Positional 3-D Chess
By George William Duke
Stated as generally as possible, the new idea is for 3-D games to use the position of pieces, not their definitional movement capability, in one game board to establish the squares available to move (or switch, or drop, the words being used synonymously) to another board. Hence the title 'Positional 3-D Chess'.
Board: First 3-D Version: 8x8x2 (128 cells)
Two boards juxtapose without rotation, or for convenience lie end to end preserving orientations (like you would play Alice Chess).
('Square' and 'cell' are used interchangeably since play would generally be
with boards laid end to end. Actual 3-D cells could be visualized from 2-D
squares by imagining one board above another. Movement between boards, or
levels, comes about by virtue of the 'position', that is which particular square
a piece rests on. Therefore, we are not concerned with faces, edges and corners
of cube, or cell, as in most 3-D chesses.)
8 * * * * * * * *
8 * * * * * * * *
7 * * * * * * * * 7 * * * * * * * *
6 N F B K R B F N 6 N F B K R B F N
5 P P P P P P P P 5 P P P P P P P P
4 p p p p p p p p 4 p p p p p p p p
3 n f b k r b f n 3 n f b k r b f n
2 * * * * * * * * 2 * * * * * * * *
1 * * * * * * * * 1 * * * * * * * *
a b c d e f g h a b c d e f g h
Passed Pawns line-up for 8x8.
Pawns promote in three steps to Rook, Knight, Bishop, or Falcon.
Upon promotion of a White Pawn at rank 8 of board X, its piece-conversion is placed to any empty square in rank 1 of Board Y. Likewise, Black Pawn's promotion at board X-rank 1 becomes its piece-counterpart at Board Y-rank 8. Continuing in the same pattern, White promotion in Board Y (Rank 8) goes to an empty square of choice in Board X-rank 1; Black Board Y-rank 1 to Board X-rank 8. Note that all these are the reverse of the usual. It works because of the separate boards and Passed Pawns line-up.
Two moves per turn, meaning one on each board, and checkmate of any King wins. Taking place as it does on both boards, Promotion counts as two moves: a pawn's promotion is a player's complete move for a turn.
A player would strategically hold off from a mandatory-promotion pawn move until favorable conditions exist at the board of destination.
As should be apparent, the title 'Positional 3-D Chess' does not refer to strategy in game play of three-dimensional chesses. This article might be called '3-D Passed Pawns Chess' instead, or prosaically 'Multi-Board Passed Pawns chess'. The initial arrays used are like those in Passed Pawns, Scorpions and Dragon for 6x6, 7x7 and 8x8. Extensions of those set-ups are respectively to 6x6x4, 7x7x3 and 8x8x2. 'Positional' in the name refers to the way of translating movement from 2-D to 3-D, to be applied to still more games than included in this article. In this first series of 3-D games, only Pawns are available for placement on other board levels--a chessic shift through the third dimension. A future article is to consider Pieces' moving, or switching, through three dimensions. Here Pawns (not pieces) change levels and at that only upon PROMOTION. By the unusual nature of the initial Passed Pawns line-ups, Pawns are already just two, or three, or four steps away from promotion. Simply put and covering all the variations generally in one sentence:--a Pawn that promotes disappears from its board (level) and is placed as its chosen promoted piece to any vacant square allowable in a designated row (either one rank or one file or two files) of another board (level)(s).
Relying on adjacency, 3-D chesses by and large try to extend 2-D notions (motions) to 3-D. There are described almost 100 3-D games within the Chess Variant Pages (CVP) and about as many in Pritchard's 'Encyclopedia of Chess Variants'. Conceptually in 3-D, 'cubes' rather than 'squares' are used to visualize the moves of the pieces. Adjacencies from cube to cube through face, edge and corner are unfortunately subject to differing interpretations. CVP discussions about 'tetragonal', 'hippogonal', 'triagonal' and so on show difficulties in agreeing on definitions. Rook, Bishop, Knight, and even super-elementary Wazir and Ferz have been inconsistently transcribed in 3-D fashion. In contrasting approach, Positional 3-D Chess maintains in principle that a clearer means for translation entails movement (automatically) from one board to one of a set of squares in another board, not necessarily being an inclusive rank or file. The specific square is at the option of the player, but the choice comes after the movement of the pawn (or piece) within the originating board. There is no attempt to project a 2-D mode of movement into 3-D.
