💡📝Charles Gilman wrote on Wed, Apr 14, 2010 06:27 AM UTC:
Give me a chance to answer already! As it happens I've been offline analysing your analysis:
'If I'm looking at this right, the Viceroy is not merely colorbound, but also
rank-bound, visiting only 1 in 4 cells on the board.' It is not rank-bound but rank- (and filestack- and level-) switching. It always moves from an odd to an even plane or vice versa in all three dimensions. Nor is it colourbound in the same way as the Ferz. It is in fact bound to one quarter of each Ferz binding, rather than half of just one. A Dabbaba binding (on a cubic board) is the intersection of a Ferz and a Viceroy one.
'The Eunuch is colorbound, rankbound, and filebound, and given the particular geometry of this board, can only access 3 cells by itself.' True, but as the rules specify, it can never actually be by itself in this game.
'The Baron [FF'] and the Elk [AA'] can never get together to form their one allowable compound, the Imam, if I'm figuring the moves properly.' You're not, as the Baron, uniquely among two-component non-Wazir compounds, is unbound due to the Ferz and Viceroy bindings being independent. A Baron can reach an Elk square in two Ferz moves and a Viceroy one, without even interacting with another piece en route, e.g. a1-e2-j2-m1. Given that, are you now happy with the original array, or is your mind too blown to decide yet?
This all suggests that thinking of the Ferz, Viceroy, and Baron as variants of the same piece is not that helpful. Likewise for oblique directions the colourswitching 2:1:0 leaper, the 2d Knight, is a very different piece from a combined 2:1:1 and 2:2:1 leaper, let alone the compound of all three.
'If I'm looking at this right, the Viceroy is not merely colorbound, but also rank-bound, visiting only 1 in 4 cells on the board.' It is not rank-bound but rank- (and filestack- and level-) switching. It always moves from an odd to an even plane or vice versa in all three dimensions. Nor is it colourbound in the same way as the Ferz. It is in fact bound to one quarter of each Ferz binding, rather than half of just one. A Dabbaba binding (on a cubic board) is the intersection of a Ferz and a Viceroy one.
'The Eunuch is colorbound, rankbound, and filebound, and given the particular geometry of this board, can only access 3 cells by itself.' True, but as the rules specify, it can never actually be by itself in this game.
'The Baron [FF'] and the Elk [AA'] can never get together to form their one allowable compound, the Imam, if I'm figuring the moves properly.' You're not, as the Baron, uniquely among two-component non-Wazir compounds, is unbound due to the Ferz and Viceroy bindings being independent. A Baron can reach an Elk square in two Ferz moves and a Viceroy one, without even interacting with another piece en route, e.g. a1-e2-j2-m1. Given that, are you now happy with the original array, or is your mind too blown to decide yet?
This all suggests that thinking of the Ferz, Viceroy, and Baron as variants of the same piece is not that helpful. Likewise for oblique directions the colourswitching 2:1:0 leaper, the 2d Knight, is a very different piece from a combined 2:1:1 and 2:2:1 leaper, let alone the compound of all three.