I have written a small C program which looks at all 16,777,215 possible leapers that move at most two squares. Some findings:
I expected around half of all possible pieces to be colorbound in some way. Wrong. 16,452,080 (over 98%) pieces are not colorbound.
There are 104 non-colorbound pieces with three moves, 2,512 pieces with four moves, and some 2,696,337 pieces with 12 moves.
Only 2,944 possible pieces are Bishop colorbound: These relatively few pieces can go to the same 32 squares a Bishop can go to.
With some 16,452,080 non-colorbound pieces, if we replace the knight, bishop, and queen with a random non-colorbound short leaper, that gives us 4,453,099,898,116,838,912,000 which is, what, 4 hextillion possible variants, and that’s keeping the king, pawns, and rook.
OK, if that’s not enough possible variants, we can also add the ability for a given random piece to be able to be a rider in any direction it can leap (e.g. a fers-rider is our bishop; a wazir-rider is a rook, and a knight-rider is, well, a knightrider), where we randomly choose, from all the moves a given leaper has, for it to be able to ride in a random number of directions. For example, if we look at the wazir, then randomly choose which directions it moves like a rook and which directions it can only move one square, we get 16 possible pieces. If we do this for all 16,452,080 non-colorbound short range pieces, we get some 282,232,643,280 possible pieces, just over 2 to the power of 38 (2^38 or 2 ** 38 in Python notation).
This means an 8x8 board with random non-colorbound pieces and using a standard chess set has some 6,344,961,231,517,063,209,074,884,200,517,463,972,290,560,000 possible variants (the pawns and kings can keep their moves), just over 2 to the power of 152.
A while ago, I looked at 31 possible short range pieces. I have now expanded this research.
I have written a small C program which looks at all 16,777,215 possible leapers that move at most two squares. Some findings:
With some 16,452,080 non-colorbound pieces, if we replace the knight, bishop, and queen with a random non-colorbound short leaper, that gives us 4,453,099,898,116,838,912,000 which is, what, 4 hextillion possible variants, and that’s keeping the king, pawns, and rook.
OK, if that’s not enough possible variants, we can also add the ability for a given random piece to be able to be a rider in any direction it can leap (e.g. a fers-rider is our bishop; a wazir-rider is a rook, and a knight-rider is, well, a knightrider), where we randomly choose, from all the moves a given leaper has, for it to be able to ride in a random number of directions. For example, if we look at the wazir, then randomly choose which directions it moves like a rook and which directions it can only move one square, we get 16 possible pieces. If we do this for all 16,452,080 non-colorbound short range pieces, we get some 282,232,643,280 possible pieces, just over 2 to the power of 38 (2^38 or 2 ** 38 in Python notation).
This means an 8x8 board with random non-colorbound pieces and using a standard chess set has some 6,344,961,231,517,063,209,074,884,200,517,463,972,290,560,000 possible variants (the pawns and kings can keep their moves), just over 2 to the power of 152.