Comparable to the Positional 3-D paradigm herein described, 50-year-old Alice
Chess uses same-cell correspondence to determine piece placement. These
three-dimensional forms are large chesses by their nature. Even classical
Raumschach (5x5x5) is 125 cells. Simple placement by position in 3-D, having so
many cells to confound as they invariably do, adds the extra dimension without
confusion. Two or more boards, or levels, are enough to manage without figuring
out what is meant by "orthogonal-oblique," "warp leap,"
"directed correspondence," "3-D modality," and like terms in
other over-two-dimensional game descriptions. Better to rely on positional, as
opposed to motional, criteria to achieve clarity in 3-D Chess.
Board: Second 3-D Version: 7x7x3 (147 cells)
7 * * * * * * * 7 * * * * * * * 7 * * * * * * *
6 R N B K N B F 6 R N B K N B F 6 R N B K N B F
5 P P P P P P P 5 P P P P P P P 5 P P P P P P P
4 * * * * * * * 4 * * * * * * * 4 * * * * * * *
3 p p p p p p p 3 p p p p p p p 3 p p p p p p p
2 r n b k n b f 2 r n b k n b f 2 r n b k n b f
1 * * * * * * * 1 * * * * * * * 1 * * * * * * *
a b c d e f g a b c d e f g a b c d e f g
Passed Pawns Chess line-up for 7x7.
Any promotion of Pawn goes to an empty square one of a2, a3, a4, a5, a6, g2, g3, g4, g5, or g6 at option, immediately on either of the other two boards. Black and White sides have the very same promotion-destination squares available. Pawn is at once transferred to its piece of choice, and that is the player's move for the turn. Without a Pawn promoting, a player's turn consists of any two moves on two different boards of the three available. Notice that the promotee in this version appears at its arrival board not in a rank at all, but in 'edge file', on the flanks, laterally introduced from the other board. Also note that a player may make more moves on one particular board (level) than another, as the turns progress; but in no case is there to be a double move on one individual board per turn. Two out of three checkmates establish the winner. Necessarily strategy expands to foresee promotions from the other two boards.
Board: Third 3-D Version: 6x6x4 (144 cells)
6 * * * * * * 6 * * * * * * 6 * * * * * * 6 * * * * * *
5 R N B B N K 5 R N B B N K 5 R N B B N K 5 R N B B N K
4 P P P P P P 4 P P P P P P 4 P P P P P P 4 P P P P P P
3 p p p p p p 3 p p p p p p 3 p p p p p p 3 p p p p p p
2 r n b b n k 2 r n b b n k 2 r n b b n k 2 r n b b n k
1 * * * * * * 1 * * * * * * 1 * * * * * * 1 * * * * * *
a b c d e f a b c d e f a b c d e f a b c d e f
Passed Pawns line-up 6x6.
Occupying inclusive rows, Black pawns and pieces are not always prefixed by 'B'(=Black). In this version promotion has the usual venue, the last rank, but takes only two steps and differs in its destination from board to board. Above from left to right A overlays B, B overlays C, and C over D in the 3-D format. For convenience the boards would be set adjacent to one another, as they appear here, preserving orientations. For 6x6x4, Board A promotions go to Board B, Board B's to C, C's to D and D's to A. More specifically (adding a twist by varying destination rank or file), White Board A promotee in rank 6 goes to Board B rank 1 square of choice, and the reverse for Black. White Board B promotion goes to Board C file a, Black to same Board C file f. White Board C pawn promotion goes to Board D file f, Black to D file a. Board D promotions, going to Board A, are to ranks 6 and 1 respectively for White and Black. Summing it up another way, Board B has reverse rank promotion received from A, Board C has lateral file promotion from B, Board D has the same side file promotion (from C) but with White's and Black's destinations reversed, and Board A has normal last rank promotion received from D. The first two checkmates establish the winner. Once a mate occurs on a board, its pieces are frozen and never move again. For rare cases of no empty square available for a promotion piece, a player is permitted to choose a square of a perimeter rank or file orthogonal to the official destination row. This alternative placement, though infrequent, becomes a further component of strategy. In general for 6x6xn Chess the nth board has promotion from the (n-1) board with placement to a perimeter row shifted systematically either 90 degrees or 180 degrees according to some pre-established formula.
Roberto Lavieri's Altair furnishes the idea for Pawns or Pieces to have an entire rank or file to move, though in Altair it is within the same board.