Sesqui-dimensional Chess

Some time ago I worked on a 1-dimensional chess variant. After considering the natural ways to translate traditional moves into one dimension, I ended up deriving nearly the exact same game as One Ring Chess. I had settled on a different knight move, and a different opening setup, but otherwise the two games were identical. To summarize, One Ring Chess and the game I concocted both translated diagonal movement in traditional chess into movement by leaping two squares at a time in one dimension. This preserves the colorboundness of the bishops. Orthogonal movement is of course translated into sliding one cell at a time.

I continued to work on the idea, partly because it was disappointing to see essentially the same game had already been invented, but mainly for three reasons:
1) The rooks seem too trapped in one dimension. They have absolutely no provision for getting past their own pieces.
2) Neither my own version of the knight's move, nor One Ring's, was entirely satisfying.
3) Even with two fronts of the conflict, the game seems a bit too cramped and simple.

Sesqui-dimensional Chess addresses all three of those issues with one key idea, inspired by the natural representation of the board as a circle: pieces can move across the center of the ring to the opposite cell, as well as moving clockwise and counterclockwise. Everything else stems from that idea. The two armies can't start directly opposite each other, or you'd get an instant bloodbath, so instead each player's army is split into two groups that are opposite each other, with the enemy armies 90 degrees around the circle in either direction from either group. This naturally suggests a 4-way symmetry in the spacing of the armies, which guarantees that any two opposite cells are the same color. So moving across the center to the opposite cell should be thought of as a bishop-like step, which determines what a knight-move should look like. But since a bishop-like step in one dimension translates to simply leaping two squares at a time in a rook-like direction, there's no reason the rook can't jump to the opposite cell just like the bishop, sliding through an imaginary intermediate cell to reach the opposite side of the circle. This makes the rook less trapped. Lastly, splitting up the armies creates a total of four fronts for the conflict, enriching the tactical complexity of the game.

Setup

The board consists of 48 linearly adjacent cells that wrap around in a circle. Although the game is one-dimensional, the movements of the pieces are easier to visualize if the cells are put in a zig-zag pattern as well as wrapped into a circle. See the initial setup below.

This arrangement of the board makes bishop and knight moves look familiar from traditional chess, and compresses the radius of the circle, making it easier to find the opposite of any given cell. The contrasting light and dark sectors in the central area are also intended to make it easier to spot the opposite cell, though they also suggest a basis for a coordinate system (more on that in the closing notes).

You may notice dark grey spots marking the starting cells of the kings, queens, and rooks. These are the promotion squares for pawns.

Pieces

Pawns: Pawns promote on the starting cells of the opponent's king, queen, or rooks. Pawns always move in the direction of the nearest promotion cell (and therefore they can never jump across to the opposite side of the board like other pieces can). For simplicity, let's refer to any given pawn's direction of movement as 'forward' for that pawn. Pawns can move without capturing a single step forward (like a rook step). Pawns can make a capturing move by leaping exactly two steps forward (like a bishop step). A pawn on the starting cell for a pawn of its color has the option of making a non-capturing bishop-like step forward, leaping over the intermediate cell just like the pawn capturing move. Note that in the opening setup, there are four 'inner' pawns and four 'outer' pawns. If an inner pawn takes a single step forward, it ends its turn on the starting cell of an outer pawn. From there, that pawn still has the option of making a double-step forward, even though that's not that pawn's first move. There is no en passant capture.

Bishops: Bishops can leap 2 cells at a time in either direction, continuing likewise as long as each landing square along the way is unoccupied. The bishop can also leap exactly 24 cells, landing exactly opposite its starting cell. See below for an example of a bishop's movement options with just a few pawns on the board. The bishop's possible destinations are marked with X's.

Knights: Knights leap exactly 3 cells in either direction, or exactly 23 cells in either direction (landing adjacent to the opposite cell from the starting position). These are the squares that can be reached on an empty board by a single bishop step and a single rook step that don't go in opposite directions (the natural translation of the traditional knight's move to 1d). See below for an example of a knight's options on an empty board.

Rooks: Rooks slide 1 cell at a time in either direction, or leap exactly 24 cells, landing opposite from where they started. Example below.

Queen: The queen combines the abilities of rook and bishop.

King: The king can move a single step as rook or bishop. That is, the king can move 1 cell in either direction, leap exactly 2 cells in either direction, or leap exactly 24 cells.

Rules

There is no castling, no en passant capture, and the board and pieces are as described above. All other rules are as in FIDE chess.

Notes

There are 14 possible opening moves. Any of the 4 outer pawns can move 1 or 2 steps forward, any of the 4 inner pawns can make a double step forward, or either of the knights can leap out in front of its pawns.

6 of the 8 pawns are defended in the initial setup. The 2 that aren't defended cannot be immediately threatened by any of the 14 opening moves. There are 2 other pawns that may appear undefended at first glance, but look again: they are defended by the knight on the opposite side of the board.

Note again that even though jumping across the center is considered a bishop-like step, pawns cannot move or capture this way, because such a move does not bring them closer to promotion.

The 8 contrasting light and dark sectors in the central area are primarily to aid in identifying the opposite of any given cell, but they also suggest one possible coordinate system for this board. Take the cells exactly on the line between sectors as belonging to the more counter-clockwise of the two, take the white king's sector as sector A and label the rest counterclockwise as B through H, and number the cells within a sector as 1 through 6 counterclockwise. These are just the conventions I personally find the most appealing, but such details are immaterial to the game and can of course be changed if others find a different system easier to use. As for my conventions, the resulting notation for each sector and cell can be seen below.

Although I maintain that this game is genuinely 1-dimensional (for example because a rook on an empty board can reach every cell in 1 move), I also recognize that the moves across the center bring an odor of 2-dimensionality. But since there's no natural way of scaling up that dimension, it's not quite entirely there. Hence the name "Sesqui-dimensional Chess", "Sesqui-" being the latin prefix for one-and-a-half.

Last revised by Jeff Cornell.

Revisions of MSsesqui-dimensional-chess

Sesqui-dimensional Chess #500 by Jeff Cornell on 2022-11-27 12:54:56 as HTML