Foresight

Here’s a section from the H-group Hanabi strategy page:

LINES

During your turn, part of figuring out the best move involves looking into the future to see what the next player will do. If they discard, will it be okay? Is there some obvious clue that they will do? And so on.

As you get better at Hanabi, you will need to do this prediction not just for the next player, but for an entire go-around of the table. And as you really get good at Hanabi, you will need to do this for as far in the future as you can reasonably predict. (Sometimes, this means 15 moves or more in the future.)

Similar to chess, initiating a move in which you can predict the next sequence of moves is called initiating a “line”.

In post-game reviews, we will often compare and hypothetically “play through” two different lines to see which one is better.

It occurred to me that I see the same skill being tested by math olympiad problems.

For example, in setting up a complex numbers approach, I tell my students that they should be able to see an entire viable path, from start to finish, before diving into calculation. Something like: “if I set this up with ABC as the unit circle, then points D and E can be computed using this formula and will be maybe 5 terms of degree 2, which means F would have about 15 terms of degree 4”, and so on.

That’s just a concrete example. In general, if you’re trying to prove something, you can think of the various techniques and tools you have much like chess moves or Hanabi lines. Just like in turn-based games, you’ll find there are dead ends, e.g. trying to apply so-and-so theorem to reduce the problem to proving X, but X turns out to be false. Or there will be lots of paths that look more promising, but you can’t see far enough into the future to completely evaluate them all, and then you have to use heuristics and intuition to prioritize between approaches.

(Though one thing that makes this easier for math is that you know exactly what your desired end state looks like, so you can actually work in both directions. That is, to prove “if A then B”, you can search starting from A towards B, or starting from B towards A. And it’s to your advantage to do both, because that makes searching easier.)

So it seems like this is a skill that’s common to a lot of problem-solving domains, but as far as I can tell there’s no established name for it. I asked my students about it, and I was told “look-ahead” is used sometimes by the Rubik’s cube community, but no other jargon came up.

I like the word “foresight” suggested by one of the OTIS instructors. What do you all think?