Tri-dimensional board games: How does the additional dimension extend possible player requirements & game structure?

Recently I saw the Star Trek chess game in a serial and looked it up on wikipedia. It exists as a real game, but it seems it's not too popular, too tricky, too unwieldy to carry and play everywhere, and the rules are too complex (?). There seem also to be no world-wide championships or other questions on boardgames.SE ;)

Does anyone know of a good scientific site/report (maybe a topic in neuroscience experiments) describing different rule sets for e.g. 3D-chess which covers a bit the theory how in general 2D games differ from 3D games? Differences might include more possible game moves, the role of spatial perception (afaik men and women have different strong faculties here - so maybe 3D games are not gender-neutral and less popular besides hardly portable/digital playable?), or mappings of well-known game strategies from 2D.

PS: My first question here. I have no idea if this question is too open, so please reformulate if so. I'm more asking for some good links shedding some light on the general differences in game theory/structure between 2D and 3D.

• The most problems are physical representation of boards, i think.
– Zhen
Sep 28, 2012 at 11:40

While I've not seen serious work on it... I have played trek-style 3d chess

Take the pawn. In 2d, it has one move option. in 3d, given the start locations, it has 2, sometime 3, options Twice that many "covered" squares it can attack to.

The 3D has several effects:

1. increasing piece movement options
2. different board shape reduces flat move options for many pieces
3. perception of good versus bad moves is more difficult
4. occasional adjustment of board results in different dynamic (small boards are mobile)

this al means a direct comparison is difficult as the needed strategies change.

3D tic tac toe, however, merely gets more move options - the same strategies apply. So it varies by how the 3D is done.

• This answer seems too specific to examples, not the general question. Perhaps the question can be clarified to be one or the other? Sep 13, 2011 at 22:36
• The general question is practically unanswerable because it's too general, and not much is really done on it academically. Sep 14, 2011 at 5:58
• @aramis thx. What academic branches deal in general with this topic? Psychology, Game Theory...The star trek chess looks also quite unsymmetric :), so you go constantly around the board to view from diff. angles? Sep 15, 2011 at 8:40
• Star Trek chess is actually fairly symmetric along one axis. It just doesn't look it. The few times I've played, we just both sat to the sides; one's playing upwards, the other downwards, but it's easiest to see moves from above and to the sides. Sep 16, 2011 at 18:17

Summary

3D games are not fundamentally different, but are less common because they are usually harder for people to understand the basic game mechanics. The main problem with 3D chess is that spaces on the board are adjacent without easy visual indication of such.

Full Explanation

Let's start with games with discrete spaces (like Chess, Risk, etc), the important principle is not the "dimensionality" of the board (2D vs 3D), it's the graph of the spaces on the board. 2D games usually have a planar graph, whereas 3D games are usually made that way to intentionally have a non-planar graph. They could still be made on 2D boards, but are not for the sake of novelty. There are still plenty of examples of games with 2D boards that still have non-planar graphs, such as the following:

The thing about non-planar graphs is that they are harder to reason about because there the visual cues for adjacency of spaces are either weaker or abstract. Edge detection is a key facet of both the neuroscientific study of human vision and the machine learning approach to computer vision. Thus, having adjacent territories share an edge means that you can have a human "understand" that adjacency in the Occipital Lobe. Two adjacent territories that are physically separate and only indicated to be adjacent on the board need to make it through the Occipital lobe and to the Cerebrum for someone to understand the adjacency, though there are at least high level visual cues they can use to help.

Two adjacent territories that are adjacent by means of game rules and not visually indicated at all or using something other than color (such as "vertical overlay plus 2D adjacency" in your 3D chess example) are probably the hardest to handle because there is no support whatsoever from the visual cortex, and this is purely effortful abstract reasoning. Effortful abstract reasoning is a major obstacle to gameplay when present in the basic mechanics. Take the classic Diplomacy map as an example of how much visual cues matter: many players miss the fact that Norway and St. Petersburg are adjacent because the border between them isn't very wide, even though the rules for adjacency are quite unambiguous.

Games that are popular tend to be ones that people get "intuitively". This is a really hard concept to define, but is best understood through examples. If, in Magic the Gathering, a goblin could fly and an angel couldn't, this would be really hard for people to remember (even though there is no rules reason this could not be the case), whereas the other way around is quite easy. If Settlers of Catan used species of plankton as the five resources, it would be an identical game, but would be far harder for people to remember what resource did what (since plankton have nothing to do with building roads and cities) and would consequently be massively harder to play. Similarly, that physically adjacent spaces allow movement between then is easy to understand, whereas physically disjoint spaces with no visual indicator allowing movement between them is hard.

Even in regular chess, the knight is usually the hardest piece for new players to "visualize" the movement of due to the fact that it cheats adjacency in it's movement, and consequently has fewer visual cues as to how it moves. Try playing chess on a board that is all one color (instead of alternating colors) and see how hard it is to visualize the movement of bishops.

