John Fremlin's blog: Wordle winning word unknown

Posted 2022-01-15 23:00:00 GMT

Winning at wordle (fun word guessing game) means to guess the hidden word within six tries, but ideally also quickly and without a complicated strategy.

What is the best opener? Justin provides a summary of approaches. If we accept that it's best to reduce the worst case number of words to guess between, then any anagram of raise is good; but then aesir is the best in terms of number of words you can correctly guess immediately.

However, looking at all pairs of words as an opener, then "roast incel" is attractive as worst case you have to choose between 16 words. There are many other pairs like this.

For triplets - assuming you just type in the three words before considering other choices - the best three leave you with five words to choose between, allowing you to win Absurdle in five guesses (three for the triplet, one to disambiguate the five words, then one to win). The computation for finding triplets which leave you with just five remaining words is more involved and took several days, hope I got it right:

The problem this brings up is that the best single opener under this metric is not in the best two words under the same metric, and general the best two words are not in the best three words under the same metric.

While for the first opener, the biggest set is of words that don't have any matching letters, with a triplet there are many sets of five words with different groups of matching letters. Going to four words does help, but not enough to disambiguate all these groups. For example, you might be left with angle,angel in one group and rival,viral in another. A feedback free strategy to win in six seems hard or impossible, though I haven't searched all quadruplets or deeper. I don't think we can be confident that an anagram of aesir is the best opener.

PS. If you play on hard mode, where you must use the letters you find, the worst happens when you guess 'right': forced to choose between tight, wight, fight, might, night, sight, light, eight, and have to go through each one in turn as you have to use .ight each time.

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