Kevin Pacey wrote on Thu, Jul 20, 2017 12:12 AM UTC:
Hi Joe
I'm not entirely confident of my formula for the estimated fighting value of a King (or Guard). The formula doesn't seem too bad when applied to 4D chess (e.g. 256 cells) where a King has many, many legal moves usually, fwiw.
On a 12x12 board I'm assuming if my formula makes for a good estimate (1.75 Pawns) it's because of such things as it taking a King many moves to cross from one edge of the board to the opposite one. On a 12x12 board a knight takes only two more moves to do so minimally than on an 8x8 board. Still, it might be quite reasonable to have a knight worth only, say, 2.5 on a 12x12 board. Big boards would seem to handicap short-range pieces. However, I recall the wikipedia entry for Grand Chess puts a knight in that variant at worth only 2.5 on its 10x10 board, which I don't agree with.
Hi Joe
I'm not entirely confident of my formula for the estimated fighting value of a King (or Guard). The formula doesn't seem too bad when applied to 4D chess (e.g. 256 cells) where a King has many, many legal moves usually, fwiw.
On a 12x12 board I'm assuming if my formula makes for a good estimate (1.75 Pawns) it's because of such things as it taking a King many moves to cross from one edge of the board to the opposite one. On a 12x12 board a knight takes only two more moves to do so minimally than on an 8x8 board. Still, it might be quite reasonable to have a knight worth only, say, 2.5 on a 12x12 board. Big boards would seem to handicap short-range pieces. However, I recall the wikipedia entry for Grand Chess puts a knight in that variant at worth only 2.5 on its 10x10 board, which I don't agree with.