The 3D chess game you give as the example is most likely unpopular primarily due to all of the reasons above making moving non-intuitive. The rules of the game are intentionally complex to take advantage of the novelty of the 3D structure of the board. While this is certainly entertaining for a game or two, it leads to a game that is more about not making mistakes than one with interesting strategic analysis, since you have to spend so much cognitive effort even understanding what moves are legal. From what I can find about the rules the proper way to visualize a move is to look at the board from above, but due to the overlap of the boards, this requires you to look at the board from a number of sides to see what is obscured by the bird's eye view. Add on top of this the fact that some of the boards can move to different positions and intuitive adjacency goes out the window. The lack of portability of the game is a minor inconvenience in comparison.

All of the above has been with regard to games with discrete spaces. There are plenty of examples of 3D games that are very successful that aren't about spaces:

The success here is that they don't require reasoning about complex 3D structures; they're just object manipulation and the human intuition about physics. I'd file Blacksmith puzzles (also known as tavern puzzles) as also having the attribute of successfully using 3D geometry to create engagement, but these are intended as solo exercises rather than having competitive rules draped on top of them.

As an extreme example, Allan Calhamer (the inventor of Diplomacy) made a four-dimensional game called "Hyperspace", though embedded the four dimensions onto a 2D board with some interesting movement rules. This ended up being sufficiently unintuitive that the answer to multiple questions in the included FAQ in the rulebook is "You don't understand hyperspace."

I have played an 8x8x3 version of Chess, somewhat similar to Millennium 3D chess But since I received my set in 1978 nd that dates from 2001 they can't be quite the same. The board had three plastic chessboards stacked one above the other (not offset as in the Star Trek version), and pieces could make their regular flat moves or make related moves across levels.

At the tiem I was a fairly inexperienced chess player, and I did not find the experience very different, except that the end game was harder with another way for a king so slip away from a pending mate. One had to have at least one piece on the adjacent level to block the king's escape, and it was pointless to try to mate on the middle level except with overwhelming strength. The physical positioning allowed fairly easy visualization of relative positions and move. It helped that the "white" squares were actually transparent.

This question possible does need to be a bit more specific, so I am going to restrict my answer to tri dimensional chess. In tri dimensional chess, where the different levels of boards overlap, the overlapping squares are considered to be the same positions and a piece ending its move on an overlapping square has a choice of levels to end on. This aspect alone completely over hauls a 2D chess players rule book. Depending on which rule set is employed. By far, the most played rules are Andrew Bartmess' Federation Standard rules, adopted by memorabilia 3D chess board makers and sanctioned, initially, by the makers of Star Trek. The additional strategic mechanisms open a whole new range of options for each move. Unfortunately, Federation Standard rules offer a major tactical advantage to whoever plays from the top board, in what is commonly referred to as the 'highest board' move. I won't go into it here but there's a good explanation on boardgame geeks:

Two other popular rule sets are Jens Meder's and the jedi smurf rules, both utilised in many computer versions of the game. These severely undermine the point of the overlapping squares as a piece on any level can block the path of any other piece.

To really explore the 3D space across all the boards, I recommend the World Tri Dimensional Chess Federation rules.

http://w3dcf.com/information/laws

They make blocking harder as pieces may move along any path, provided there are corresponding empty squares. They are also more intuitive for 2D chess players.

You have grafics, or, pictorals, &, symbolics in, any 3d communications. ONEdemention is always simple "graphics." The other, 2 are "symbolics &, pictoral" because, it's a 3 D/demention, &, 3D conceptual design. THEREFORE, It's HOW your brain views the strategy, of, the game, as, a cube, OR, a flat surface graf, not, unlike "graff paper."

The 3D is a 3d "concept," W/, invisable sides, a top, midle, &, base/floor demention.

• It's a more solid open, constructive play, automatically, vs. the flat 1-demention graff paper, flat, foward, backward, corner, to corner moves.

The 1 dementional is more "grafic" not, unlike a stick man represents a person drawing, to the mind. whereas, the 3D dementional is more "pictoral" &, the moves played, ARE on, more than, 1 level, in, one single move per, piece is highly "symbolic," in otherwords, I move here, &, below, & impose a pictoral, upon, the oponent, a 3d concept when, I start my piece moving, in a cube sphere.

The instantaneous pictures, create solid symbolics, in the shape of, posts, ladels, &, sides, which, in, turn, invisablly contains the Opponents piece's &, imprisons the moves, by the mere 3d design &, conceptual piece.

ALL the opponents moves are "symbolic" attempts, on, levels above, or, below, their pieces.

If, a pyramid, or triangle were 3 D conceptual design, INSTEAD OF THE 3 CHESS BOARD TRIPLE STACK, you cant move, or even leave the game, unless, you go outside, the invisable boundaries, or resort back into, the one demention flat "graphics" With no 3d conceptual design communications, because, AGAIN, In order, to play the game you must use "pictorials &, symbolics" in a 3d conceptual design, to communicate ALL your moves.
Theres no concept structure, In 1 demention, you just, keep playing in a flat 1dementional graphic, non-pictoral level, completely, w/ out any higher "symbolic" required thinking.

*Uno.

Understand? Its a "pictoral "game of "symbolics" &, intentions, vs. Simple "graffics" 1 piece moves flat demention no conceptual 3d design communications just 1 "grafic" cross stick movements.