That a Bishop is more valuable than a Rook on that board is mainly a mobility matter: a move can at most have 4 moves, a Bishop will have many more. Even when you give a bonus to orthogonally adjacent move targets, a Bishop would probably still be more valuable on that board.
Whatever the board shape is, a diagonal slide will not be able to confine a King the way an orthogonal slide can. Kings tend to slip between attacked squares that are not orthogonally adjacent, and Pawns can dodge attacks by just stepping forward. So it might have to do with the move of the royal piece and Pawns. When the Royal pieces was a Ferz a Bishop would probably be much more valuable.
I am not sure the graph diameter would be the dominant factor. E.g. on a normal 8x8 board a Knight will have a much smaller graph diameter than a Commoner (= non-royal King).. But they hardly differ in value. For most of the game it isn't really important when a piece would be unable to reach a certain part of the board in practice. Because you have other pieces, and you just assign tasks to each of those in the area close to them.
Dynamic piece square tables for chess variants?
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hgm
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- Full name: H G Muller
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zulban
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Re: Dynamic piece square tables for chess variants?
Indeed. Not sure how to address this by algorithm though. I've also thought about using "average path length". Given a function D(piece,start,end), D(knight,A1,B1)=1, whereas D(commoner,A1,B1)=1. Also note D(knight,A1,G7) < D(commoner,A1,G7). So I could get an average for D for each piece.hgm wrote:I am not sure the graph diameter would be the dominant factor. E.g. on a normal 8x8 board a Knight will have a much smaller graph diameter than a Commoner (= non-royal King).. But they hardly differ in value. For most of the game it isn't really important when a piece would be unable to reach a certain part of the board in practice. Because you have other pieces, and you just assign tasks to each of those in the area close to them.
I'm probably just going to implement them all (approximating if an algorithm is too heavy) and just see how learned weights use the information, if at all.
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zulban
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Re: Dynamic piece square tables for chess variants?
Oops, D(knight,A1,B1)=3, I mean.zulban wrote:Given a function D(piece,start,end), D(knight,A1,B1)=1, whereas D(commoner,A1,B1)=1.