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Finding the value of pieces

@philodendron68 said in #16:
> @DERG_CHESS Du verstehst nicht, dass ich von der reinen Kampfkraft eines Königs spreche, wenn man davon ausgeht, dass er auch geschlagen werden dürfte, ohne dass man dadurch die Partie verliert! So läuft es übrigens im ANTISCHACH, das ich sehr schätze, aber nicht gut beherrsche. Im ANTISCHACH kann man auch Bauern in Könige umwandeln.
Aber für antischach wird hier nicht geredet. Außerdem hattest du dies nicht in deinem Post erklärt
Interesting post thanks. It seems strange, though, that two rooks 9.86 are almost worth exactly exactly a queen 9.82
I think that does not match the experience of most players. Even if Magnus recently won vs Anish a complicated game (with a queen vs rooks)
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Chess engines have an internal piece value. The simulation doesn't make sense since all you are recovering are position-weighted built-in parameters.
great article ! liked and followed ツ

would love to see how the #s for 3 check would come out. Especially some equation where there is already one or two checks. With 2 checks a queen might be +10 or above!?
If you normalize this a bit, ({9.82, 4.93, 3.28, 3.16, 1}/3.28*3), you get

8.9817073, 4.5091463, 3.0000000, 2.8902439, 0.9146341
So, a queen is worth 9, a rook is 4.5, a bishop is worth 3, a knight is worth slightly less than 3, and a pawn is worth slightly less than 1. This seems like a pretty sound way to think of the game. These values are of course dependent on the situation and the players. Ultimately, the king if the only piece that matters. (0 points for the king is simply because all positions included a king and no information could be gained about who will win from its existence. The king is actually worth ∞, but including it (basically, including positions where the king is already dead) would mess up our ability to fit the logistic model.)

This mostly teaches me I've been overvaluing rooks by calling them 5s. But it also points to what experience has been showing me: three pawns are a little weak when paired by themselves against a knight or bishop in the end game.
@vr235 said in #26:
> Chess engines have an internal piece value. The simulation doesn't make sense since all you are recovering are position-weighted built-in parameters.
This is a solid point, because who wins is determined by Stockfish. But it should still give us a pretty good idea.

Do we think it would be smart to update Stockfish to evaluate positions using these values? Maybe Stockfish already uses them internally though, because at the higher levels it applies a neural network, which would be equivalently aware of this. I'm mostly just talking about the eval bar.

(I haven't studied the Stockfish source code. I don't know exactly how it works and at each depth.)
@boilingFrog said in #14:
> Yes, but how can the king have no correlation with the game result ?
See my above comment about why King is 0 instead of infinity. It's just a consequence of how logistic regression works and the fact that we don't have data where no king exists.