Piece Value

Date: 12 Oct 2006 11:31:37
From:
Subject: Piece Value

Hello.
I took up chess programming as a free time project.
I have come up with some ideas and any comment or suggestion would be
highly appreciated.

First of all, i have no intention to write the strongest engine
possible. I don't want another computer style, but something
interesting and fun for people to play against. (In that category
Gothmog and Doctor may be, but i want to go further) I want an engine
with as less chess knowledge as possible. I want it to be based
strictly on the moving patterns and a few geometric factors of the
pieces. So i came up with a question: What is the relevant value of the
pieces? Could the classical p, N=B=3p, R=5p, Q=9p be completely wrong?
Could the engines get an ELO boost with a differrent rating system? I
formed a few rating models that unfortunately none can be proved more
or less aqurate than the other. The classical rating as far as i know
was based on practise much before computers where available. My models
are based only on the moving and capturing patterns of the pieces on a
64 square board and in all cases they get a "clear" number which is no
way connected with the other pieces and then a relevant number is
calculated. So here are my values (A-F) together with the Turing
evaluations as well:

classical: p, N=3p, B=3p, R=5p, Q=9p,
K=?
Turing: p, N=3p, B=3,5p, R=5p, Q=10p,
K=1000p?
A: p, N=3p, B=3,375p, R=5p, Q=8,375p,
K=3,75p
B: p, N=3p, B=5p, R=8p, Q=13p,
K=3,75p
C: p, N=4p, B=2,25(4,5)p, R=6,666p, Q=11,166p,
K=5p
D: p, N=4p, B=3,333(6,666)p, R=10,666p, Q=17,333p, K=5p
E: p, N=5,333p, B=2,222(8,888)p, R=14,222p, Q=23,111p,
K=6,666p
F: p, N=5.333p, B=1,5(3)p, R=12,222p, Q=14,888p,
K=6,666p

As you can see we get values that in first look would appear in amateur
level, but coupled to a deep searching algorithm to avoid blunders may
give an interesting style.(By the way do you know any engine that let
you declare values up to Q=23p?)

My first problem comes with the knights: How could i turn the jumping
advantage of the knight into a number? I have find no way! HELP! In all
my evaluations knights are underrated because the jumping factor is not
taken into account. By how much the values are off i have no idea.
Also, the king should get a tiny gain because of the two square move in
the castling as well as the rook for its jump in this case.

Kings also get a value and since i dont want to include much chess
knowledge it may produce active king play right from the beggining. Now
a problem appears: King must be highly rated in order not to be
sacrificed, higly rated in order to direct the evaluation towards its
capture and so win the game but not too high because in that case they
may get into trouble due to overestimation. Keeping my values, the
problem could be solved with a bit of chess knowledge but that is what
i was trying to avoid right from the beggining. Any suggestions? Maybe
2 evaluations: one with my values in order to find a good move and then
a second one with a high value in order to keep the king safe? But how
could they be combined?

Then you can see that some bishops get 2 values. The problem comes from
the fact that a bishop can only move on half the board. Because bishop
values seem off by lot, i had to adjust the value as if they were
moving on the whole board. Should we just accept that or keep the
original value and the new one only for a pair of bishops? As you may
have noticed allready, the new number in the parenthesis is not the
double of the original and that is because the adjustment takes place
in an earlier step of the algorithm and not in the end. Or should i
just double the value in the end?

Evaluation: My early evaluation function follows the next steps: First
a value is given to each side based on piece values. Then captures and
exchanges are examined. A capture will occur if there is a gain or an
equality after the exchange because the less pieces are on the board
the more aqurate the computer will play (at least in most cases.) I
might adjust the later (in order to avoid endgame openings with no
middlegame) using the results of the next function. Then my favourite
part of the evaluation will come. Each piece will try to find a move in
order to be placed on a square that will get it as close as possible to
each original "clear" number that i mentioned in the beggining and was
calculated on a empty board and at the same time threaten pieces with
the highest possible sum.

