we need to think about this in a different way. It is not so much about the first word, but where you are by the time you get to the fifth or sixth play. Somehow, after your fourth word you would need to have reduced the possible solutions to just a couple of words**!

Well, that isn’t possible. Not quite – but you can get very close. More interestingly, this is achieved by a quite counter-intuitive play:

Play these words in this order:

(Yes, you can win earlier if you find out 5 letters before playing VEXED or NYMPH)

These are not great words for getting green or yellow hits – but there is great value in the grey hits …this is how you narrow down the possible solutions. Sometimes, what seems like a failure is actually a success!

Optimised strategies are not always the most obvious ones – and the more important part is giving plenty of thought about what to optimise for.

Don’t believe this strategy works? Here is a Wordle solver that you can try for yourself with this pdf. (It uses 3729 words from “Collins Scrabble Words (2019)” that I consider to be most common – and loses only 16 times …that’s 1 in 230 games)

If you want the best starting word for quick win play, avoiding losses as much as possible – well the choice comes down to which words narrow down the possible words the fastest (on average). Good ones include:
PLUSH will give a pretty low loss rate if you are a good player

* At least I think so. Certainly it is not possible in hard mode. Maybe there is a way if you focus on finding new letters rather than placing letters you already know – but this also isn’t going to get you the quickest wins. I tried several ways to do it and couldn’t better this quite straightforward play strategy for not losing (almost at all).
** Yes, it could be more than two words if the result for one of those words definitely narrows down the list to one by the sixth play.

Bonus 1 – a great introduction to information theory through wordle

Bonus 2 – a version made with Excel, which contains some cool Excel tricks

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