New game I'm messing around with

[Dave Boll]

I've been checking out the following strategy game, and am not really
getting anywhere wrt finding a strategy. But, the game is (maybe)
interesting, so here goes:

Board: NxN, square, I'll illustrate below for N=3
Starting config:

B B B
- - -
W W W

Movement: pieces can take one rookwise step to any unoccupied square

Piece types: There are 3 types of pieces: (B)lack, (W)hite, and
(N)eutral. Any move that results in 2 pieces of different types becoming
adjacent flips both pieces to the third type. On any turn, a player may move
their own piece or any of the Neutral ones.

Goal: Win by wiping out your opponant - all pieces on the board are either
yours or neutral.

Sample game, with comments:

B B B Starting position
- - -
W W W

N B B W has only 2 unique moves, and the center one is a loser, since
N - - B could just push the N piece in the middle back down for an
- W W instant win

N B B Moving the N piece to the center doesn't result in any flips,
- N - since it is now adjacent to more than one kind of piece.
- W W

N B B Again, no flips, since the W piece toughes both a B and a N
- N W
- W -

N B B
N - W
- W -

N B B Is W on the ropes? Hard to say!
N W -
- W -

N B B B takes the greedy move
- W -
B B -

N B W W gets some pieces back, and threatens from the upper left corner.
- - W
B B -

N B W B isn't worried about that yet...
- - B
B - B

- B W
W - B
W - B

Anyway, I can't yet tell if there is some meat in this game, or am I
just flipping stuff around on a board? Maybe larger sizes would show some
additional strategies.

I thought it was interesting due to the 3 piece types...
Any thoughts?

--
Dave Boll db...@pacifier.com
"Never use an outhouse toilet while holding your car keys in your mouth."
Homepage: http://www.pacifier.com/~dboll/ Stop by for a visit! Lots
of stuff on amateur Astronomy, recreational mathematics, etc.

[Dave Boll]

Sorry to follow up my own post, but I made a couple errors in
the sample semi-game, and I wanted to clear up any confusion.
Especially mine! So, I finished up the game, starting from the
point where I had a brain fart in the previous post.

:
: Board: NxN, square, I'll illustrate below for N=3

Error: this should be

N B N Since the W just moved to a square where it was touching only
- - N B, they both flip to N's
B B -

So it would have been a pretty silly move by W, since W just got
cleaned out.
So, if we back up to before the move:

N B B
- W -
B B -

W only has 2 other choices here: moving the N piece down, and moving
the W piece to the left. Moving the N piece down loses on the next turn,
so we'll move W left:

N B B No flip here.
W - -
B B -

And now B can force a win like so:

N B B No flip, since B, the moved piece, touches both B and W
W B -
B - -

Now W is moveless. I guess I hadn't specified stalemate conditions, let's
say in this game, if you have no moves, you just lose your turn.

N B B And now W is forced to suicide the next turn
W B -
- B -

N B B B wins.
- B -
N N -

Hmmm - maybe there is some meat in this game after all! Hopefully
I didn't make any more errors...

If anyone wants to try out a 5x5 email game, let me know.

[Eric Martin]

I've haven't tried your game out yet but the concept seems pretty intriguing.
After looking at your example, though, I'm wondering if the game could go
on forever?
Maybe a rule about dissappearing board spaces or the just moved piece is
removed while the other still turns to the third colour.Something to give
it an ending point.
I'll be playing with this idea for a while
Good luck
ERic MARtin

--
______ _______ __ __ {Icman: ae...@freenet.unbc.edu}
[ ____] [___ ___][ \ / ] { }
[ ___] ___[ ] [ ] \/ [ ] {"A wise man once said }
[______] \____] [_]\__/[_] { something." }

[Jason Reed]

In article <59qdbc$1...@freenet.unbc.edu>,

ae...@freenet.unbc.edu (Eric Martin) wrote:
>
>I've haven't tried your game out yet but the concept seems pretty intriguing.
>After looking at your example, though, I'm wondering if the game could go
>on forever?
>Maybe a rule about dissappearing board spaces or the just moved piece is
>removed while the other still turns to the third colour.Something to give
>it an ending point.
>I'll be playing with this idea for a while
>Good luck
>ERic MARtin

Just prohibit previous board positions from reappearing, like go.

It does seem to be a rather interesting game, though.

---PAscal

[Wlodzimierz Holsztynski]

Dave Boll wrote:
>
> I've been checking out the following strategy game, and am not really
> getting anywhere wrt finding a strategy. But, the game is (maybe)
> interesting, so here goes:
>

> Board: NxN, square, I'll illustrate below for N=3
> Starting config:
>
> B B B
> - - -
> W W W
>
> Movement: pieces can take one rookwise step to any unoccupied square
>
> Piece types: There are 3 types of pieces: (B)lack, (W)hite, and
> (N)eutral. Any move that results in 2 pieces of different types becoming
> adjacent flips both pieces to the third type. On any turn, a player may move
> their own piece or any of the Neutral ones.
>
> Goal: Win by wiping out your opponant - all pieces on the board are either
> yours or neutral.

What is the initial position in the NxN general case?

Wlod

[Dave Boll]

Wlodzimierz Holsztynski (wl...@mich.com) wrote:
:
: What is the initial position in the NxN general case?

I'm thinking one player occupies the top row, and the other
player occupies the bottom.

[rr...@pge.com]

In article <59mtgd$a...@news.pacifier.com> db...@pacifier.com (Dave Boll) writes:
>From: db...@pacifier.com (Dave Boll)
>Subject: Re: New game I'm messing around with
>Date: 23 Dec 1996 21:27:41 GMT

>:
>: Board: NxN, square, I'll illustrate below for N=3

>: Starting config:
>:
>: B B B
>: - - -
>: W W W
>:
>: Movement: pieces can take one rookwise step to any unoccupied square
>:
>: Piece types: There are 3 types of pieces: (B)lack, (W)hite, and
>: (N)eutral. Any move that results in 2 pieces of different types becoming
>: adjacent flips both pieces to the third type. On any turn, a player may move
>: their own piece or any of the Neutral ones.
>:
>: Goal: Win by wiping out your opponant - all pieces on the board are either
>: yours or neutral.

>:

Unfortunately, I found an obvious problem with your game: What happens when a
piece is moved adjacent to each of the two other types: Say a white piece
moves between a black and neutral piece--does it combine with the black (and
become neutral) or neutral (and become black)
In this case,

BWN --> NNN (if the BW pairing happens first)

or

BWN -> BBB (If the NW pairing happens first)

What happens when a piece is adjacent to ALL 3 colors:

B*W
-N-

If the * is a B, you'd get:

BBW
-N-

BWW or BNN
-W- -N-

NNW or WWN
-W- -N-

etc.

Also does "one rookwise step" mean 1 square orthogonally or any number of
squares orthogonally without jumping over an intervening piece (which is how a
rook moves).

--
Richard Irving rr...@pge.com

I don't like disclaimers, but I have to put them in. The opinions here
are my own and not necessarily PG&E's.
(As if it had any opinions about this stuff!)

Made with recycled electrons.