My last problem: Pawn value. Pawn promotion is the game's second goal
or the first if a checkmate cannot occur. How to force the engine to
rush the pawns to the 8th row? Is the pawn worth a pawn? Allways? Or
does it get a value gain with each forward step until it equals the
queen on the final row? And if that is the case should the value step
be fixed? For example in the classical evaluation: p, 2,333p, 3,666p,
5p=R, 6,333p, 7,666p, 9p=Q in the 8th row. It doesn't look right. Does
it? Maybe the step should't be fixed. And what happens in case of an
underpromotion? What if it reaches the 8th row and needs to be
underpromoted for example into a knight? Then the sequence is wrong.
Should the sequence be calculated not for the queen but for a bishop or
knight, whichever has the lowest value for example: p, 1,333p, 1,666p,
2p, 2,333p, 2,666p, 3p=N=B. That looks logical. Doesn't it?

Any comment or suggestion will be welcomed and appreciated.
Thank you.

Date: 13 Oct 2006 13:53:49
From: Sumerian
Subject: Re: Piece Value

I recommend to have a look at:
http://www.chessbox.de/Compu/schachveri1_e.html and the pages around,
where a universal derivation of piece values on different board
geometries is explained. Nevertheles also there the values finally have
been adjusted to be compared to Pawn values.

Regards, Reinhard.

Date: 13 Oct 2006 05:10:58
From: Sanny
Subject: Getclub Chess Game.

GetClub used

Pawn: 1
Bishop : 3
Rook : 5
Queen : 9

If you want to save time, you can put GetClub Chess game on your
WebSite. It will display your Domain Name.

http://tinyurl.com/sfoo5 (Get Chess Code here.)

Bye
Sanny

Play Chess at: http://www.GetClub.com/Chess.html

Date: 12 Oct 2006 14:57:00
From:
Subject: Re: Piece Value

Thanks for the reply, but it seems that you didn't get a few points
right or i didn't make myself clear enough.

1)I am aware of the Kaufman findings. But his values as well as any
other effort i have studied use the pawn as the unit of measurement and
produce ratings relevant to each other. I didn't use that approach. My
pieces are assigned values on an empty board, irrelevant of each other
with the exception of the bishop pair. Then given a position "Each
piece will try to find a move in order to be placed on a square that
will get it as close as possible to each original "clear" number that i
mentioned in the beggining and was calculated on a empty board and at
the same time threaten pieces with the highest possible sum." Even the
presense of the 2 kings on a board next to a piece is enough to bring
down its rating. In a given position all my "absolute" values and the
relevant ones will be smaller than on a clear board.

2)My question still stands: "Could the engines get an ELO boost with a
differrent rating system?" since they play chess in a completely
different way than people.

3)"How can you overestimate your king?" Although Kings have infinite
value, they still posses tactical abilities, attacking, defending or
improving their position. They do have a relevant value which in most
evaluations that i have seen is 3 up to 5 pawns.

4)I have to agree that only passed advanced pawns are appreciated and
doubled and isolated ones are considered some sort of a problem. But,
you got it wrong, i m afraid. Read (1) again, please. I m optimistic
that my search function when it will be fully coded will avoid doubled
and isolated or similar strategical disavantages with no chess theory
coded into it.

