The closing thoughts of determining the value of a controlled square makes me think of piece square tables in chess engines. They’re piece-specific, which I originally thought was a drawback but I think opens up some interesting analysis you can do of a position. For example if White has strong control over squares which have a high value in the knight’s piece square table, then in theory white should prioritize keeping his knights and black should prioritize fighting for those squares and trading off white’s knights.
Although I think the way the control calculation would have to function for something like this, is that control by a lower-valued piece is considered “absolute”. It doesn’t matter if my two knights, a bishop, both rooks and my queen are controlling a powerful square, if a pawn is defending it. I wonder if fixing this would be as easy as taking the squared reciprocal of the piece values instead?
I don't think that piece square tables would work to determine the value of the squares, as a knight on the edge would be weak but controlling the h7 square when the king is on h8 is usually very powerful. My intuition is that controlling squares around both kings is the most important thing.
As for the absoluteness, I thought about it but it may also be misleading as one side could sacrifice a piece on the square to gain control over it which might be justified. In general, it seems like handling such dynamics is very difficult. But adjusting the values in general is certainly something that can improve the score.
The closing thoughts of determining the value of a controlled square makes me think of piece square tables in chess engines. They’re piece-specific, which I originally thought was a drawback but I think opens up some interesting analysis you can do of a position. For example if White has strong control over squares which have a high value in the knight’s piece square table, then in theory white should prioritize keeping his knights and black should prioritize fighting for those squares and trading off white’s knights.
Although I think the way the control calculation would have to function for something like this, is that control by a lower-valued piece is considered “absolute”. It doesn’t matter if my two knights, a bishop, both rooks and my queen are controlling a powerful square, if a pawn is defending it. I wonder if fixing this would be as easy as taking the squared reciprocal of the piece values instead?
Really interesting stuff, thanks for the post!
I don't think that piece square tables would work to determine the value of the squares, as a knight on the edge would be weak but controlling the h7 square when the king is on h8 is usually very powerful. My intuition is that controlling squares around both kings is the most important thing.
As for the absoluteness, I thought about it but it may also be misleading as one side could sacrifice a piece on the square to gain control over it which might be justified. In general, it seems like handling such dynamics is very difficult. But adjusting the values in general is certainly something that can improve the score.