Comments/Ratings for a Single Item

Visualize for a moment that we have software that displays the game of
Prince on binocular-vision LCD glasses. The glasses superimpose images
onto a transparent view of the wearer's real environment-- not virtual
reality, but augmented reality. Imagine also that we have two telemetry
gloves. The index finger and thumb are tracked in 3D and 'mouse click'
when they touch-- the two fingertips are displayed as two cursors floating
in the image. I would want to play this game.

Since a computer simulation has no gravity, we do not need surfaces on
which to rest pieces. Each piece sits on an intersection of three
translucent lines, one for each dimension, in an eight-by-eight cube.
Grasping and pulling any edge of the cube allows free rotation. The cube
should fill half the visual field, since the user's reach can be
transposed on a huge scale, or the user can also change to the size of the
pieces and stand inside the cube when desired. Ideally though, the glasses
would be tracked with telemetry so that the cube would always float in the
same space in the user's real environment while the user moved around it.
In this mode the whole cube should fit within easy reach, perhaps three
feet to a side.

Without gravity there is no reason for pieces to be stable pedestals with
radial symmetry along only one axis as they are in 2-D chess. The shapes
that represent one-dimensional ranged movers could be 3-D stars. The piece
is formed of arms extending from the intersection it occupies, and
dwindling to tips before reaching adjacent intersections. Each arm points
out toward an intersection to which the piece could move if it weren't
obstructed. So, a rook looks like a thickening of bright, bold opacity
along the three translucent board-lines of its intersection. Arms of
bishops and merchants do not lie along the board lines; they reach across
the gap toward adjacent line segments and intersections respectively.
Leaper pieces have thinner, threadlike arms, that fork into Y's tipped
with spheres. Two-dimensional movers are formed of a set of intersecting
surfaces. Pawns are half-spheres. Kings are large spheres.

For a game this complex, no one should complain if there is as much
graphical computer assistance as possible. All pieces glow when under
threat. A large crown symbol appears outside the cube when check is given.
When a piece is grasped and dragged, the intersections to which it can
legally move light up. Moving an index finger onto a piece, without
touching the fingers together on it, causes its name and animated graphic
description to display in the space above the cube. The piece on the board
grows without thickening its arms: the arms stretch as far as they can
without being blocked, to show all the intersections to which it can
legally move. At the option of the user, all pieces on the board
simultaneously extend their arms/spheres/surfaces as ghostly fogs of
color. Since the sides are red and blue, they blend into purple where they
cross. This represents threat from the red and blue sides, and varies with
intensity based on how many pieces have a line of sight to the
intersection.

I can tell you from personal experience that a planar-type piece is even
more powerful in 4D chess than in 3D. I would also recommend a smaller
board than 8x8x8x8. The problem with any planar-type piece is that it's
so powerful that you have to clog the board up with lesser pieces to
prevent instant checkmates. The more powerful the strong pieces, the more
plentiful the weak pieces is a really easy and very bad trap to fall into,
if you want a game that can be played by humans. And simple leapers work
fine in 4D. I used a knight that no longer has the leaping ability, and it
kicks butt, for my version of hyperchess. In 2D, you can add a lot of
pieces; the complications are in piece interaction. By the time you get to
4D, the board provides a good bit of the complication, so the pieces should
be simple, to balance. In hyperchess (does this need a new name - am I
infringing - how does Hyperchess 4D sound - that's what I thought). In
H4D only the standard 8 pieces and 8 pawns per side are used, on a 4x4x4x4
board, giving a starting piece density of 12.5%. And the movement rules are
basically simple translations from 2 to 4D. I would argue that good
movement rules and piece densities are very board-dependent. Ok, guess
I'm saying geometry-dependent, both the topology and the exact
measurements (as I'm finding out in a variant that mixes 2D-moving and
4D-moving pieces; ie: some pieces treat the board as 2D, some as 4D, and
some may choose.)
Is there a more appropriate forum for this discussion? Guess I'm too new
to know.                               Joe

Very nice update; it looks really good. The new diagrams are quite good and very helpful. 
This would be more of a strategic than tactical game for humans, no? ;-) 
Nice to see you back.

Excellent graphics. I finally got to appreciate the starting position (and I just realized that there's no Prince in the starting setup.)

However, I still don't think this game is playable for humans. Not because of it's complexity, but because of the many piece types.

I made an attempt to simplify this game, a whole lot, to make it more playable and closer to Standard two dimensional Chess. I called it the Tower's Game because it's played on a tower-like board.

For me the planar pieces are what makes this game what it is. The Towers
Game is just another variant using the same pieces as a good many 3d
variants (including a couple of my own). A front rank dominated by planar
pieces in number rather than just strength might be interesting.
	An interesting way to increase the range of planar pieces is to consider
the Scientist a compound piece, as it covers two quite different kinds of
plane, and the University and Spy as triple compounds. As the names seem
to be the only ones for planar pieces I will stick with them and try to
follow the theme, so let's call the Scientist a compound of the Theorist
(where the diagonals are at right angles) and the Technician (where they
are at 60°). For the additional compounds of one but not both Scientist
components I suggest Base+Theorist=Study, Base+Technician=Laboratory,
Theorist+Reporter=Reviewer, Technician+Reporter=Printer,
Base+Theorist+Reporter=Library, and Base+Technician+Reporter=Press.

