Piece Material Value Analysis

[Han]

Geschrieben von: / Posted by: Han at 13 July 2000 16:32:52:
All these are taken from my pages. I put this here to start an arguement!
I will attempt to formulate some equations for getting the piece values. Most of them are based on logical reasoning (which you may disagree completely with), while some others are just my preferences
My system assumes that all the differences between the left and right of the inequalities are very small, and therefore are assumed to be the same, which is denoted by a.
P =Pawn, N = Knight, B = Bishop, R = Rook, Q = Queen, a = unknown constant
Inequality Equation Reason
N > 3P ; N = 3P + a Knights are slightly stronger than 3 pawns.
B > N ; B = N + a Generally, bishops are better than knights due to its range.
R < 2N-P ; R = 2N - P - a Generally, 2 minor pieces exert more pressure than a lone rook can.
Q > 3B ; Q = 3B + a The queen attacks laterally too.
Q > R + B+ P ; Q = R+ B+ P+ a This is controversial. But the queen is able to cover all of the diagonals, which the bishop cannot.
Let's solve the equations. P = 100, a= any reasonable value.
In this table, a is assumed to be 10. The biggest value overrides others to satisfy all inequalities.
Piece Expressions Piece Values , a = 10
Pawn P 100
Knight =3P + a =310
Bishop =3P + 2a =320 320 Overrides smaller value.
=3P = 300
Rook =5P + a = 510 510 Overrides smaller value.
=5P - a = 490
Queen =9P + 7a = 970 970 Overrides smaller value.
=9P + 4a = 940
The main idea in this is that a is relatively small, and are therefore quite equal.

[Han]

Geschrieben von: / Posted by: Han at 13 July 2000 16:36:13:
Als Antwort auf: / As an answer to: Piece Material Value Analysis geschrieben von: / posted by: Han at 13 July 2000 16:32:52:

All these are taken from my pages. I put this here to start an arguement!
I will attempt to formulate some equations for getting the piece values. Most of them are based on logical reasoning (which you may disagree completely with), while some others are just my preferences
My system assumes that all the differences between the left and right of the inequalities are very small, and therefore are assumed to be the same, which is denoted by a.
P =Pawn, N = Knight, B = Bishop, R = Rook, Q = Queen, a = unknown constant
Inequality Equation Reason
N > 3P ; N = 3P + a Knights are slightly stronger than 3 pawns.
B > N ; B = N + a Generally, bishops are better than knights due to its range.
R < 2N-P ; R = 2N - P - a Generally, 2 minor pieces exert more pressure than a lone rook can.
Q > 3B ; Q = 3B + a The queen attacks laterally too.
Q > R + B+ P ; Q = R+ B+ P+ a This is controversial. But the queen is able to cover all of the diagonals, which the bishop cannot.
Let's solve the equations. P = 100, a= any reasonable value.
In this table, a is assumed to be 10. The biggest value overrides others to satisfy all inequalities.
Piece Expressions Piece Values , a = 10
Pawn P 100
Knight =3P + a =310
Bishop =3P + 2a =320 320 Overrides smaller value.
=3P = 300
Rook =5P + a = 510 510 Overrides smaller value.
=5P - a = 490
Queen =9P + 7a = 970 970 Overrides smaller value.
=9P + 4a = 940
The main idea in this is that a is relatively small, and are therefore quite equal.

[Dann Corbit]

Geschrieben von: / Posted by: Dann Corbit at 13 July 2000 20:30:50:
Als Antwort auf: / As an answer to: Piece Material Value Analysis geschrieben von: / posted by: Han at 13 July 2000 16:32:52:
How much are these two bishops worth?
3k4/5b2/3p4/2pPp3/1pP1Pp1p/pP3PpP/P5P1/1B1K4 w - -
Pieces have a static value but also a dynamic value. A pawn or piece can have it's value multiplied or driven to zero.
How much is this pawn worth?
8/1P6/6k1/8/2K5/8/8/8 w - -
More than 100 centipawns, I would say. In fact, I will trade a rook for it in a heartbeat.


my ftp site

[Han]

Geschrieben von: / Posted by: Han at 14 July 2000 11:31:56:
Als Antwort auf: / As an answer to: Re: Piece Material Value Analysis geschrieben von: / posted by: Dann Corbit at 13 July 2000 20:30:50:

How much are these two bishops worth?
3k4/5b2/3p4/2pPp3/1pP1Pp1p/pP3PpP/P5P1/1B1K4 w - -
Pieces have a static value but also a dynamic value. A pawn or piece can have it's value multiplied or driven to zero.
How much is this pawn worth?
8/1P6/6k1/8/2K5/8/8/8 w - -
More than 100 centipawns, I would say. In fact, I will trade a rook for it in a heartbeat.

