A New Perspective on Chess Complexity

[rblasingame]

@syzygy, What does piece positioning have to do with my model which is specifically agnostic to spatial-temporal board states? A Pawn does not remain on the board after it promotes, it therefore cannot be captured, only the promoted piece class can be captured, but the pawn used to gain a promotion is already in the graveyard at the point where the promoted piece class would be captured. A player can never choose to not promote a pawn that reaches the last rank, it's against the rules of the game.

[syzygy]

@syzygy, What does piece positioning have to do with my model which is specifically agnostic to spatial-temporal board states? A Pawn does not remain on the board after it promotes, it therefore cannot be captured, only the promoted piece class can be captured, but the pawn used to gain a promotion is already in the graveyard at the point where the promoted piece class would be captured. A player can never choose to not promote a pawn that reaches the last rank, it's against the rules of the game.

What does your model have to do with chess or computer chess?

I am a math teacher/independent researcher and I believe I have developed a new measure of chess complexity, Asset-Configuration Complexity, that I believe will sharply reduce computational loads in chess engines and database tables.

So can we agree that it does not do any of that.

[Tibono]

Hi, just sharing my humble opinion here... First, I am happy to read the discussion evolved to more objective arguments. Second, my most probably poor understanding summarizes the whole paper as: material, considered separately light/dark pieces and including the graveyard is an asset that matters and provides an interesting footprint, irrespective of the journey (moves) that led to it and of the actual distribution (position) across the board (squares) and graveyard.
Well, I must agree with syzygy, this is sophistication about the material balance that has since long been a very basic... hence far from a new perspective. To say it in a positive way, maybe you should write a section clearly explaining how your work differs?

And please: Stop Using Caps on Every Word Anytime You Title Something. You are not using German language, are you?

[hgm]

Note that the total number of material compositions is not simply the product of the possible white and black compositions. It is not possible to promote all Pawns without capturing a lot of material. To promote 8 Pawns of one color, the 8 opponent Pawns that were blocking those would have to be passed, which can only be done by capturing them, having them capture something, or capture something with the Pawn that passes them.

[syzygy]

Note that the total number of material compositions is not simply the product of the possible white and black compositions. It is not possible to promote all Pawns without capturing a lot of material. To promote 8 Pawns of one color, the 8 opponent Pawns that were blocking those would have to be passed, which can only be done by capturing them, having them capture something, or capture something with the Pawn that passes them.

The total number of reachable configurations is 58,084,310:
https://chess.stackexchange.com/questio ... -are-legal

And I remember seeing this before here:
https://kirill-kryukov.com/chess/counti ... mes/#Chess
which refers to this 1999 post:
https://web.archive.org/web/20171209014 ... p?id=77068