Back to top

100,000,000 possible Chess Variant pieces

Let’s first look at all of the possible short range leapers on a square board. Let’s look at pieces which can leap, at most, two squares away. One possible leaper is the knight: 
- O - O -
O - - - O
- - X - -
O - - - O
- O - O -
Other leapers also exist. We include pieces like a piece which moves like a king (mann or commoner): 
- - - - -
- O O O -
- O X O -
- O O O -
- - - - -
Given this, how many non-colorbound leapers do we have? We know that we have 2^24 total possible pieces (24 possible squares to move to), but some of them are colorbound, i.e. a given piece can not reach every square on the board.

Let’s look at the historical form of the Queen, the Ferz, which exists in Shatranj and some modern regional chess variants including Senterej, Makruk, Sittuyin, and Asean chess: 

- - - - -
- O - O -
- - X - -
- O - O -
- - - - -
The piece moves like the modern bishop, but only one square. Like this bishop, this piece is colorbound; it can only reach 32 of the 64 squares on an 8x8 chess board.

Point being, some pieces are colorbound (there are other forms where a piece can not reach all 64 possible squares, such as the pawn, discussed in more detail below). How many?

Of the 16,777,215 pieces that exist, only 325,135 are in any form colorbound. Some 16,452,080 pieces are not colorbound.

What about riders

I described the historical ferz above (Russian still uses the word “Ferz” for the Queen, but the piece now has the modern move); we can also have a “ferz-rider” where, after moving one square, if the following square in the same direction is empty or occupied by an enemy piece, we can move again. This process continues as long as the square is empty (the move stops when capturing an enemy piece).

A “ferz-rider” is today’s bishop piece. Other riders exist: The queen can be thought of as a king-move-rider, and the Rook is the rider form of a piece called the “wazir”.

So, let’s look at that grid again: 

\ O | O /
O \ | / O
< - X - >
O / | \ O
/ O | O \
Let’s have the following rules:
  • A piece can have any combination of the eight possible knight moves, but knight moves are short-range leaps (no knightriders in this variant)
  • A piece can have one of five possible moves for each of the eight compass directions: It can go one square in the given direction, or it can jump two squares in the direction, or it can either go one square or jump two squares in the direction, or it is a rider in the given direction, or finally it simply has no move in the given direction.
With these restructions, we have precisely 100,000,000 possible pieces. Of those pieces, 99,028,469 pieces are not colorbound (all of these pieces can go to any square on the board from any square).

Chess15,538,181,​035,900,961,​358,171,344

If we have the knight, bishop, and queen be instead one of these 99,028,469 possible pieces, and in turn have the King be a piece which moves like a wazir (like a rook but only one square), with all four possible ferz (one square like a bishop) moves possible (so the king could move like a king, like a wazir, like a gold general, or any other of the 16 combinations of possible subsets of ferz moves), we get some 15,538,181,035,900,961,358,171,344 possible variants.

There aren’t any bishops in any of those variants, mind you, since the bishop is colorbound.

Semi-pinwheel, not colorbound

While looking for colorbound pieces, I found an interesting non-colorbound piece: 
O - - - -
- - - - O
- - X - -
O - - - -
- - - O -
(There is a mirror image form of this piece also) Here is the number of moves to get to a given square on an 8x8 board, starting at “0”. We will use hex numbers (“A” is 10, etc.): 
2 D B 9 7 5 3 E
A 8 6 4 2 D B 9
5 3 1 C A 8 6 4
2 B 9 7 5 3 1 C
8 6 4 2 0 B 9 7
5 3 1 A 8 6 4 2
2 B 7 5 3 1 C A
8 6 4 2 B 9 7 5