H. G. Muller wrote on Tue, Oct 30, 2018 12:26 PM UTC:
I would recommend to forget about the protected-Pawn restrictions in the numbering system. The inconvenience of not having direct mapping formulas between numbers and positions seems much worse than having some numbers that correspond to invalid positions.
Note that WinBoard already allows positions to be entered by number, and that the World probably would not become a better place by having ChessV and WinBoard use incompatible numbering systems.
The WinBoard system is a generalization of the traditional Chess960 numbering, to make that applicable to almost any variant. For each piece type you divide the total number by the number of placements for that type (for determining placement of subsequent pieces), and use the remainder as placement code for the current piece type. If the variant has normal castling rather than Fischer castling, you first place the King and Rooks (or whatever serves as castling partner) in their normal positions. If the board width is even you then place all pairs of color-bound pieces such that they are on different shade. Then you place all remaining pieces on the still open squares, ignoring square shade. In games with Fischer castling you are then left with 3 opens squares, and occupy them by the King between the castling partners.
Currently the WinBoard implementation has some limitations: numbering is not unique if a certain color-bound type occurs in more than two copies. (As this never happened in any of the supported variants, I did not bother with that case.) Also, the order in which pieces are placed depends on the piece encoding WinBoard happens to use, traversed high to low in order to make sure Q is placed before N. And it only recognizes Bishop, Ferz and Alfil as color bound, placing them in the order A, F, B. (Relevant for 'Courier960'!)
Especially the piece order seems hard to objectively define so it would cover every conceivable variant. I want to propose to derive it from a 'mother position', which for Chess960 obviously would be the FIDE array. The pieces can then be ordered according to where they stand on the baseline in this reference position, e.g. for white from left to right this would lead to the order R, N, B, Q, K. They would then be placed in top-down order: K, Q, B, N, R. But B is color bound and present in multiple copies, so it gets precedence: B, K, Q, N, R. Now in variants with castling K and R drop out (either done first or last, but always in a predetermined way), so the final order is B, Q, N, as in Chess960. For CRC it seems logical to use the Capablanca position as reference (as the name suggests that).
It should be easy to write a universal shuffling routine that takes a given position and a random number, and then shuffles that position according to the number. Unfortunately WinBoard now places the super-pieces in the order C, A, Q, which is not what the Capablanca start position would suggest when traversed from left to right.
I would recommend to forget about the protected-Pawn restrictions in the numbering system. The inconvenience of not having direct mapping formulas between numbers and positions seems much worse than having some numbers that correspond to invalid positions.
Note that WinBoard already allows positions to be entered by number, and that the World probably would not become a better place by having ChessV and WinBoard use incompatible numbering systems.
The WinBoard system is a generalization of the traditional Chess960 numbering, to make that applicable to almost any variant. For each piece type you divide the total number by the number of placements for that type (for determining placement of subsequent pieces), and use the remainder as placement code for the current piece type. If the variant has normal castling rather than Fischer castling, you first place the King and Rooks (or whatever serves as castling partner) in their normal positions. If the board width is even you then place all pairs of color-bound pieces such that they are on different shade. Then you place all remaining pieces on the still open squares, ignoring square shade. In games with Fischer castling you are then left with 3 opens squares, and occupy them by the King between the castling partners.
Currently the WinBoard implementation has some limitations: numbering is not unique if a certain color-bound type occurs in more than two copies. (As this never happened in any of the supported variants, I did not bother with that case.) Also, the order in which pieces are placed depends on the piece encoding WinBoard happens to use, traversed high to low in order to make sure Q is placed before N. And it only recognizes Bishop, Ferz and Alfil as color bound, placing them in the order A, F, B. (Relevant for 'Courier960'!)
Especially the piece order seems hard to objectively define so it would cover every conceivable variant. I want to propose to derive it from a 'mother position', which for Chess960 obviously would be the FIDE array. The pieces can then be ordered according to where they stand on the baseline in this reference position, e.g. for white from left to right this would lead to the order R, N, B, Q, K. They would then be placed in top-down order: K, Q, B, N, R. But B is color bound and present in multiple copies, so it gets precedence: B, K, Q, N, R. Now in variants with castling K and R drop out (either done first or last, but always in a predetermined way), so the final order is B, Q, N, as in Chess960. For CRC it seems logical to use the Capablanca position as reference (as the name suggests that).
It should be easy to write a universal shuffling routine that takes a given position and a random number, and then shuffles that position according to the number. Unfortunately WinBoard now places the super-pieces in the order C, A, Q, which is not what the Capablanca start position would suggest when traversed from left to right.