In principle, Summer supposes, you could only do it while on GABAergics, but that sounds a little excessive even for her. She never has very strong opinions about what would make sense with more advanced mindhacking than can be accomplished with modern drugs and psychotech, because it's just far too confusing a topic.

....Celene has no opinions on this.

Oo! Summer found a setup of one of the classic Eifweni board games that Celene has presumably never played. She's going to drag Celene into a match.

"Hey Celene! Come play Shashangua."

....Murder Mount Melon?

"Oh! Uh, sure! How is it played?"

...Huh. That must be one of today's lucky 7776?

Celene finds herself in front of a Shashangua board, which has been depicted below with piece designs that are perhaps slightly more abstract than those Celene is watsonianly seeing.

Summer is... yeah she's going to just pull up the wiki page that explains piece movement on her phone and slide it over to Celene. The diagrams will probably help her follow along with Summer's explanation.

Suppose, as one often does, that you are an ancient Eifweni board game artist and are considering the different ways in which a piece might move along a honeycomb grid. Obviously there could be any number of those, so you focus in on ones that contain a certain sort of symmetry that might later be identified with the dihedral group of order twelve.

That is to say, if you allow a piece to move across an edge to an adjacent hexagon, you will allow it to move to any of the adjacent six—this sort of piece would later be called the vizier. If you allow it to move through a vertex and along an edge to the closest hexagon in that direction, you'll allow it to do this in any of the six directions—this piece would be named the counselor. (The counselor's move, you may notice, keeps the piece confined to one of three different portions of the board, corresponding to a regular coloring of the hexagonal tiling.) And then, to see the full twelve-way symmetry... consider a piece which can move two steps upwards, and then turn 60° widdershins and move one more step. You'd take this to imply that it could also turn deosil, and could've started in any of the six directions. (This is the move of the paladin in early Shashangua, but it received buffs before the canonical modern form of the game settled.)

The obvious way to describe a move on a boring square tiling would be with a simple vector (a,b), assuming without loss of generality that a ≥ b. This in fact generalizes perfectly well to a hexagonal grid, except for the minor adjustment that your second basis vector should be at a τ/6 angle to the first rather than a τ/4 angle. So you can say that a vizier makes (1,0) moves, a counsellor makes (1,1) moves, and a paladin makes (2,1) moves.

Now, there are a lot of vectors here you could play with to get new move types, but really it starts getting kind of unwieldy quickly. (You also might note that unless a and b are coprime, the move has the same result as taking multiple steps as some piece with a shorter move.) The fool is a piece that can make (3,1) and (3,2) moves, but larger than that starts getting uninteresting (though there is a special case that we will return to later).

So the next thing to consider is sliding moves. A marquess is like a vizier, except once it moves one step it can continue making more steps in the same direction in a single move, until it is intercepted by an obstacle of some sort. An elephant is similar, except that it makes repeated counsellor moves.

The modern paladin piece can continue with a second step in a single move, though unlike the marquess and counsellor it cannot make a third (or more).

The final thing you can do is consider pieces that are compounds, rather than only having one type of move. The archon is a marquess-elephant compound, and can make the moves of either; the duchess is a marquess-paladin compound; and the hierarch is an elephant-paladin compound. The fool is sometimes described as a compound of a camel that makes (3,1) moves and a zebra that makes (3,2) moves, though neither of those pieces exist in the particular standard form of Shashangua that Summer is showing Celene now.

You can capture your opponent's piece by moving one of your pieces onto the hex it occupies; the game is won upon the capture of your opponent's seal. Generally, the seal moves as a vizier-counsellor compound, but once per game it is permitted to make a (4,1) giraffe move. The typical result of this is that a single strong attack on the seal uses up an important resource of your opponent's, but does not necessarily immediately lead to a loss if your opponent has prepared a safe-enough getaway region.

Generally if you are challenging a weaker opponent, such as for example an alien, it is considered polite to allow them to go first, so it's Celene's move.

Did Celene get all that?

Uh

Not really 

This seems, uh, like a rather complicated game that will take some time to learn and her head is spinning keeping track of all the different piece movements

It reminds her a lot of chess? But like, way more complicated, and at the same time, way... simpler? Like the platonic ideal of chess, with less of the weird technicalities bogging it down, but also on a HEXAGONAL BOARD with MULTIPLE PIECES THAT JUMP TILES and SOME THAT EVEN JUMP TILES REPEATEDLY

What's weird about a hexagonal board? You're the one who brought up hexmaps.

Yeah but all of our hex games just use hexagonal taxicab moves, if that! We don't have... all of this

You haven't even seen counselor moves before? Surely you've seen counselor moves before.

No! No she hasn't! Not in a *game*. Maybe in like, a math problem, but probably not that either!

Counselor moves, she thinks, or rather, (1,1) moves, makes a lot more sense to the human mind on a square grid rather than a hexagonal grid, because the corners are touching, rather than the tiles being entirely disconnected.

The pieces do have the same names on square boards. I recommend not trying to get me to explain triangular Shashangua, some things get annoying when the tiles aren't even-sided.

Anyways it's certainly plausible that such moves are more intuitive on a square grid when you are a small child but most Eifweni aren't small children anymore and do not find counselor moves very confusing!

Does Shashangua (or is it Summer telling her this?) think that possibly it might also have to do with the part where they've had time to be exposed to this game and familiarized with it? And that she, as an Earthling,.is used only to games with square grids or, if hexmaps, taxicab movement?

Celene is learning information through some combination of Summer's attempts to explain and scrolling through the wiki page on Summer's phone!

Summer thinks Celene is probably right but it still feels bizarre to her, it's not like she only encounters game elements that move like this in Shashangua.

Anyways uh

Is Summer sure playing this is a, good idea? She doesn't really have experience with this game and it seems really complicated and difficult to grasp the first time.