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Dan, thanks for taking the time on this entry. The basic idea is that the Nexus squares/cells are the same on each side. When you go to the 7th row, you are effectively on both planes at the same time, however, bending space dimensions mean that they are different cells, but it is up to the player to decide which of the two cells the piece is in, or has moved to. That is, moving from 6 to 7 you can choose to be in T17 or F67. This is confusing, and looking again at the pictures that I created representing the moves of the pieces, I realize that there are some errors. For example, the knight when moving from the flipside to the topside, didn't take the flipping of the board into account. The picture shows the topside final position of the knight incorrectly, they should be flipped with respect to the 11 o'clock, 5 o'clock axis. So the final possible positions are actually still on dark spaces, which is a change from conventional chess where the knight always changes color. Regarding the board diagrams and pictures, using your notation, the flipside of T21 is F51, and F12 is on the other side of T62. The 11 o'clock, 5 o'clock diagonal is the axis of rotation for thinking about the flipside.
(I'm John's father, and we did discuss this... but the game and the design is entirely John's.) The 'Nexus' spaces are certainly a novel idea. After discussions with John they can be thought of as being that each space has its parallel universe space on the flipside. Probably this would create a challenge for a deterministic chess rule set, since the player can decide whether the piece stays in its current universe (flipside/topside), or shifts to the other (topside/flipside respectively), EVEN in the MIDDLE of a move. Thus a Knight can move through a Nexus space and the player can decide if the Knight remains in the current 'universe' or has shifted to the other. There is one piece which can only move in one direction through the Nexus spaces, and that is the Pawn. By the above logic, the move from flipside to topside does not take up a pawn's move. A Pawn could go from Circle 6 to 7, for example on the Topside. The next move that the Pawn could make is to go from Circle 7 on the Flipside to Circle 6 on the Flipside.
If transitioning from square 7 top to square 7 flip is indeed a non-move, some ambiguities concerning capture remain. Imagine that a Topside Pawn moves to square 7 topside. Then a Flipside Knight moves to square 7 flipside. Since it is essentially the same square, is it compulsory that Knight takes Pawn, or can they co-exist? How long can they co-exist? If capturing is not compulsory, can Pawn take Knight instead in the same 'inter-turn / between-turn'? Could Topside move a different piece, and Pawn would/could still take Knight in a non-move? If capturing is compulsory, which I would suggest for logic's and clarity's sake, does the board have 84 or 78 unique cells?
In thinking about this, there were a couple of options. The nexus spaces could have been regarded as the 'tunnel' spaces, or 'lift' spaces that take you from one plane to the other. However, to fit with the notion of reverse sides, reverse worlds, the concept is that the nexus spaces are, each individually, like revolving doors; or like those walls in movies where you go from one side of a room to the other side by spinning on an axis. Hence the different color schemes in each world. So, we say that there are 84 individual spaces. When in Topside you move to or through the 7th circuit, you can choose whether to remain in the Topside or to 'flip' to the Flipside. A Pawn in the 7th circuit of Topside can be directly opposite a Knight on the Flipside: capture of an opponent's piece is not compulsory. With the below-described optional rule, capture of a piece is not even possible. John calls the following optional rule the 'Indiana Jones' rule: If you choose to do the 'non-move' of changing from Topside to Flipside during a piece's move, then any piece which is in the corresponding 'flip' position will also get flipped to your original world. This would match with the rotating wall concept. Another parallel is that the nexus spaces would be like elevators, where when you use Elevator A to go from floor T to floor F, then Elevator B automatically takes whoever is in it from floor F to floor T. Some of the diagrammed possible moves for the pieces show that a given piece can move to multiple nexus spaces. If so, it can choose which of those multiple nexus spaces it may flip in. Pieces that are moving through a nexus space can choose which of the nexus spaces they flip in. We think that the logic is that you can only flip your piece once during a move (i.e. rook cannot go from circuit 6 to 7 in topside, then flip to flipside, then cross the centre of the circle, then flip again). Thanks for spending the time examining this unique game concept.
Another interesting circular CV for this week's Pi Day. RNBKQP get two additions, weak Tocop and strong Starman, which could be explained better. The inner circuits will have most of the action. Really the Nexus, or tunnel, or lift, is not common to the different teams Topside and Flipside, because player specifies which it is on if a piece stops there. Tesselations mixed square- and triangle-boards, like Round Table Chess, stretched topologically to over-all roundness, can play with more clarity than hexagonal ones. Yet Flipworld may not have erased all ambiguity about transit through its six Nexus cells(triangles).
INTERESTING.
Wow. I like.
Bishop moves are darn tricky. They have an abundance of paths to take, I'm guessing they are valued approxamently the same as a rook.
Also, don't rooks tend to be more dangerous on a circuar board?
Consequently, the queen might be overly powerful.
I honestly think that there could be more peices to play with the different angles.
I think this has a germ of brilliance, but incomplete. This definitly has some unrealized potential.
So, there are 3 things I find interesting about this board.
1) It's a round board, with a way across the center...rare, but there are others.
2) The nexus allows for forking both top and flipside, even with a rook.
3) The nexus connection between top and flipside allows for some really interesting gateway interplay. Unlike typical board squares, two squares may simultaneously be the target of a single move.
Unfortunately, the setup of army pieces does not take advantage of 1 & 2. Having the topside all one color and flipside the other essentially neuters two thirds of what I find interesting. Another variant is forming in my brain.....
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