Value of pieces

In addition to its complex way of handling piece value, Stockfish includes something called the "quadratic imbalance terms". That is a phrase used by the chess programming community. Stockfish in the comments calls it "Polynomial material imbalance parameters"
github.com/official-stockfish/Stockfish/blob/master/src/material.cpp#L32

What that code is doing is computing an "imbalance" score.
There is a score for each pair (our piece, another of our pieces) and a score for each pair (our piece, their piece). But this is misleading because all such pairs are not considered! The supposed 6x6 matrix (bishop-pair, pawn, knight, bishop, rook, queen) is actually a triangle! Note that this includes the 'bishop pair' concept as well!

So where did this code come from?
It seems to have its beginnings in work done by Mark J. Sturman, a chess and computer chess researcher.
www.chessprogramming.org/Mark_Sturman

There is an interesting article by Larry Kaufman here
www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman
This was first published in Chess Life, March 1999. The chess.com version is edited by Dan Heisman.
Kaufman references Sturman.
www.chessprogramming.org/Larry_Kaufman
en.wikipedia.org/wiki/Larry_Kaufman
Kaufman is an American GM who is a professional computer chess programmer.

@EwoudUtrecht said in #16:
> now I'm starting to doubt if a pawn is really worth 1 point...
that is worthy thing to consider. a and h pawn in opening are worth less than a pawn and e&d worth more tha a pawn.
And in endgame it typically is the other way around

@efreixar #1
Where does Lichess give that relation between rook and Queen?
~ And, 2 Rooks are almost as worth as a Queen and a pawn.

Read: en.m.wikipedia.org/wiki/Chess_piece_relative_value#Changing_valuations_in_the_endgame

@Akbar2thegreat said in #23:
> @efreixar #1
> Where does Lichess give that relation between rook and Queen?
> ~ And, 2 Rooks are almost as worth as a Queen and a pawn.
>
> Read: en.m.wikipedia.org/wiki/Chess_piece_relative_value#Changing_valuations_in_the_endgame

He probably got a queen vs 2 rooks + pawn ending and saw a draw from a perpetual, so a +0, so he might inferred that that was their value.

@Alientcp
Oh! That was the case.
Well, so it was draw due to position since evaluation isn't only based on material.
He went for wrong inference though!

That doesn't matter, what matters is that you know that two rooks coordinate better than a queen.

@alej01 said in #26:
> That doesn't matter, what matters is that you know that two rooks coordinate better than a queen.

Only when they are connected and have enough tempos to shift when they have to, because, well, they have to be connected and cant move diagonally.

They dont coordinate better than a queen always, only when the position allows it.

Fun fact: if there are several Queens the value depreciates, the board‘s too small. And, the pair of Bishops counts more than 2x one Bishop.

@Alientcp said in #27:
> Only when they are connected and have enough tempos to shift when they have to, because, well, they have to be connected and cant move diagonally.
>
> They dont coordinate better than a queen always, only when the position allows it.

Yes @Alientcp