InSight - a combinatorial quickie

Hello all, thanks for the math in the "how many initial positions" thread. As it turns out the game it was about is played on a 7x7 board with an initial setup of 4 white and 3 black men.

On grounds of these considerations I think it would be safe to assume that the number of possible initial setups is bordering on the 100.000 range, and in any case, quite enough.

The game is called InSight and there's more to it than meets the eye. It will end in about ten or twelve moves each.

InSight rules @ mindsports

I got 21557 positions.

That's less than I estimated from the other thread (I figured about half of the minimum there) but still a lot, considering that similar games like Clobber or Konane have only one and a few respectively.

Thanks for doing the math :)

(P.S. "similar" in that they're simple, combinatorial and finite. Of course InSight fills up, though far from completely, and Clobber and Konane thin out, likewise not completely. But that's just reverse mechanics.)

I got 354,844 positions in the 8×8 version. I would expect this to be divided by 8 (since there are 7! and 8! = 8 × 7! placements, not considering colours and symmetry) and then by 2 (since there are half as many colourings). The quotient is about 16.46 so it seems OK.

Am I missing something? The rules don't state anything about how a move is made?

can I just pick up any piece and place it anywhere else (yes 'in sight of' and so on)? Or are there limitations, like move in a row or column only? or also diagonally??

The rules state:

_On his move a player must place a man satisfying the following conditions:

The man may not be placed orthogonally adjacent to a like colored man.

The man must have at least one like colored man horizontally or vertically 'in sight'._

That's 'place', not 'move', so you add a man each turn (how would the object be achieved otherwise).

'In sight' means having an unobstructed view.

I changed "On his move a player must place a man satisfying the following conditions:" to "On his turn a player must place a new man satisfying the following conditions:" and clarified what "in sight" means. Thanks.

Interesting design, Christian! I'd like to play InSight online.

I did, against Gert Buschmann in the Sandbox at iGGC. It were my first two games (he had played it before against Arty) and the thing surpassed my expectations. Normally I'm not a 'last move' fanatic. In fact I considered it about as low as one can get, thematically. But I noticed how a tactical funny like Monkey Trap got a lot more reactions than a far great concept like Sygo.

I discussed this with Benedikt Rosenau and his view was that the simple mechanics and the easy to visualize goal played a role in that. So I took a look at Clobber and Konane, who both have lasting appeal, especially among Combinatorial Game Theorists. And I wasn't in for anything major, but still 'in the mood'.

The game eventually turned out far simpler than the process that led to it - in terms of rules that is. Playing it isn't simple at all and there's some real tactics emerging already. The wins weren't close either: I was out of moves when Gert had three secure moves left in the first game, and in the second it was the reverse, so there's some real strategy involved.

Eventually mindsports.nl will have applets, but I've been inventing faster since October last year than my partner in crime Ed van Zon can make the applets :)