[email protected] wrote:
> [email protected] wrote:
> > Hello.
> > I took up chess programming as a free time project.
> > I have come up with some ideas and any comment or suggestion would be
> > highly appreciated.
> >
> > pieces. So i came up with a question: What is the relevant value of the
> > pieces?
>
> > Could the classical p, N=B=3p, R=5p, Q=9p be completely wrong?
>
> Capablanca came up with those values in Chess Fundamentals, 1921.
>
> > Could the engines get an ELO boost with a differrent rating system?
> > formed a few rating models that unfortunately none can be proved more
> > or less aqurate than the other.
>
> You're re-inventing the wheel. Kaufman did computer-aided statistical
> analysis on a large set of master-level games and came up with:
>
> P=1.00, N=3.25, B=3.25, R=5.00, Q=9.75, K=Infinity, Bishop Pair=0.50.
>
> > B: p, N=3p, B=5p, R=8p, Q=13p,
> > K=3,75p
>
> Compare these values against the Kaufman values.
>
> > (By the way do you know any engine that let you declare values up to Q=23p?)
>
> Chessmaster lets you re-assign piece values. I'm not sure what the
> upper- or lower-bounds are--you would have to check on that.
>
> > capture and so win the game but not too high because in that case they
> > may get into trouble due to overestimation.
>
> How can you overestimate your king? If you lose him, it's game-over.
> It's often assigned the maximum possible value--32,365.
>
> > moving on the whole board. Should we just accept that or keep the
> > original value and the new one only for a pair of bishops?
>
> A separate value for the bishop pair, if accuracy's important.
>
> > rush the pawns to the 8th row? Is the pawn worth a pawn? Allways? Or
> > does it get a value gain with each forward step until it equals the
> > queen on the final row?
>
> It's not so simple.
>
> A "passed" pawn is usually worth two pawns. An "isolated, doubled or
> tripled pawn". is usually worth half a pawn.
>
> Pawns barely appreciate as they advance, except passed pawns, which
> rapidly increase in value... especially on the 5th, 6th, and 7th ranks.
>
> >
> > Any comment or suggestion will be welcomed and appreciated.
> > Thank you.
>
> ---
> likesforests
> Become a Chess Expert -- http://likesforests.blogspot.com/

Date: 12 Oct 2006 14:19:00
From:
Subject: Re: Piece Value

[email protected] wrote:
> [email protected] wrote:
> > (By the way do you know any engine that let you declare values up to Q=23p?)
>
> Chessmaster lets you re-assign piece values. I'm not sure what the
> upper- or lower-bounds are--you would have to check on that.

The upper limit in Chessmaster 9000 was 15 pawns. I don't know if that
was changed for CM 10th Edition.

Regarding this whole discussion, I may be wrong but I would suggest
simply starting out with the "generally accepted" values of
1,3,3,5,9,infinity and then adjusting them only if required and WELL
AFTER you have finished your evaluation functions, based on whatever
new findings you come up with during testing.

In a nutshell, ANY reasonable starting values can work as long as they
are adjusted properly by the positional evaluation, which is far more
important.

jm

Date: 12 Oct 2006 13:05:22
From:
Subject: Re: Piece Value

[email protected] wrote:
> Hello.
> I took up chess programming as a free time project.
> I have come up with some ideas and any comment or suggestion would be
> highly appreciated.
>
> pieces. So i came up with a question: What is the relevant value of the
> pieces?

> Could the classical p, N=B=3p, R=5p, Q=9p be completely wrong?

Capablanca came up with those values in Chess Fundamentals, 1921.

> Could the engines get an ELO boost with a differrent rating system?
> formed a few rating models that unfortunately none can be proved more
> or less aqurate than the other.

You're re-inventing the wheel. Kaufman did computer-aided statistical
analysis on a large set of master-level games and came up with:

P=1.00, N=3.25, B=3.25, R=5.00, Q=9.75, K=Infinity, Bishop Pair=0.50.

> B: p, N=3p, B=5p, R=8p, Q=13p,
> K=3,75p

Compare these values against the Kaufman values.

> (By the way do you know any engine that let you declare values up to Q=23p?)

Chessmaster lets you re-assign piece values. I'm not sure what the
upper- or lower-bounds are--you would have to check on that.

> capture and so win the game but not too high because in that case they
> may get into trouble due to overestimation.

How can you overestimate your king? If you lose him, it's game-over.
It's often assigned the maximum possible value--32,365.

> moving on the whole board. Should we just accept that or keep the
> original value and the new one only for a pair of bishops?

A separate value for the bishop pair, if accuracy's important.

> rush the pawns to the 8th row? Is the pawn worth a pawn? Allways? Or
> does it get a value gain with each forward step until it equals the
> queen on the final row?

It's not so simple.

A "passed" pawn is usually worth two pawns. An "isolated, doubled or
tripled pawn". is usually worth half a pawn.

Pawns barely appreciate as they advance, except passed pawns, which
rapidly increase in value... especially on the 5th, 6th, and 7th ranks.

>
> Any comment or suggestion will be welcomed and appreciated.
> Thank you.

---
likesforests
Become a Chess Expert -- http://likesforests.blogspot.com/

Date: 12 Oct 2006 13:05:17
From:
Subject: Re: Piece Value