Relative Piece Values

[FrancoisK]

Hi,

I am using 1000 : 3250 : 3250 : 5000 : 9750 in BugChess2.
However Miquel is right : the average bonus added by evaluation should be take into account if it changes with piece type.

As I think there is room for improvement in this area in my engine, i have started generating my material table.
I am not taking positions from actual games like Alessandro suggested in a very interesting thread, my positions are randomly taken from my engine's analysis trees and selfplayed by my engine to know the result. I am already seeing significant improvements in fast selfplay matches after a few weeks.

Cheers

François

[hgm]

Say, H.G., what values are you using for 10x8 these days? I seem to recall you did some significant research in this area.

Thanks!

P = 85
N = 300
B = 350 (+40 for pair)
R = 475 (w.o. open-file bonus)
A = 875
C = 900
Q = 950

still modulated by piece-square positional values, of course. These are the values the pieces have on the squares where you typically find them in games. Note that this is not the same as averaging the PST values over the board, as in practice the pieces will avoid the squares with low values. So simple averagng would overestimate the importance of very bad squares (like corner squares for Knights).

But this is opening value, and since then I have done some tests in connection with Superchess that showed that the end-game values of the heavy pieces differ by more, and that Q-A is definitely more than a Pawn there.

I have not implemented this in any of my programs yet, though. It seems what is needed is a material interaction term, which discounts the value of high pieces for every lower (non-pawn) piece the opponent has. Due to such a term a Q vs R+B trade might be favorable in the precence of 2+2 other Queens (or C/A),, but not for a single Queen.

[MattieShoes]

It occurred to me while reading this that making values relative to pawns is probably terrible, because pawns values are the most situational -- passed pawns, isolated pawns, backwards pawns, doubled pawns, tripled pawns, edge pawns, central pawns, pawns in front of the king, your LAST pawn, etc. In some cases, a pawn could approach the value of a queen, and in others, the value of the pawn might be negative.

I know we're talking about "average" pawns, and I guess we use it because it's typically worth the least, but it just seems odd to me to use it as a baseline. All pieces change value based on situation, but surely the pawn is the most unstable. I'm assuming the 1/4/4/6/12 scheme has average pawn value of >1.0 due to bonuses for centrality, king safety, and whatnot.

[diep]

Years ago I discovered a little known fact about the value of pieces. What I did was to count the number of square that each piece could attack. I then added one point to each piece that could attack both colors with the exception of the King which I subtracted one point. When all the pieces were totaled I diveded the totals by three. It comes out to an amazingly close answer to what the pieces have been rated over the years.
Have a few spare minutes, give it a try.
Bill

That would give values:

pawn: 2 + 1 ==> 3 / 3 = 1.0
knight: 8+1 ==> 9 / 3 = 3.0
bishop: 13 ==> 13 / 3 = 4.33
rook: 15 ==> 15 / 3 = 5.0
queen: 27+1 ==> 28/3 = 9.33

Total ballony again.

Above piece values lose every single game in todays computerchess.

Vincent

[diep]

Most strong program seem to sue relative piece values of P:N:B:R:Q of roughly 1:4:4:6:12

I recently did a bunch of runs with roughly 1:4:4:5.5:12 and it did a lot better. Are these what others are using now?

I'm using 100, 325, 325, 500, 975. Strelka uses 100,300,300,500,1000 but there's a material correction table.

Oh comeon, it's so obvious you're not knowing what you use in your own software that even the biggest fool realizes, based upon the PLAY of your software in combination what you spam here, that you aren't using the above values.

Your proggie would lose every game when using the above values that you CLAIM you use.

Please recheck the code you cut'n pasted.

Your proggie of course doesn't have pawn at 100, but at 70 (toga) or 80 (fruit).

If you divide Fruit with that:
3.25 / 0.8 = 4.06 for a piece

Toga is a bit over agressive there (though that doesn't change its style much from Fruit) :
3.25 / 0.7 = 4.64 for a piece

With piece >= 4.0 THAT is how "twistedlogic" plays online, and not with 3.25 / 100 = 3.25.

Thanks,
Vincent

[diep]

Most strong program seem to use relative piece values of P:N:B:R:Q of roughly 1:4:4:6:12

I recently did a bunch of runs with roughly 1:4:4:5.5:12 and it did a lot better. Are these what others are using now?

You sure you aren't hiding some sort of "1 pawn bonus for inequal material" that the rook gets added in your eval somewhere?

I'm actually just fixing a game where diep against rybka was too happy taking a bishop+knight in endgame against rybka rook+knight, diep having 2 connected passers on one wing.

Default difference light piece vs rook is 2+ pawn in diep. Some other logics in eval talks that diff down quickly, but not to just 1 pawn.

I'd argue a rook is at least 2 pawns better than a light piece in most cases.

[frankp]

Perhaps there is a subtle point I am missing. You can either build the 'solution' to 3p for piece etc into the piece values, or fix with special terms in the eval?

[hgm]

It occurred to me while reading this that making values relative to pawns is probably terrible, because pawns values are the most situational -- passed pawns, isolated pawns, backwards pawns, doubled pawns, tripled pawns, edge pawns, central pawns, pawns in front of the king, your LAST pawn, etc. In some cases, a pawn could approach the value of a queen, and in others, the value of the pawn might be negative.

I know we're talking about "average" pawns, and I guess we use it because it's typically worth the least, but it just seems odd to me to use it as a baseline. All pieces change value based on situation, but surely the pawn is the most unstable. I'm assuming the 1/4/4/6/12 scheme has average pawn value of >1.0 due to bonuses for centrality, king safety, and whatnot.

This is why I always normalize everything to Q=950.That makes it much easier to compare different value sets.

[bob]

Perhaps there is a subtle point I am missing. You can either build the 'solution' to 3p for piece etc into the piece values, or fix with special terms in the eval?

Yes. The difference is that hard-coded piece values are there for the game, anything you do in the eval can be adjusted as you wish... For example, a knight for 3 passed pawns on the 6th rank is not a -1.0 trade...

[frankp]

Perhaps there is a subtle point I am missing. You can either build the 'solution' to 3p for piece etc into the piece values, or fix with special terms in the eval?

Yes. The difference is that hard-coded piece values are there for the game, anything you do in the eval can be adjusted as you wish... For example, a knight for 3 passed pawns on the 6th rank is not a -1.0 trade...

OK. But I was not suggesting that it was one or the other approach, merely that the hard-wired values address some basic trade issues. (Probably a rook for 3 connected passers on the 6th is not a good trade either.).