Sam Trenholme wrote on Sat, Mar 4, 2006 06:22 AM UTC:
I like this idea because I like the idea of having a chess variant template which makes for a huge number of playable games; I'm not just talking about the 960 games of Fischer Random Chess or the 252,000 possible games using a 8x10 Carrera setup where the bishops are on opposite colors; I'm talking a Chess variant that allows a number of games with a number like 6,670,903,752,021,072,936,960 (the number of possible Sudoku solutions).
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.
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.