What are examples of Go played on non-flat surfaces, like on a sphere? [closed]

Question

I know there was some thought put into how Go looks or feels like if it's not plaey on a flat, rectangular surface, but the surface of a 3-d object like a sphere or a donut. I'm mostly interested in:

• How is the grid mapped to the surface, so that every node has 4 neighbors (the number of neighbors is important for how hard it is to capture stones)?

• What does the absence of a border and corners mean for the game?

• What are variants that are actually taken seriously as a game and played, and not only seen as obscure applications of weird topologies?

Answer 1

I started writing another comment, but it got too large, so I'm putting this as an answer instead.

Your other question suggests that you're envisaging playing go on the surface of an actual sphere/torus. In particular that question mentions that you want "all nodes more or less equidistant". Searching on the internet, I didn't find much evidence that this is how go is played on other topologies.

There are a few reasons why I doubt torus/sphere go has been played on actual spheres or tori. Firstly - who has a suitable torus lying around that they could use? Secondly - getting the stones to stay in place would be awkward, and examining the position would be even worse!

Instead I suggest that the usual* way to convert a flat board game into one on a sphere/torus/Klein bottle is by imagining that the edges are joined up. For some diagrams of how the edges of the board should be joined see here.

I found a few references to playing tic tac toe and gomoku (5-in-a-row) on different surfaces, and one to playing go. All of these assumed a standard square grid with the edges defined to be connected in some way. The main differences from standard go seem to be:

• Fewer corners and edges: A cylindrical board has just two edges, and a torus or Klein bottle surface game has no corners or edges.
• The lack of corners and edges makes it harder to create immortal groups.

I did also come across a game of go on a cylindrical surface which was not just made of a standard board with edges connected. Each point still has four liberties, but the regions between edges are not all square:

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*I'm not sure a 'usual' actually exists here, but this is at least the usual way to draw diagrams on these surfaces in mathematics.

Answer 2

I found this program that a guy at university made to abstract Go to any topology, using any number of vertices as well, it is called 3D Tashoku Go. Other than as a curiosity I haven't seen anyone take play in this way as a serious variant of Go.

Just changing the size of the grid leads to games that feel very different from a standard 19x19 game.

You shouldn't let that really dissuade you from exploring weird variants of Go, the game was originally played on a 17x17 board and I've seen people play on up to 31x31 on KGS at times.

These games are vastly different strategically. At 23x23 and greater the rush for the corners and sides feel less important than the fight for the center. Life is easy to be had and the game feels fairly relaxed and open.

Answer 3

The implications in the game are that board boundaries are used by players for defensive purposes (corner and side enclosures).

The game usually starts with corner approaching moves because turns spent in the corner are more point efficient as they protect more territory with fewer moves (with the help of the board boundary).

Answer 4

Although not strictly a new topology, I often play where the regular bound board is present, but on top of that draw n lines diagonally through points, connecting them. Through having a bottom left to top right, and a top left to bottom right diagonal go through the centre point. Through having 3 to 5 of these pairs of lines, they significantly change the strategy, also making it more interesting to amateur players. Of course this has significant FTA(first turn advantage), which is another reason its useful with large skill differences.

Finally, with the few diagonal lines running along the board, connect these lines at the edges so that they are continuous, while the normal vertical/horizontal grid is bound.

NB:Alternative rule: Territory only needs to surround the regular vertical/horizontal lines, not the diagonals.

Answer 5

I recently developed a new type of spherical Go game with different topologies. Although this board game is still in its early stages, it offers a vast expanse of unknown game space to explore. Prior to my experiment, the typical approach was to use a conventional grid-like topology. However, I introduced the concept of Archimedean solids to this domain. As we know, the ancient Greeks were aware of only five Platonic solids, which is a mathematical theorem. However, the vertices of these Platonic solids are too few to make the game interesting. Therefore, I explored the table of Archimedean solids—an extension of Platonic solids—and found the snub dodecahedron particularly interesting. It most closely resembles a sphere and features 60 vertices, 150 edges, and 92 faces, totaling 302 game elements, which is complex enough. This shows the potential for possibilities, where we can incorporate vertices, edges, and faces—all these geometric elements—into an engaging game space. After weeks of research, I discovered a unique board topology that naturally accommodates all 302 elements while still adhering to the traditional Go game rule set.

To ensure the complex board is easily recognizable, I studied the symmetries of the solid and ultimately devised a solution. The design features four distinct 'continents' distributed across the sphere, separated by 'oceans'. In the diagram above, I used a specific color to identify one continent. However, globally, there are four symmetrical axes, which influenced the layout shown in the diagram below. This symmetrical arrangement not only enhances visual clarity but also underscores the strategic possibilities inherent in the game's topology.

It should be noted that the terms 'continents' and 'oceans' are purely symbolic labels within the game's design. They do not directly influence gameplay decisions, similar to the origin and star points in traditional Go. These labels serve merely as visual aids to help players navigate the complex topology of the board.

The rules have been slightly modified in terms of area calculation; in this version, pentagons and triangles contribute differently to the final game results. This adjustment accommodates the unique geometry of the board, ensuring that the varying sizes and shapes of the regions are accurately reflected in the scoring.

The final diagram illustrates how the seven black stones are placed to form a shape that possesses sufficient liberties to survive. This configuration is the minimal in the game.

Please check with this https://github.com/spherical-go/polyclash