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Re: [pbmserv] New game: Cubox
Is it possible that the option to pass could result in a deadlock? I'm not
sure I'm visualizing correctly here.
Steve
----- Original Message -----
From: "Cameron Browne" <cameronb@optusnet.com.au>
To: <pbmserv-users@gamerz.net>
Sent: Wednesday, March 23, 2005 4:11 AM
Subject: [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.
>
>
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>
>