The original Hook Mover can be found in Taikyoku Shogi. This piece makes makes one or two moves like a Rook, but must stop immediately upon making a capture. It is called an Android in The Toddler. See Adrian King's Jupiter (not indexed) for the Great Hook, a Hook Mover which is limited to at most three squares on the second leg of its move.

An unrestricted Hook Mover will sweep out three planes in a 3-D board. Now I am going to attempt to provide an alternate definition of the move of the Base in Prince. Choose a plane containing the Base and place pennies in every cell that has at least one of the possible 'hook moves' to that cell blocked. [RULE 1] The Base cannot move to any cell containing a penny. [RULE 2] The Base cannot move through any cell containing a penny.

Thank you for the comment, Dave.  The idea of a 'hook mover' as you
describe it, with the alternate definition you provide of how blocking
works, accurately describes the Base, and I believe also the Scientist. 
Hopefully this can provide clarity to anyone confused.

The 'hook move' idea is not quite accurate for the Reporter in all
cases.  In particular, if a Reporter is near one corner of an open field,
there are some spaces near other corners that cannot be reached with a
hook move unless you allow the hook to pass outside the field, but can be
reached by the Reporter nevertheless.  

Also, the penny definition of blocking is not quite accurate for the
Reporter and combination planar movers.  The multiple planes some spaces
are in messes it up, and you may end up placing pennies in spaces that can
be reached using other planes.

L. Lynn Smith and I discussed this when I first introduced Prince.  He too
wanted to call the planar movers hook movers at first.  But I will stick to
my appellation of 'planar' move, partly because it is essentially the 2
dimensions of the move that characterize it, and partly because of the
technicalities described above.

But hey, I'm thrilled you get it.  Thanks again.

As I don't think Gavin will mind, and since you insist, George, I'll transfer this part of the discussion from Charles Gilman's MAB Overview and glossary Comments section to here. 

Multipath is a too-inclusive term for a good definition of a piece. Let's consider some multipath pieces. First, the Falcon - it has 16 destination squares, all at range 3, and there are 3 paths to each target square. The Falcon is, however, an 'Or' piece; it takes this path OR that path OR this other path, traversing only a single physical route from origin to destination in its actual move. The 'hook rook', the 'planar' piece of Chris Witham, is similar to the falcon, in that it has 2 possible routes to any destination square, and uses only one to go from origin to destination. In terms of physics, these pieces are both representative of the 'billiard ball' theory of atomic particles. While they may change directions on the trip, the pieces travel a well-defined and measurable path from beginning to end. As long as 1 path is open, they are good to go.

The 'planar rook' of Prince is like a quantum particle. It travels, and must travel, every possible minimal path simultaneously in going from origin to destination, and thus it can be blocked by a single piece anywhere in the area over which it travels. This is an 'And' multipath piece. It travels by this path And that path And the other path And ... and that's why it's so blockable. This refines the 'Multipath' classification.

One of the key features of planar pieces in Prince is the shape of the shadow that blocks a planar piece, a rook, say. In Prince, it is always a rectangular shadow that starts at the near edge of the blocking square and runs perpendicular to the line between the 2 pieces that blocks the planar rook in Prince. This is not the only possible shape for a shadow. Another very reasonable shape would be a cone, with the tip being the blocking square and the triangular shadow spreading out directly 'behind' the block, away from the planar piece. This would allow a planar rook to penetrate past the first obstacle. Varying the angle of opening of the shadow would give other effects, including bending the shadow back toward the planar piece by making the angle of opening greater than 180 degrees. The current angle of opening for a block's shadow of the planar rook is exactly 180 degrees. And I would argue this is yet another way to classify planar pieces. 

Charles, if you are following this, would any of this comment be pertinent to any definitions or classifications you might use?

I'm glad folks are reading, and having this discussion!
Sorry I've been too focused on other things to particiapte much myself.
Please let me know if there's anything I should clarify.

On that note, after re-reading David Paulowich's comment and my response
dated 12-28-2008, let me clarify one detail:  Though Scientists can be
thought of as hook movers, David's penny definition has the same potential
problem with Scientists as it does with Reporters and combination planar
movers because some spaces are in more than one possible plane of
movement.

Again, I'm flattered people are reading.  Maybe someday someone will
actually finish a game! :P

I was thinking about this the other day.

If a Rook in 2D chess is defined as a piece which controls the whole line
it's sitting on, then perhaps a rook in 3D chess should be defined so that
it controls the whole plain. But I was having trouble thinking how to
define it.

Your definition of 'Making too rook moves in the same plain fixes this
problem by allowing it to be blocked, etc.

This way you can CheckMate the king too. You can't force check-mate with
only a 3D Queen.

Remembering all the different varieties of night moves I think will be the
hardest thing with this.

In 4D Chess then, a extending out this way, would make 3 Rook moves with-in
the same 'cube.' (Obviously 6 of the 8 cubes will be distrorted in the 3D
projection we play in.) 

TRacy 

Tracy