Piece Values on 6x6x6 I am calling the original triagonal mover in Raumschach an Alicorn and the (Alicorn + Ferz) compound a Unicorn. After looking over the ZRF for Tim's 6x6x6 3D Chess, I decided to set the Knight equal to 30 points and use Zillions to calculate some numbers. NOTE: I had to estimate the Alicorn value by subtracting the Rook and Bishop values from the Queen, which is a (R+B+A) compound in both 3D variants. That approach is consistent with Zillions behavior I have observed in other games.
P=6.4, A=13, R=23.8, N=30, B=30, Q=66.8
Now I am going try a very simple pencil and paper system. Set the Pawn value at an abitrary 10 points. Start estimating the other piece values by adding their minimum possible moves (from one of the 8 corners) to their maximum possible moves (from one of the 8 central cells).
I am mostly interested in 3D variants using weaker pieces than this 26-directions Queen, so I have little knowledge of it. Perhaps its true value is somewhere between 80 and 100 points. The (New! Improved!) Unicorn can visit all 216 cells, which suggests that it is actually worth 3.7 Pawns. I would multiply the (limited to 108 cells) Bishop by 0.8, resulting in a value of 33.6 points, and the (limited to 54 cells) Alicorn by 0.6, resulting in a value of 13.2 points. The Rook can reach any cell on an empty 3D board in three moves, which often turns out to be one move too late. Setting it equal to the Knight seems reasonable. All in all, this 'pencil and paper' system seems to give surprisingly good results. But one thing I have learned from playing chess all these years is not to push my luck too far. I do not trust Zillions, nor my little system, to cope with the subtle behavior of the 5x5x5 Raumschach board, where (my) Unicorn still attacks 28 cells from the unique central cell.
[2008 EDIT] I added the Guard moving like a nonroyal King. Worth 33 points, its value almost equals the adjusted 33.6 points of a Bishop. There are legal checkmate positions involving King and Guard against a lone King.
Piece Values on 6x6x6 I am calling the original triagonal mover in Raumschach an Alicorn and the (Alicorn + Ferz) compound a Unicorn. After looking over the ZRF for Tim's 6x6x6 3D Chess, I decided to set the Knight equal to 30 points and use Zillions to calculate some numbers. NOTE: I had to estimate the Alicorn value by subtracting the Rook and Bishop values from the Queen, which is a (R+B+A) compound in both 3D variants. That approach is consistent with Zillions behavior I have observed in other games.
Now I am going try a very simple pencil and paper system. Set the Pawn value at an abitrary 10 points. Start estimating the other piece values by adding their minimum possible moves (from one of the 8 corners) to their maximum possible moves (from one of the 8 central cells).
I am mostly interested in 3D variants using weaker pieces than this 26-directions Queen, so I have little knowledge of it. Perhaps its true value is somewhere between 80 and 100 points. The (New! Improved!) Unicorn can visit all 216 cells, which suggests that it is actually worth 3.7 Pawns. I would multiply the (limited to 108 cells) Bishop by 0.8, resulting in a value of 33.6 points, and the (limited to 54 cells) Alicorn by 0.6, resulting in a value of 13.2 points. The Rook can reach any cell on an empty 3D board in three moves, which often turns out to be one move too late. Setting it equal to the Knight seems reasonable. All in all, this 'pencil and paper' system seems to give surprisingly good results. But one thing I have learned from playing chess all these years is not to push my luck too far. I do not trust Zillions, nor my little system, to cope with the subtle behavior of the 5x5x5 Raumschach board, where (my) Unicorn still attacks 28 cells from the unique central cell.
[2008 EDIT] I added the Guard moving like a nonroyal King. Worth 33 points, its value almost equals the adjusted 33.6 points of a Bishop. There are legal checkmate positions involving King and Guard against a lone King.