Wordle, Wheel of Fortune, Jotto, & the Mathematics of Information Theory

Apparently I’m the only person in the world who doesn’t play Wordle.

I’m not entirely sure why I don’t, but I can think of a couple of possibilities: it’s far too competitive, it’s far too rigid, and it’s far too popular.

Okay, that’s three, not a couple. Big deal.

First, though, a little history: when I was a kid, I used to play Jotto all the time. Jotto, invented back in 1955, was a nice, calm, two-person pencil-and-paper game, which gave you as many guesses as you needed until one of you got the five-letter word that the other had picked. Also, inventor Morton M. Rosenfeld didn’t sell it to the Times or anyone else for three million dollars (he sold it to a different company, for—I’m sure—far less). Otherwise it was just like Wordle.

And now our paths diverge, even though we’re not in a yellow wood (nor a green one, for that matter):

  • If you’re in a mood for some real math (no, it’s not too heavy—just Algebra II level, and fully explained), check out this excellent article in Quanta. It will tell you a great strategy for Wordle (or Jotto). If you find it counterintuitive, so much the better. And, as a bonus, it gives you a fine introduction to the basics of information theory. It even gives you a real-life use of logarithms, a nice example of an answer to the ubiquitous “When will I ever use this in real life?” question.
  • Or, if you’re in a mood for popular culture, notice a curious fact about Wheel of Fortune. Suppose it’s the bonus round, or whatever they call the equivalent of Final Jeopardy, and the category is “What are you doing?”, so you’re sure that one of the words ends in “-ing.” Altogether too many contestants proceed to guess “g” as one of their consonants and “i” as their vowel. These are almost always wasted guesses, since they usually just confirm what you already know. But the trouble is that people like to be right (confirmation bias) even when being wrong is more useful! I often see this in the classroom.

Categories: Linguistics, Math