Slime trail, a new (?) two player game.

[dave boll]

The traffic on this group has died recently - is no one doing interesting
stuff with games?

I thought I'd post some results for a game called Slime Trail - invented
(as far as we know) by Bill Taylor. He and I corresponded for a while
re: game trees and strategy for this game, and this is what we came up
with:

Slimetrail:
played on an NxM rectangle of squares. Each player takes turns moving
a piece around the board. The piece can take one step orthogonally,
and may not re-visit a visited square. Each player tries to move
the piece into his/her goal square. The two goal squares are located
at diagonally opposite corners of the rectangle. The piece starts on
any mutually agreed upon square.

Note: It doesn't matter which player actually ends up moving the
piece into a goal square; just the fact that it is there means
that someone won.

Normal slime trail:
A first player win exists, starting from any square, provided at least
one of the board dimensions is even. On an odd by odd board, winning
and losing start squares alternate in a checkerboard pattern. A draw is
only possible via cooperation; if one player moves to avoid draws, the
other can never force them. We're still wondering if the winning/losing
start square pattern means there is an easy strategy for this game that
neither of us has seen yet.

Variations:
Chess king slime trail: The piece moved around the board has the movement
capabilities of a chess king. Results for small boards (1st player
goes to upper left, 2nd to lower right)

W = Winning start square for 1st player, assuming perfect play.
L = Losing start square for 1st player
T = Tied game with perfect play. (A game is tied if neither player
has a move)

3x3 4x3 4x4 4x5 3x5
* W L * W W L * W L W * W W W * W W W L
W W W W W W W W W W L W W W W W W W W W
L W * L W W * L W W W W W W W L W W W *
W L W * W W W W
W W W *

(the additional movement capabilities makes deep search difficult)
Seems to be biased toward the 1st player, with losses only cccuring
(sometimes) in the vincinity of the non-goal corners. It should be noted
that some of the start squares marked W have only one winning move out
of the eight available, and the direction of that winning move is not
obvious at all - so they still make for fairly good games.

Hex slime trail, targets in obtuse corner: Probably the best version
of this game. Here's some small board results:

4x4 5x5 5x4 4x6
* W T L * W T W T * W T W T * W T L
W W L T W W W W W W W W W W W W L T
T L W W T W W W T W W W W W T L W W
L T W * W W W W W W T T W * W W L T
T W T W * T L W W
L T W *
I think this variation is 'best' because of relative balance of
start squares that lead to W, L, or T. We really haven't playtested this
one enough to vouch for superior play-ability.

Hex slime trail, targets in acute corner:

4x4, 4x5: all squares win for 1st player

5x5
* W T T T
W L T T T
T T L T T
T T T L W
T T T W *

Draws are too easy to come by in this version.
--
------------------------------------------------------------
Dave Boll bo...@handel.cs.colostate.edu
"The speed of time is 1 second per second"
------------------------------------------------------------

[Barney Pell]

In article <Jan18.165...@yuma.ACNS.ColoState.EDU>, bo...@CS.ColoState.EDU (dave boll) writes:
|>
|> I thought I'd post some results for a game called Slime Trail - invented
|> (as far as we know) by Bill Taylor. He and I corresponded for a while
|> re: game trees and strategy for this game, and this is what we came up
|> with:
|>
|> Slimetrail:
|> played on an NxM rectangle of squares. Each player takes turns moving
|> a piece around the board. The piece can take one step orthogonally,
|> and may not re-visit a visited square. Each player tries to move
|> the piece into his/her goal square. The two goal squares are located
|> at diagonally opposite corners of the rectangle. The piece starts on
|> any mutually agreed upon square.
|>
|> Note: It doesn't matter which player actually ends up moving the
|> piece into a goal square; just the fact that it is there means
|> that someone won.
|>
|> Normal slime trail:
|> A first player win exists, starting from any square, provided at least
|> one of the board dimensions is even. On an odd by odd board, winning
|> and losing start squares alternate in a checkerboard pattern. A draw is
|> only possible via cooperation; if one player moves to avoid draws, the
|> other can never force them. We're still wondering if the winning/losing
|> start square pattern means there is an easy strategy for this game that
|> neither of us has seen yet.
|>

|> etc...
|> --

That sounds fun. I notice that this game falls into my class of
symmetric chess-like games, for which I have a Metaame program which
plays every such game by analysing its rules. When I have some
time I'll enter this game to the program, and see what it comes up
with!

|> ------------------------------------------------------------
|> Dave Boll bo...@handel.cs.colostate.edu
|> "The speed of time is 1 second per second"
|> ------------------------------------------------------------

--
==================================================

Barney Pell
Computer Laboratory
University of Cambridge
phone: (0223) 334622
e-mail: b...@cl.cam.ac.uk

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