In my system, it is only the static value that is being calculated. Only in the process of the game, then the dynamic material values come in. And anyway, you have selected a too extreme example to state your point:-)
Han

[Dan Andersson]

Geschrieben von: / Posted by: Dan Andersson at 14 July 2000 19:34:52:
Als Antwort auf: / As an answer to: Re: Piece Material Value Analysis geschrieben von: / posted by: Han at 14 July 2000 11:31:56:

How much are these two bishops worth?
3k4/5b2/3p4/2pPp3/1pP1Pp1p/pP3PpP/P5P1/1B1K4 w - -
Pieces have a static value but also a dynamic value. A pawn or piece can have it's value multiplied or driven to zero.
How much is this pawn worth?
8/1P6/6k1/8/2K5/8/8/8 w - -
More than 100 centipawns, I would say. In fact, I will trade a rook for it in a heartbeat.

In my system, it is only the static value that is being calculated. Only in the process of the game, then the dynamic material values come in. And anyway, you have selected a too extreme example to state your point:-)
Han

There is nothing especially extreme about these positions, about one in ten games I play feature these kinds of abnormal (?) positions in the post game analysis. As to evaluating material, I have found that a bonus based on number of pieces work really well. For example:
if linear
(noOfWhitePieces-noOfBlackPieces)*positiveConstant
or discrete
PieceBonus[noOfWhitePieces-noOfBlackPieces]

[Tom King]

Geschrieben von: / Posted by: Tom King at 14 July 2000 23:57:07:
Als Antwort auf: / As an answer to: It is quite messy, so visit my website for a neater version, computer chess geschrieben von: / posted by: Han at 13 July 2000 16:36:13:

All these are taken from my pages. I put this here to start an arguement!
I will attempt to formulate some equations for getting the piece values. Most of them are based on logical reasoning (which you may disagree completely with), while some others are just my preferences
My system assumes that all the differences between the left and right of the inequalities are very small, and therefore are assumed to be the same, which is denoted by a.
P =Pawn, N = Knight, B = Bishop, R = Rook, Q = Queen, a = unknown constant
Inequality Equation Reason
N > 3P ; N = 3P + a Knights are slightly stronger than 3 pawns.
B > N ; B = N + a Generally, bishops are better than knights due to its range.
R < 2N-P ; R = 2N - P - a Generally, 2 minor pieces exert more pressure than a lone rook can.
Q > 3B ; Q = 3B + a The queen attacks laterally too.
Q > R + B+ P ; Q = R+ B+ P+ a This is controversial. But the queen is able to cover all of the diagonals, which the bishop cannot.
Let's solve the equations. P = 100, a= any reasonable value.
In this table, a is assumed to be 10. The biggest value overrides others to satisfy all inequalities.
Piece Expressions Piece Values , a = 10
Pawn P 100
Knight =3P + a =310
Bishop =3P + 2a =320 320 Overrides smaller value.
=3P = 300
Rook =5P + a = 510 510 Overrides smaller value.
=5P - a = 490
Queen =9P + 7a = 970 970 Overrides smaller value.
=9P + 4a = 940
The main idea in this is that a is relatively small, and are therefore quite equal.

Hey, Han, what's the URL of your website?

[Han]

Geschrieben von: / Posted by: Han at 15 July 2000 11:54:40:
Als Antwort auf: / As an answer to: Re: It is quite messy, so visit my website for a neater version, computer chess geschrieben von: / posted by: Tom King at 14 July 2000 23:57:07:

[Han]

Geschrieben von: / Posted by: Han at 15 July 2000 11:55:58:
Als Antwort auf: / As an answer to: Re: It is quite messy, so visit my website for a neater version, computer chess geschrieben von: / posted by: Tom King at 14 July 2000 23:57:07:
Url is www.chess1.homepage.com
I accidentally clicked on the button too many times!