C.I.T.O.K.A.T.E.

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

To wrap up yesterday's discussion, FIDE Chess is just another variant that happens to have won a monopoly on mindshare, but just because we can change it doesn't mean we want to set out to design a card game involving charades and throwing a ball through a hoop. What are we talking about when we say "chesslike"? It's a radial category, so a game can change a few of the following elements and still be recognizably chesslike. Typically, this category of game has no secret information and no element of chance. It involves players taking turns moving a piece on a lattice of discrete positions such as a grid or honeycomb; each position is occupied by only one piece at a time, each piece occupies only one position at a time. A piece superimposes its position on that of a piece from the opposing team to remove it from the playing area. That's what we're trying to do in 3-D.

Part Two: Which Way Is Diagonal?

Let's go over linemovers. Not all of these necessarily need to be used in the design of space chess. This entry owes much to Gavin and Larry Smith from their description of "Prince." I've also imitated Larry Smith's style of illustration. In these examples, the piece is supposed to be starting at the center of the cube.

	You probably know the word diagonal, but its relative, orthogonal, is less familiar. A rook in regular Chess only changes its location along one coordinate, either rank or file. In 3D there is a third dimension along which to move. Notice that the cubes of the spaces touch on the face.
	The Bishop in regular Chess changes its location along exactly two coordinates, no more and no less, the same number of spaces for each coordinate. That's the definition of diagonal movement from the standpoint of geometry, and it can apply in 3D. See how the cubes touch on the edge.
	This is where people become confused about how to move a Bishop in space chess. Should a diagonal move be through the edge of the cube or the corner? It's simpler to keep track of if you keep in mind that a triagonal move changes all three coordinates, no more and no less, the same number of spaces for each coordinate. The confusion stemmed from the fact that the corner is something different from diagonal.
	What we have here are really three different geometric primitives. The Rook is easy; it's an orthogonal linemover.
	The Bishop is a diagonal linemover.
	This piece is not possible in 2D chess. It's been called The Merchant or The Mace, but here I'll refer to a triagonal linemover as: The Mage and represent it with a crescent moon for purposes of this series. You may have noticed in Chess that a Bishop starting on black or white always stays on that color, which limits it to half the squares on the board. The Mage has that problem, doubled. It can only ever visit one-fourth of the positions in the playing field. The artificial intelligence engine in Zillions of Games scores it as worth about as much as a pawn, which should be taken into account when building an army.
	The RookBishop would be a Queen if it were regular chess, but if you are thinking of a piece that can change its location along as many or as few dimensions as desired, like a Queen in FIDE Chess, this doesn't qualify. Moving either orthogonally or diagonally means it can change either one or two coordinates in its position per move, not all three. That's why there exists this set of three pieces, called compounds.
	The RookMage, for instance, can choose orthogonal or triagonal directions.
	The BishopMage has an option of diagonal or triagonal movement. So the three compounds are RookBishop, RookMage and BishopMage.
	The Queen. Now that's what I'm talkin'bout. By changing as many or as few of her coordinates by the same number, this moves in any straight line. If you want, you can call the RookBishop the Queen, and call this the Empress or something. But they are quite different.
	The King, able to move one step in any direction. This is extremely slippery and difficult to pin down, resulting in a lot of draws in games that are not designed carefully.
	The Chess Piece Formerly Known As Prince. It can move heterogonally or homogonally. Now appearing as an opening act for Queen, and The King (thankya, thankyaveramuch). Seriously though, this is a weakened form of the King as a solution to the draw problem. It lacks the ability to take a triagonal step.

I'd like to try playing with a game that has two Princes on each team, and the victory condition is to checkmate either of them, while protecting both of your own. That way the game won't be unearthly long, because checkmate will be easier. For kicks, it would be fun to promote one of them to a King when it makes it to the other side of the board, where it is exposed to risk. A King can bring check on a Prince along a triagonal direction!

Only with the distinction between the three types of movement under our belts can we figure out the Knight.
Tomorrow: Leapers-- Seven Arabian Knights. You have been warned.

Lost Garden has an article on risk/reward systems in game design theory as applied to the Gameboy DS title "Nintendogs." "If you dig into the game mechanics at an abstract level, it has surprisingly more in common with a RPG than most virtual pet games. Yet hardcore gamers make a snap judgement and instantly assume it must be a Tamagotchi-style game. ... The theoretical designer realizes that a powerup is a powerup whether you call it a 'Quad Damage' or a 'Doggy Brush'."

Similarly, chess can be played with Staunton pieces, or with Civil War soldiers, or cartoon characters; it will still be the exact same game. The Shogi enthusiasts at Marcon strongly disagreed with this when I told them about my Shogi set, but that's because when they say the "game" of Shogi they are referring to a heritage, and a community of people. Strip away whatever differences they would experience between my intuitively-grasped pie-chart graphics and the original Japanese writing and what remains will be the definition of the word "game" used by most of the Chessvariants.com community. There is a difference between the game mechanics and the window-dressing applied to it. A real-time-strategy computer game would be the same "game" even if you take all the soldier illustrations out and replace them with ants, or dinosaurs, or Care Bears, just so long as nothing changes but the graphics.

I've kept that in mind because cosette_vajean has promised to get me the only thing on my birthday wish list this week: Gameboy DS with "Kirby's Canvas Curse," an innovative platform game which is played by drawing attack paths (OK, they are rainbows, but I will call them "attack paths"), sheilds, bridges, etc. on the screen with a stylus.

An action-platformer game.

Which is operated by drawing. *boggles*

It's like the invention of sliced bread, or the internet.

Also I recently finished last year's birthday present, Shigeru Miyamoto's creative tour-de-force "Pikmin 2" for Gamecube. I have a question about both these games. Why is it that the window-dressing of the only games with ingeniously innovative high-concept game mechanics tends to be so saccharine and infantile, as shown in the recent Penny Arcade webcomic? Why are games with an adult artistic style so derivative? As Tycho lamented, "I am a grown man who draws rainbows."

They're attack paths, dammit.

I'm throwing two parties at my house this weekend. SEMI-abstract gamers is having an all-day prototype playtest on Saturday, and the first M.O.F.O. party is on Sunday. Does anybody local have some folding chairs and tables you could let me borrow?

Last night I went to Java Hutt with a childfree who I met on the internet. It was a fascinating and animated conversation about the Universe, the unlikelihood of reincarnation, and the meaning of life, among other topics such as cable TV.

There were fruit-flavored syrups on the list at the coffee shop. This surprised me so I decided to try Grape syrup in my coffee because I love novelty for its own sake. In retrospect it was clearly intended for Italian ice sodas.

I went next door to Library Bookstore and bought Supermen, Tales of the Posthuman Future, by Gardner Dozois because it contains Border Guards by my favorite author, Greg Egan, which I somehow haven't read, and Fossil Games, by Tom Purdom, which is one of my favorite stories. I pinned up Penguicon flyers on all the bulletin boards in downtown Ferndale.

I'm hosting SEMI-Abstract Gamers at my house tonight at 7 to playtest and judge the Piecepack competition. Any games-playing friends are welcome!

I'm arranging a gathering of SEMI Abstract Gamers at my house on Saturday to celebrate the official release date of the new commercially-produced chess variant for which I have waited so long. So, I called up Masquerade Games today to see if they could confirm that Navia Dratp would be on their shelves on Saturday. "We just got that in today," she said. "We were wondering what the heck it is." So, I went right over there after work, bought both starter sets and played the game against Rachel. It's as fun and beautifully-crafted as I imagined. Time to update my Navia Dratp page on chessvariants.com!