Spherical Board Chess

Sphere Chess

I have been playing with an idea of how one could build a spherical chess board, where pieces would move almost exactly like they would on a flat board but with some small alterations to deal the the challenges of non-Euclidian geometry.

Figure 1: Here is a a mockup of the "board" (sphere? the sphord? surface where you put the pieces!) and the pieces in their starting positions. All the pieces are pretty minimalist and they correlate to their FIDE 2d counterparts. 

Understanding the Sphord

My first idea was to  divide the sphord into longitude and latitude like a globe, but that got really messy near the poles, so I used orthogonal latitudes to dived up the sphere.

Figure 2: To create the cells on the surface, the sphere is first divided by 7 latitudinal rings. Each latitudinal ring is spaced  evenly from its neighbors. Each is 1/8 of the circumference away from the next. Note that each ring lies in a plane and though the rings are equidistant on the sphere's surface, the planes marking the rings are closer together at the poles by Euclidean geometry.

 Figure 3: Further dividing the sphere by 7 more latitudinal rings that are rotated 90% from the first. Basically giving us a wonky globe with which has an east and a west pole in addition to north and south. When viewed from dead on you can see we now have a ranks a files to play on, with the ranks running north to south, and the files running east to west. But there is a problem! there are duplicates of many of the cells. For example there is a "C6" cell on the face of the sphord facing on the board in Fig3b, but there is also a "C6" cell that we can't see on the other side of the board.

Figure 4: In order to give every cell a unique coordinate of the sphord I decided to break the cells into 3 zones.

- The blue zone contains all the duplicated squares on the face of the sphord where the first rank is at the top and the a file is on the right.

- The red zone is the mirror image of the blue. When viewing the red zone head on, with the first rank facing upward, the a file will be on the left.

- The grey zone runs in a ring between the blue and red zones and contains all unduplicated cells.

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In the future I may post about piece movement and special rules that would make spherical chess playable, but I am realizing that just explaining the layout of the board is a lot. Obviously making a digital playable version of this would require 3d rendering not suitable for chess.com but I figured if anyone would care about my crazy idea it would be you people. I have some 3d modeling skills, but I don't know how to code. If anyone with game design savvy is reading this maybe we can talk.

Wow

Pawns

(For brevity I will explain all piece movements and abilities from the perspective of the white pieces, the parameters of the black pieces are identical but flipped just as in FIDE.)

 Figure 5: Pawns start on the third rank. 4 pawns start in the red zone, 4 in the blue zone, and 2 in the grey zone (on b3 and g3). 

Figure 6:  Pawn movement in the middle of the red and blue zones is identical for FIDE chess. White pawns promote when they reach the 7th rank. The white pawn moves forward one cell without capturing (Blue marker) or captures one cell forward and diagonally. The definition of "forward" and "diagonal" starts to get a little wonky in the grey zone.

Figure 7: The b3 and g3 pawns start life in the grey zone and face some interesting challenges. There are two moves  that allow the b3 pawn to go orthogonally forward, and it threatens three are diagonally forward. This means that on if it wants to move it will typically have to commit to playing more in the blue zone or more in the red zone.

(For future reference adjacent grey zone cells of the same color are considered to be diagonal to one another)

Figure 8: The b and g pawns are unable to simply march up to the 7th rank to promote, because the b and g files do not intersect with the 7th rank. I can only promote by capturing on c7. Pawns that end up on  dead-ends in the grey zone (b6 or g6, or a5, or h5...) are stalled unless they can make a capture on a forward facing grey zone diagonal.

 Figure 9: Pawns on the C and F files have their own quirks. If a pawn is in a red zone cell that is diagonally adjacent to its blue zone counterpart then it may capture pieces on the blue zone counterpart (confusing I know). For example the above pawn on C6Red can:

- Promote on C7Grey without capturing

- Capture on D7Red and promote

- Capture on C6Blue without promoting

Likewise a pawn on b5Red could capture on either c6Red or b5Blue.

Same applies for moving from blue zone to red zone.

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That more ore less sums up pawns. I'm considering scrapping the rule about moving from red zone rule, which would weaken the pawns, but maybe since each pawn is only 4 moves away from promotion they need to be nerfed a little bit to keep the same balance as FIDE chess. Also considering nerfing promotion, only allowing pawns to promote as high as rook or something, but that is the kind of thing I would need play testing to work out. 

My brain got 10% bigger after reading this

I sure hope not! otherwise you'd start to experience brain herniation which can be life threatening!

Yeah, this is big brain time