Kevin Pacey wrote on Sat, Jan 2, 2021 09:17 AM UTC:
@ H.G.:
I had thought I could transfer what it means for a piece to be a major one in orthodox chess to games of chess variants in general, but in light of your previous post in this thread about fortress draws, with at least some types of fairy pieces, being possible, I'll have to change my mind, if I hope to find a relatively simple and clear definition of what a major piece is for the field of chess variants in general.
Your notion (expressed elsewhere) of 'mating potential' (which I more or less understand, I think, without fully expressing it in words) might seem to do the trick, i.e. let's try saying a piece type would be a major one if it (a priori) has (any) mating potential (that is, for the situation of the single piece + K vs. lone K).
Then, even though the percent of mates a Silver General can deliver that you gave is a low percentage, since it (a priori) has mating potential, it might be considered a major piece, after all - nice if we want to have a simple and clear definition of what is a major piece.
There are still possible problems, though. A rook (kind of?) has mating potential on a Circular Chess board, even, but it only can (quickly) deliver mate in a very low number of kinds of positions that are generally unforceable. Might we still consider it a major piece on a circular board since it has mating potential, even though it forces mate in a very tiny percentage of cases? If not, what might an (arbitrary) cutoff percentage for a given piece type be that should not be considered major (for a given board size and shape, I should have noted from the start)?
@ H.G.:
I had thought I could transfer what it means for a piece to be a major one in orthodox chess to games of chess variants in general, but in light of your previous post in this thread about fortress draws, with at least some types of fairy pieces, being possible, I'll have to change my mind, if I hope to find a relatively simple and clear definition of what a major piece is for the field of chess variants in general.
Your notion (expressed elsewhere) of 'mating potential' (which I more or less understand, I think, without fully expressing it in words) might seem to do the trick, i.e. let's try saying a piece type would be a major one if it (a priori) has (any) mating potential (that is, for the situation of the single piece + K vs. lone K).
Then, even though the percent of mates a Silver General can deliver that you gave is a low percentage, since it (a priori) has mating potential, it might be considered a major piece, after all - nice if we want to have a simple and clear definition of what is a major piece.
There are still possible problems, though. A rook (kind of?) has mating potential on a Circular Chess board, even, but it only can (quickly) deliver mate in a very low number of kinds of positions that are generally unforceable. Might we still consider it a major piece on a circular board since it has mating potential, even though it forces mate in a very tiny percentage of cases? If not, what might an (arbitrary) cutoff percentage for a given piece type be that should not be considered major (for a given board size and shape, I should have noted from the start)?