Archive for March 8th, 2022


The Things We Guess

For some reason I vaguely think of Mastermind as annoyingly confusing, due I think to edge-cases that are problems only in my imagination. Like, what if the target has two reds, but the probe has three, one of which is in the position that’s red in the target, and another one is…

As it turns out, this is not really a problem in practice, and people play the game all the time without having to have a philosophical debate about what response is correct in any actual case.

In Mastermind, the target can be any pattern of N colored dots, each of which is one of K colors; N=4 and K=6 for the standard game. In the “Word Mastermind” variant, the target is a three or four letter word in some language (English, say), and one is competing with the other player, so it’s okay if it takes lots of guesses, which is good because while a probe response may tell you that you have two letters exactly right, it doesn’t tell you which two.

8kCuxwZ7yVum6FPWordle (you probably know about Wordle, and apologies if you’re in the “Everyone shut up about Wordle!!!” camp) is a clever variant, in that rather than just being told how many “right thing in the right place” and “right thing in the wrong place” you have, you’re told, for each position in the probe, which kind of thing it is (right thing in right place, right thing in wrong place, or wrong thing entirely). This makes the problem much easier; what makes it much harder again is that you get only six probes (😱). It also has social-engineering stuff that turns out to be great, like there being only one per day, everyone getting the same one, and it being easy to share your results.

With those subtle but brilliant changes out there, a whole bunch of related “lots of information per probe, but limited probes, share to Twitter” (as well as some broader variants) games come into view, and given that we are all still bored out of our minds and at the same time overstimulated, many have caught on. All I’m really doing here other than talking to hear my own voice, is listing the ones that I’ve been playing more or less regularly. :) There are surely lots more (I’ve vaguely heard of a sound-based one, for instance, but never tried it); feel free to mention in comments!

I have I think a legitimately perfect record at Wordle itself, partly due to luck. I have a starting word that I always use, that I’m sure isn’t optimal but I don’t care :) and I always play in hard mode because although I can imagine a situation in which it would be a good idea to use one of my precious probes on a word that I know is wrong, it seems unlikely that it’ll ever occur. (The example in the image included here may be the closest I’ve come to that, but I prevailed!)

I have a not-nearly-perfect record at Octordle, which is just (“just”) eight Wordle boards at once, with just one additional guess allowed for each additional board (so 13 total). I do feel like I’m getting better over time, so that’s good. In general I’m not patient enough to plan my next probe with reference to more than like two boards at once, though, so winning for me mostly depends on winning each board with few enough probes that I have enough left for the rest. Or something like that.

(I gather that there is a four-board version also, but I haven’t played that more than once or twice. All or nothing, eh? YOLO and all!)

There’s the adversarial Wordle Absurdle, which is funny and evil, from qntm of the incredible Antimimetics Division stories. It doesn’t actually choose a word, it just gives as negative as possible a response to your probes, without eliminating all possible words. Which (unless I’ve missed a twist) means that for a given set of probes it always returns the same thing. The fun there is… I’m not sure exactly; maybe seeing how you can steer negatively through the space of words, and where you end up.

Going from words to numbers, we have Nerdle, which is just the same :) except that there are eight slots, the alphabet is 0123456789, +-*/, and =, and the target and valid probes are valid arithmetic equations (with exactly one “=” as the last non-digit symbol, for that matter, although that might not be required of probes I dunno). This is fun, feels the same as and also different from Wordle, and I think I have a perfect record there also so far.

Then jumping rather far (but there are lots and lots of directions!) there is Semantle. Here the probes are basically any word at all (although if it’s a word the game doesn’t know, you’ll get no signal), and the responses to the probes are similarity measures, in some similarity metric derived by some AI from some big corpus of news stories or something. You get as many guesses as you want; the instructions say it takes “dozens” (hahaha), and I think my best is like sixty-something, and typical is like a couple of hundred.

Playing Semantle is interesting; it’s feeling around in a very-high-dimensional space for the center of a big N-sphere, given just linear distance measurements, where the distance measure is a lot like our own feeling of concept relatedness, but is also different from it in ways that one is also feeling out.

“Hey, those words are basically synonyms, how can they have completely different distances from the target?” And then sometimes there’s an “Oh, that sense of the word” moment and you realize why, and other times there isn’t and you think maybe the AI is just weird.

I’ve definitely failed on Semantle, in the sense of wandering off before solving it, and then not wandering back until the next day when that one had expired.

So my routine now is that as soon as I think of it in a day, I do Wordle relatively quickly, start working on the day’s Semantle, and then or perhaps in parallel do the Octordle and/or Nerdle when I think of it. And occasionally go and poke at Absurdle just for fun. :)