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The silver elephant has inspired me to look at all of the rider pieces whose ride movements are to an adjacent square and whose movement is left-right symmetrical on a square board.

There are 31 such pieces; of those 31 pieces, 16 can traverse the entire board (if the board is not a cylinder or toric board; more can traverse the entire board if it is toric depending on the board’s dimensions):

X - X        - X -        X X X        X - X        
- # -        - # -        - # -        X # X
- X -        X - X        - X -        - X -

X - X        X X X        - X -        - X -
- # -        - # -        X # X        - # -
X X X        X - X        X - X        X X X

- X -        X - X        X - X        - X -
X # X        X # X        X # X        X # X
- X -        X - X        X X X        X X X

X X X        X X X        X X X        X X X       
- # -        X # X        X # X        X # X
X X X        - X -        X - X        X X X

Here, an ‘X’ indicates that the piece can move one or more squares in the indicated direction, as long as the path in question is not blocked by a friendly or enemy piece. This piece can capture an enemy piece by going to the square the enemy piece is at, just like in FIDE Chess.

In the above table, the piece on the third row in the left column is the Rook, and the piece in the lower right corner is the FIDE Queen. The rest of the pieces are fairy pieces; the second piece in the second row is a rider version of Shogi’s Silver; the second piece in the fourth row is a rider version of Shogi’s Gold.

Let’s take an 8x8 board and add FIDE Chess’ pawns and king to the board, putting the pawns on the player’s second row and the King in the E file (just like in FIDE Chess). We then, for the seven remaining positions in the player’s back row, randomly choose one of the 16 above pieces. This results in about 250 million possible opening setups.

How powerful are these pieces? While I haven’t done a full analysis of these pieces, the majority of the pieces are at least as powerful as a rook. This means that White will probably have a strong advantage in the majority of setups; to compensate for this, I would implement the “Pie rule”: Player one chooses White’s first move, then player two chooses whether to play white or black.

Castling could be handled by allowing the king to, once in the game, swap pieces with another piece, as long as the king and the other piece have not yet moved.

If 250 million is not enough possible opening setups, or if people find the pieces too powerful, we can have each piece, instead of being able to move any number of unobstructed squares, randomly choose whether a piece can only move one square in a given direction, be able to move square or leap two squares in that direction, or be able to move any number of unobstructed squares in the direction. This results in 15,120 different possible pieces. If we have seven such pieces, we have some 180,660,221,412,287,006,638,080,000,000 possible opening setups.

If we insist on left-right symmetry in all aspects, we have 882 different pieces to play with. If we make the game compatible with a FIDE chess board, where the pieces representing the rooks, knights, bishops, and queens are in their FIDE opening position, there are 605,165,749,776 possible opening setups.

Have I tested these variants? Nope; all it is so far is an interesting thought experiment.