The recent thread involving a possible game Torex,
suggests it might be about time to release into the wild,
a new game of my composing, that Joao Neto and myself
and Cameron Browne have tested somewhat.
I am particularly pleased that the game seems to be
a somewhat "natural" form of Quad style game,
and played on a torus, and nevertheless has a win
criterion which EXACTLY MATCHES the acronym "NZ",
which is also the name of the country of the inventor!
How kool is that? ;-)
- - - - -
Firstly, as it is a Quad-connection game, we need to
sort out the rules for the resolution of local "cross-cuts"
or "stymies", as they have variously been called.
i.e. 4 stones in a mimimum square, diagonally crossing colors.
There are already a number of ways of resolving this problem,
Joao and I have experimented quite a lot with various forms.
There are...
.
O
Quadrex style: the 4th point of such a square, O X , is
automatically filled with the color of the
pair;
Crossway style: the 4th point may not be filled, and diagonal
connections automatically count.
Quax style: diagonal lines connecting opposite points
with their color may be played, using up a turn;
Swapway style(not public as yet): when a cross-cut square
is formed, a player may swap two stones so as
to make it parallel colors. This might be done
(i) by the player moving, (seems to be bad); or
(ii) by the next player to move, before his move, (better);
(iii) by either player, but takes up a whole turn, (not tried).
Doubtless there are other ways of dealing with cross-cuts,
that we have not considered yet. Perhaps some readers can?
My personal recomendation would be to opt for
EITHER Crossway style, OR Quadrex style; these seem
the best of the bunch. (Mark Steere discovered the former,
and myself the latter). The others have the problem that
they need a new sort of piece (diagonal connector), or allow
stones to be moved, which may lead to infinite play or "ko".
Which of the final two you choose is not vitally important
in that the stragegy and tactics are much the same,
(not fully identical though); so the final decision depends
on one's taste for elegance.
Quadrex style will appeal more to those who dislike prohibitions;
Crossway style will appeal more to who prefer 1-stone-per-move.
So there will be two slightly different variants of NZ:
a quadrex-style NZ, and a Crossway-style NZ.
--------------
Now - to the global properties of the game, "NZ".
They are remarkably simple!
It is played on a square-shaped checkerboard of
pre-determined (but variable) side length.
The board is a torus - the top edge is to be considered as
glued to the bottom edge; likewise for the left right & edges.
The two players are "N", (for North-south);
and "Z", (for eaZt-
weZt).
N must try to make a closed loop which runs north-south,
(or isomorphic to that i.e. when straightened out);
Z must try to make a closed loop which runs eazt-wezt.
Much of the time, both players' goals will be blocked by
the other, in which case the winner is determined by
WHICHEVER TYPE OF DIAGONAL LOOP IS MADE.
There must always be one or the other. (On a physical
torus this corresponds to a loop which "wraps around"
in both directions, radial AND circumferential.)
And who wins? Obviously (!):- Z wins if the diagonal
loop is of the "poZitive" gradient; as in the "Z" symbol(!),
and N wins if it is Negative gradient, as in the "N" symbol!
HOW KOOL IS THAT!?
It may (very rarely) happen that the players chase one
another round and round into making a loop that wraps
around the torus more than once, but in such a case
there is still a clearly identifiable direction for it -
N (Negative slope) or Z (poZitive slope).
examples:
.. N . Z N is about to win this 4x4 game.
Z . N .
Z . N Z (Z might also make a vertical loop,
Z . N . but this is useless for him.)
- - -
Z Z N N Z
.. Z Z N N N is about to win this 5x5 game.
.. . Z Z N
N . . Z . Note that Z already has made
.. N N Z Z a diagonal loop, but not in his
- - - - - own direction, so it is useless.
_______________________________________
So there it is - the first (?) fully operational torus style
connection game. And named after New Zealand - YAY!
OC it would be possible to play a similar game on
a hexagonal-gridded torus, but it would not be able
to have isomporphically tasked winning criteria -
so it could never be a "fair" game, as is quadric NZ.
And obviously a one-move PIE rule won't work - it
would have to be a 3-move PIE rule.
HAVE FUN!
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Bill Taylor W.Taylor@[EMAIL PROTECTED]
What is it when a howling wolf leaps at you and sinks in its fangs?
A: A sound bite.
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