Beginner's Guide to Space Chess, Part 4

spazzim had a great suggestion in the comments to yesterday's installment: It might make a more interesting and difficult game if the two players could choose from a subset of the available pieces. They would each have to have a certain number of each type of nearly equivalent pieces but not necessarily the same pieces as their opponent.

Building and deploying an army and then playing with it is a game called "meta-chess," and David Howe has a great proposal for it at this link on Chessvariants.com. It's not 3D-though. You could do something a little bit similar if both players get the same number of tokens to purchase troops which are priced based on the score given to them by Zillions of Games. On a matrix measuring 8 wide by 8 tall by 8 deep, using the Zillions file for Bornert's "3D8L" game it scores the 3D pieces as follows:

Rook 4	Bishop 5	Mage 2.5	King 4.5
RookBishop 9	RookMage 6.5	BishopMage 8	Queen 11.5
Knight 4.5	Jester 3	Champion 4	General 12

One of the things pointed out in a critique of the construction set idea is that the value of a piece can't be estimated in the abstract since it depends on the situation. This involves today's topic because the size and shape of the board (actually referred to in 3D as the matrix) changes the values of certain pieces. Corners disadvantage rooks, so a tetrahedral matrix as shown here with a lot of corners would advantage bishops against rooks. The longer a matrix is in the longest direction, the more a diagonal or triagonal mover is disadvantaged. Think about how poorly a bishop could perform on a 2-D chessboard measuring 8x4: it could only ever move 4 spaces.

Part Four: The Board, or "Matrix"-- Shelves Are Obsolete

With dozens of pieces, hundreds of spaces, and a thousand lines of attack to pay attention to, many 3D chess games take weeks to finish and sprawl outside the limit of the human mind. 3D8L by Ray Edward Bornert II, although magnificent, is something only a handful of people on the planet would want to play.

He makes several brilliant contributions. One such is the red, blue and green dots in the center of the spaces. These mark the triagonal lines just like a checkerboard lets you see diagonal lines by following one color.

Notice in the photo on that site how far apart the shelves are. It's easier to reach the pieces on a smaller set, such as Raumschach, but a hand must be able to fit between the levels in either case, so vertical diagonals are still out of proportion. As a result, diagonal and triagonal lines of attack are difficult to visualize. But the visual language of almost every 3D chess set so far devised carries over two-dimensional assumptions where they no longer apply.

The radial symmetry of chess pieces owes much to the simplicity of cutting them on a lathe. But we don't need to be limited to that anymore, especially with the pending advent of desktop fabrication in glued starch, plastic resin, paper lamination, or maybe even metal. Radially-symmetrical hats on pedestals of various heights makes perfect visual sense sitting on a table, but 3D is viewed differently. Silhouettes and sizes should be recognizable not just from the side but from above and below. I propose to make pieces a little more spherically symmetrical. But to have a spherically-symmetrical piece atop a stick, on a little base, sitting on a shelf, would miss the whole point.

Shelves are a visual obstruction. What about a set of grid lattices instead? A construction set might be made of cross-shaped building blocks. Spaces could be represented as intersections instead of squares, as in the chesslike game traditional to China. Each intersection piece would be either black or white, shaped like a plus sign with plugs or sockets on the four arms. That has several advantages. By adding pieces, matrices can be made in various sizes. Not only can players see through (if it were made of wire, players could still see through as they can with plexiglas, with less expense) but they can also reach through. Pieces should be short and squat, without pedestals. This way the levels can be spaced close enough together to match the width of a space, so that each space will be a cube. The pieces will have X-shaped slots cut into them, so that they sit on the intersection. A second hat on each piece hangs upside-down like the king on a playing card, symmetrically below the intersection as well as above, except for the deep slots that reach all the way to the midpoint of the piece.

Above all, the number of pieces and the number of board spaces must be limited, not only for ease of reaching into the center of the matrix to move a piece, but for legibility of what's going on in the game. We need a human-sized decision tree. According to Shannon Appelcline, "A lot of cognitive work we've done over the last several decades has shown that the human brain is able to intuitively grasp between 5 and 7 [types of] objects [in a single task] ... whether those be physical objects or decision options." Fortunately, most space chess players would not be terribly concerned with exceeding their intuitive grasp at least a little; if they were they wouldn't be interested to begin with. But I hope the improvements suggested here would put the game within the patience of even more players.

All of this will help intuitive playability, but there's so much farther it can be taken with computers.

Tomorrow: Improved Playability With Computer Graphic Mediation