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Well, if you like the large number of setups, here's another idea you may find amusing: Googol Chess. In Googol Chess, each square points to a particular non-adjacent square randomly chosen during the setup. A piece has the additional power to leap to the square pointed to by its current square, if that destination square is empty. There are at least (64-9)^64=55^64 > 2.1 x 10^111 possible setups on a standard chessboard.
I want make an overview about crossovers between chess and sudoku.
1-player
- Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece should attack the numbers 1-8 exactly once. (proposal, discussion and examples)
- Slightly Modified Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece can attack the numbers 1-8 exactly once.)
- White Knight Sudoku (each row, column and box contains the digits 1-8, a white chess knight, no white knight attacks one other knight) (example)
- Black Knight Sudoku (each row, column and box contains the digits 1-8 and a black chess knight, every knight attacks at least one other) (example)
- Black and White Knight Sudoku (each row, column and box contains the digits 1-7, a black chess knight and a white chess knight, every black knight attacks at least one other black knight, no white knight attacks one other white knight) (example)
- Knight and Queen Sudoku (each row, column and box contains the digits 1-8 and a white chess knight or a white queen (one per puzzle), no chess piece attacks one other) (example)
- White Queen Sudoku (each row, column and box contains the digits 1-8, and a white chess queen, no white queen attacks one other queen)
- Anti-Knight Sudoku (each row, column and box contains the digits 1-9, no digit is knight-move connected with the same digit) (example)
- Anti-Knight Sudoku X (each row, column, box and both main diagonals contain the digits 1-9, no digit is knight-move connected with the same digit) (example)
- Sudoku with chess piece pattern (example)
2-player
Hints to other chess sudoku crossover are welcome.
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One idea: Each pawn can be one of nine different pawn types:
- A chess pawn
- A shogi pawn
- A berolina pawn
- A 'beroshogi' pawn (moves and captures diagonally forward)
- A chess pawn that can also capture directly ahead
- A berolina pawn that can also capture diagonally forward
- A chess pawn that can also move diagonally forward
- A berolina pawn that can also move straight forward
- A 'super' pawn that can both move and capture straight or diagonally ahead.
For an 8x8 board, this results in 9 ** 8 (43,046,721) possible opening setups; for a 10 * 8 (or 10*10) board, this results in 3,486,784,401 possible opening setups.For the pieces, any of the pieces, except the king, can have any of the 15 combinations of rook, knight, bishop, and camel movements. The king exists in three forms: Can move as a ferz, can move as a wazir, and can move as a FIDE chess king. For an 8 * 8 board, this results in 512,578,125 possible setups; combine this with the pawns above and our 8x8 board now has 22,064,807,537,578,125 possible opening setups. The corresponding 8x10/10x10 board has 402,131,117,372,361,328,125 possible opening setups. Now we're starting to get what looks like a variant template with a decent number of possible starting setups. :)
As a practical matter, this template for the pieces probably usually results in arrays where white has a considerable advantage because there is so much force on the board, but this is a thought experiment, not a practical Chess variant design.
This might work a little better: Make the atoms Betza's crab (leaps from e4 to d6, f6, c3, and g3), a fers, a wazir, and a camel. But that probably makes most setups too weak. Perhaps if we add a randomizing factor with these weak atoms whick randomly strengthens one of the atoms (makes the ferz atom a bishop atom, a wazir a rook, a crab a knight, and a camel a camel + dabbah). This causes each piece to have one of 32 possible forms; for an 8x8 board this results in a grand total of 4,437,222,213,480,873,984 possible setups; for a 10x8 or 10x10 board, this results in 368,040,959,274,957,611,728,896 possible setups.