Finding the value of pieces

I consider bishop can price 4 pawns in certain positions.
If you have + 1 bishop,
YOU HAVE +3.
If you have + 2 bishops on one-colored squares,
YOU HAVE +6.
If you have + 2 bishops on different-colored squares,
YOU HAVE +8,
because you control all board on diagonals.
If you have + 1 bishop & 1 knight,
YOU HAVE +6.
If you have + 1 archbishop/hawk/princess/cardinal (B+N)
YOU HAVE +7,
because bishop can reach all squares.
If you have + 1 bishop
And opponent has + 1 knight,
YOU HAVE -1,
because

Although the Knight is generally considered to be on a par with the Bishop in strength, the latter piece is somewhat stronger in the majority of cases in which they are opposed to each other.
Jose Capablanca.

(And archbishop is from Capablanca’s chess;)
But you can’t give checkmate to your opponent with only + two knights.
Bishop is stronger than you can imagine.
Knight is strong too, and he is stronger when you have two knights on different sides of board, or board is smaller;)
Elephant from Shako chess can price as bishop.
It’s very interesting...

Is this using the same approach as the AlphaZero paper? chess.stackexchange.com/a/35337

I tried to do an analysis similar to this myself, but I ended up with larger values for the pawn, because in endgames an extra pawn is just so much more valuable. For example, in a pawn vs knight endgame, this is either a draw or a win for the pawn, so presumably this approach would come up with a value >=3 for the pawn!? Especially endgames with many moves can really skew this.

Interesting.... I always found this hard to understand.

@xjcl said in #32:
> Is this using the same approach as the AlphaZero paper? chess.stackexchange.com/a/35337

Essentially, though the fit function is slightly different. Using logistic regression to predict piece values (or to tune chess engines) isn't really anything new as mentioned in my post. The reason I did this analysis was mainly to get an easy to use generic tool that can be applied to countless chess variants. Chess is "just" a good test bed to validate the method and code, because in contrast to most variants there already is a quite clear picture of the expected results. But since there seemed to be quite some interest I decided to expand a bit on the chess part.

@xjcl said in #32:
> Is this using the same approach as the AlphaZero paper? chess.stackexchange.com/a/35337

It's similar. There is a technical difference between @ubdip's choice of logistic regression and DeepMind's choice to minimize the sum of squared error. In addition, unlike DeepMind, @ubdip includes a term for the side to move, which ends up having a very small value compared to material differences.

@Chipola14 said in #23:
> Is here Racing Kings's value of pieces ?

I will post Racing Kings piece values tomorrow at the same time (if noone else does before me). Started data generation script with count=1000000, it will take some 15 hours or smth.

@ubdip , thanks for the post and sharing results in open source!

Very good post, but horde?

@Chipola14
I got smth like this

Q 10.84
R 9.12
N 3.35
B 3.00
K 0.00

But I used 10 ms for a move when generating data, if I understand it correctly, and with longer time the estimate would be more precise.
Still, it looks reasonable to me. :)