In Winning Ways Volume 2 (pg. 334) they say

In many ways the games and behave like enormously magnified versions of and

& give us an **infinitely magnifying operation**
defined by

As an example they also give:

Which reminds me of the function ..

After reading the affine games paper & then seeing the formula in my notes again, I got to thinking…

They essentially define
.
No problems there. But they also define
.
I don’t have a *problem* with that. I just think
is, well..
*bigger* 🤷♀️

**Aside** interval
arithmetic & fuzzy numbers

It made me wonder if something like

would be valid.

I also wondered about this equation, because I find it rather aesthetic:

I might call this a *moon magnifying* operation &
speculate that

I was also trying to think about game analysis for projective games.
I think chess endgames could be a good fit since loopy situations are
possible. Also, affine theory defines *check games*. So it seems
a rather natural setting.

Was playing around with some custom cases as well just for fun ( x boards w/ 2 kings).