[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[pbmserv] New game: Cubox
Hi,
A new game Cubox has been added to the server. This is a connection game
with cuboctahedral pieces that players may stack, sort of like a 3D version
of Y. This game has some geometric niceties due to the nature of the
cuboctahedral stacking.
I'm looking for testers so if any brave souls would like to try it out,
please challenge me:
cubox challenge <yourname> camb
cubox challenge camb <yourname>
Cameron
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
http://www.gamerz.net/pbmserv/cubox.html
Help For the Game Of Cubox
Introduction
Welcome to the network Cubox server. The challenge command is
described here. Other commands are the same as for all pbmserv games.
cubox challenge userid1 userid2 [-size=S]
Starts a new game between userid1 and userid2.
The -size option specifies the board size in the range 3..16 (default
is 8).
Rules
Cubox is a 3D connection game for two players, X and O. Each player
owns a number of cuboctahedral pieces (called cubox) of their colour.
A cuboctahedron is a polyhedron formed by six squares and eight
triangles:
+-------+ +-------+
/ -_ _- \ /| |\
/ -+- \ / +-------+ \
/ / \ \ /_- \ / -_\
+_ / \ _+ +- \ / -+
\-_ / \ _-/ \ \ / /
\ +-------+ / \ _+_ /
\| |/ \ _- -_ /
+-------+ +-------+
Top Bottom
The board is a triangular field of cuboctahedral hollows, hexagonal in
cross-section, whose triangular bases all face in the same direction
(a bit like a hexagonal egg carton). The board is initially empty.
Play: Players take turns adding one of their cubox by either:
i) Dropping it on an empty board hollow, or
ii) Stacking it on top of a flat triangle formed by one friendly and
two enemy cubox.
Players must move if possible, else pass.
Aim: A player wins by connecting all three sides of the board with a
path of their cubox. Two cubox are connected if they visibly touch,
either corner-to-corner or one stacked directly upon the other.
A cubox is deemed to "touch a board edge" if it is one of the
outermost cubox for its level, that is, if it would form part of the
outer slope if the board were completely stacked with pieces.
Examples
The following example shows a legal stacking move. An X cubox is
stacked upon a flat triangle formed by one X and two O cubox. Note
that the stacked cubox points in the same direction as the three
supporting cubox. Note also that the stacked X cubox cuts the
connection between the two O cubox.
+-------+ +-------+
/ -_ _- \ / -_ _- \
/ -+- \ / -+- \
/ / \ \ / / \ \
+_ / ^ \ _+ +_ / ^ \ _+
\-_ / ^X^ \ _-/ \-_ / ^X^ \ _-/
\ +-------+ / \ +-------+ /
\| |/ Stack---> / -_ _- \
+-------+-------+-------+ +-----/ -+- \-----+
/ -_ _- \ / -_ _- \ / -_ / / \ \ _- \
/ -+- \ / -+- \ / -+_ / ^ \ _+- \
/ / \ \ / / \ \ / / \-_ / ^X^ \ _-/ \ \
+_ / ^ \ _+_ / ^ \ _+ +_ / ^ \ +-------+ / ^ \ _+
\-_ / ^O^ \ _-/ \-_ / ^O^ \ _-/ \-_ / ^O^ \| |/ ^O^ \ _-/
\ +-------+ / \ +-------+ / \ +-------+-------+-------+ /
\| |/ \| |/ \| |/ \| |/
+-------+ +-------+ +-------+ +-------+
The following example shows a game won by O. The winning chain touches
the bottom edge via D2, which is an outermost cubox for level 1 deemed
to "touch a board edge" even though it is stacked above board level.
11-- ^
10
9-- ^ ^
8 +---+ +---+
/ xxx \ / ooo \
7-- ^ + + +
\ xxx / \ ooo /
6 +---+ +---+---+---+---+---+
/ ooo \ / ooo \^/ ooo \^/ xxx \
5--+ + +---+ + + +
\ ooo / / xxx \ \ ooo / \ xxx /
4 +---+-+ +-+---+ +---+
/ oo\ xxx /xx \
3-- ^ + +---+---+ + ^ ^
/ ooo \ \ xxx /
2 +-+ +-+---+---+ +---+
/ xx\ ooo /xx \ / xxx \ / ooo \
1-- ^ + +---+ + + + ^
\ xxx / \ xxx / \ xxx / \ ooo /
+---+ +---+ +---+ +---+
/ / / / / /
A B C D E F G H I J K
Possible stacks: D6 F6
Due to limitations of the ASCII representation, cubox are simplified
and represented by their hexagonal cross-sections in an effort to keep
the board display to a reasonable size and reduce clutter.
Legal moves for the current player are marked '^'. This includes empty
board points (hollows) and possible stack moves.
The board coordinates for possible stack moves are also listed
explicitly below the board, since it becomes increasingly difficult to
determine the coordinate the higher a stack is. If in doubt, the
player should read through the list of possible stack moves to
ascertain which coordinate they want.
Notes
The fact that a winning connection must be continuously visible from
above means that it is effectively a 2D connection built upon a 3D
structure. This allows the elegant Cut/Join property of most
connection games, and means that exactly one player must win.
Winning paths require successively fewer pieces at higher levels,
although by this point the placement of pieces is entirely dictated by
the distribution of lower-level support pieces.
Each stack move breaks exactly one enemy connection. A triangle of
same-coloured pieces constitutes a strong formation whose connections
cannot be broken (e.g. the triangle of X pieces at the bottom of the
second example).
Once the board level pieces have been placed, it is only possible to
stack higher level cubox facing in the same direction, with square
faces meeting square faces (see the first example). This avoids phase
problems when stacking upon a hexagonal grid. Cubox would not work if
spheres were used instead of cuboctahedrons.
The fact that each stacked piece is placed on a majority of enemy
pieces subverts the N-1 reduction rule of Y, as a triangle dominated
by one player becomes dominated by other player after the stack. Each
stack move is therefore equivalent to an inverse N-1 reduction for
that triangle of pieces.
The stipulation that pieces can only stack on one friendly and two
enemy pieces may seem arbitrary, but is in fact critical. Allowing
pieces to stack on three enemy pieces would be an overly strong play
that would break all three connections between those enemy pieces. On
the other hand, allowing pieces to stack on two or more friendly
pieces would make it too easy to stack and in most cases would simply
reflect that triangle's N-1 reduction anyway (though it may have
implications for higher stacks).
Open Problem: I don't believe that deadlocks can occur, but have yet
to prove this. The definition of connectivity may be weakened to "two
cubox are connected if they visibly touch corners or overlap when
viewed from above" to imply a visible rather than physical connection
and resolve such deadlocks (though I don't think this is necessary).
Heard of Martian Chess? Well, Cubox could be Martian Y:
http://www.exo.net/~pauld/Mars/4snowflakes/martiansnowflakes.html
Syntax
cubox move board# userid password g4 (move at point G4)
cubox move board# userid password swap (second move only)
cubox move board# userid password pass
References and History
The basic mechanism of Cubox was devised by Cameron Browne in 2002 to
demonstrate how a connection game could avoid phase problems with
hexagonal stacking. The official version implemented above (v1.5) was
completed in March 2005.
Implementation and help file by Cameron Browne, March 2005.