interesting
comparing to other stuff
the planar piece arrangement feels different, but makes much more sense
the rook movement is (x,0,0) yes?
the knight is (2,1,0) + (2,1,1) i think
bishop is (x,x,0) or (x,x,x) right
queen is rook + bishop
pawns go only towards the other side in movement and in capture the pawn goes (1,1,0) and (1,1,1) in the forwards direction?
if this is right, you can rephrase pawn capture as "single step bishop" which is better imo
castling!?
and en passant...
lets say a white pawn is on 5e7 (white pieces start on plane 1)
and a black pawn goes from 7d7 to 5d7, then the white pawn can capture to 6d7?
bit confused on what "no 3d diagonal" means here coz that makes me think en passant requires a pawn to go on top of another pawn...
My previous thread on this is long dead and I have changed my mind about some of the ideas, so would like to share this again:
Real 3d chess is not what you see on star trek, it is a cubic 8x8x8 board with 512 cells, and potentially 256 pieces in total. The initial set up would be all of each sides pieces on their 1st "plane", such as the following:
Something to this effect, and a mirror image for black (but unsure exactly where the kings would be). Both sides would need all the extra pieces to account for all the extra cubes pieces have available. The 2nd plane would be 64 pawns. Now for piece movements:
King: This would be the simplest, the king could move to any adjacent cell horizontally, vertically, up or down, and along 3 dimensional diagonals 1 cube away as well. This yields 26 different cubes a king could move to from the center. Think of a rubiks cube, the king is in the core of it, it can move to any of the cubes on the surface from the center.
Queen: Can move in the same 26 directions as the king, but any number of cubes away obviously. This totals 86, which will become clear once you calculate the rook and bishop type moves..
Rook: Very easy, Just like normal chess, except it could also move up and down, so 21 total moves. There are no 3 dimensional moves when it comes to rook moves, they all can be represented in a single plane, so it only has those 21 (7 in each of the 3 perpendicular straight lines).
Bishop: The bishop could move along any of the 6 2d diagonals. There are 2 perpendicular diagonals in each of the 3 two-dimensional planes it is in, and since there are 13 squares in a normal 2d plane it could move to, x3 = 39. Now here's where it gets a little tricky..there are 3 dimensional diagonals the bishop could move within as well. Think of the cube in the lower-front-left, and the cube in the upper-back-right, a line connecting those two through the cubes constitutes a 3 dimensional diagonal. From the center, these can be summed up by 2 slanted planes with 13 possible moves each = 39 + 26 = 65 total moves. Point being all pieces can make both normal 2 dimensional moves, 2 dimensional moves in perpendicular planes, and 3 dimensional diagonal moves. The bishop is actually more powerful than a rook in 3d chess.
Queen = Rook + Bishop Moves Combined = 86.
Knight: Calculation of all the 2d moves is simple. 6 directions to choose from for the initial 2 square straight line movement, and 4 possible 1 square movements perpendicular to that, which is 24. But remember, 3d diagonals moves have to be taken into account as well, a knight could also make a 1 cube diagonal move that's still perpendicular to the initial 2 cube move, so that's another possible 24 moves. So the number is even higher but haven't calculated exactly what it would be. Once again, more than twice as powerful as the rook. As weird as it sounds a 3 dimension knight can fork 2 pieces that are right next to each other. In fact, a knight in say, the cube "d-5-5" could fork all of these pieces assuming this is plane 7:
Pawn: Each side would have 64 pawns covering the entire 2nd rank, or 2nd plane. Same first move 2 cube ability rule applies. However, a pawn could capture on 8 different cubes. It could capture a piece on any cube that's one cube above it, except the cube directly above it (4 2d diagonals moves upward, and 4 3d diagonals moves upward. Pawns could only make moves that advance it one rank. They couldn't move back and forth or side to side within the same rank, only up toward the top. En passant could theoretically be done 2 different ways on the same pawn, depending on how you interpret the pawn capture in 3d, but for simplicity sake, we'll say a 3d en passant capturing move would land the pawn directly above it vertically, not 1 cube away from it on any diagonals. So the pawn on a starting square, not on the edge, could potentially have 10 different moves.
What's very hard to calculate is if a king and queen could force checkmate. A checkmate position would be a basic support mate with the king in the corner, a queen 1 cube diagonally away, and a king 1 cube away from the queen, but it may not be forcible, even with 2 rooks or a queen and rook it may not be forcible. All of this would have to be calculated from scratch to determine what is a draw or not!