Pawn value estimation

[Dann Corbit]

Is there any scientific measurement that yields reliable pawn value estimation?

It seems that the standard methods are very good at showing the relative values of pieces (compared to one another), but not pawns.

By definition, the value of a pawn is 100cp.

I don't understand the point of your question. Simply pawn=100 (or rather pawn value endgame = 100) is a fixed point, and all other piece values (and any eval terms) are relative to that value.

Engines tend to use other values (see, for instance Stockfish)
PawnValueMg = 198, PawnValueEg = 258,

Though pawns are generally reported to the user as 100 centipawns.

Be that as it may, I am talking about the ratio of the value of a pawn to the value of other chessmen.

The fitting methods arrive at very similar ratios for the value of any two pieces, using many different input data sets, if there are enough games.
However, the ratio of a pawn to the other chessmen varies wildly.

Let me make this even more clear, because you don't seem to understand it:
* centipawn: "centi" means 1/100, hence centipawn = pawn/100. It's like centimeter = 1/100 * meter, ok ?
* pawn = 100 * centipawn

It's completely tautologic. Your question is ill defined, really.

Let's make it more clear, since you clearly do not comprehend my questions.

I did NOT ask:
"How many centipawns is a pawn"
which is the question you answered.

The name of the unit is its own answer to that question and so I doubt if anyone is seeking it.

I asked what it the ratio in value of a pawn to other chessmen?

IOW:

pawnvalue/knightvalue = x
pawnvalue/bishipvalue = y
etc.

All the other chessmen have very stable ratios for things like:
knightvalue/bishopvalue
knightvalue/queenvalue

but pawns do not have a stable ratio according to the methods for computation that I have seen so far. They look like random number generators.

So I asked is there some reasonable (and stable, and reliable) way to calculate the relative value of a pawn to other pieces?

Perhaps Miguel hints that the pawn should be calculated purely positionally. This would indicate that its intrinsic value is zero. Hence, only positional scores would apply to a pawn.

I suppose that Philodor would blanch to know that a pawn has no intrinsic value.

[Dann Corbit]

Is there any scientific measurement that yields reliable pawn value estimation?

It seems that the standard methods are very good at showing the relative values of pieces (compared to one another), but not pawns.

By definition, the value of a pawn is 100cp.

I don't understand the point of your question. Simply pawn=100 (or rather pawn value endgame = 100) is a fixed point, and all other piece values (and any eval terms) are relative to that value.

The point is the values of pieces are much stable than the values of a pawn.
For example, a sample with pawn=100 and the same players with knight=300 :

Code: Select all

	      Anand 	Carlsen 	Andersen 
Pawn	  100		100		100
Knight	216		213		286
Bishop	230		243		289
Rook	  355		352		531
Queen	 762		786		1013
King	∞		∞		∞

Code: Select all

          Anand   Carlsen  Andersen 
Pawn        139		141		105
Knight      300		300		300
Bishop      319		342		303
Rook	     493		496		557
Queen      1058 	 1107	  1063
King	       ∞		 ∞		  ∞	

One can see that more values are much stable.

Yes, exactly.

[BBauer]

Lucas wrote

By definition, the value of a pawn is 100cp.

That is true, look at this position.
[d]7k/7p/8/8/8/8/P7/7K w - - 0 1
Scientific definition: a pawn = 100cp = winning
Covered by G. Kasparov who once said: "a pawn is a pawn".

This may lead to the question:
What is the value of h pawn? Is it different?
Obviously!
h pawn = 000cp = drawing

Hope that helps to answer those very important questions at least for the a and h pawn.
Kind regards
Bernhard

[jdart]

I think the point is, if you don't fix the value of one of the pieces, you can't get stable values from tuning because pawn = 200 and knight = 600 looks the same as pawn = 100 and knight = 300 (actually not because smaller positional factors don't vary, but approximately so). If you fix the pawn value then you get a stable score for Knights, etc. and stable rations of those to the pawn value.

(There is the complication that some engines use different piece/pawn scores for endgame and middlegame - but still, you need to fix at least one of these values).

--Jon

[lkaufman]

Is there any scientific measurement that yields reliable pawn value estimation?

It seems that the standard methods are very good at showing the relative values of pieces (compared to one another), but not pawns.

Here are several conclusions based on my Komodo work:

1. It is best to define a constant value for the knight, because we have found that there is no measurable benefit to having a higher or lower endgame value than opening value for the knight, so we just keep it a constant. Of course this might not be true for all engines, it depends on how positional terms are scored. In Komodo, the bishop value is also constant, because although the bishop gains a bit relative to knights in the endgame, this is accounted for by increased mobility and some other terms. Due to the huge importance of the bishop pair it is best to define the knight as the constant piece. The rook and the pawn both rise sharply in value in the endgame, so they are not suitable to hold constant; the queen rises much less sharply but is not "level".
2. Because the pawn value rises so sharply as the pieces come off, it is not very useful to talk about its "average" value (relative to knight always). I use a ratio of 3.5 in teaching humans, but in Komodo it probably averages closer to 4 (pawns per knight).
3. The nominal value of the pawn is also severely affected by the fact that in general three pawns are part of the king's shelter and hence rather valuable. In Komodo the nominal opening value of a pawn is surprisingly low, but that's largely because the three king-protecing pawns get large bonuses. To be honest I don't fully understand why the nominal pawn value is as low as it is in Komodo; in actual games it scores positions with multiple pawns for a piece about right.
4. Regarding the recent Russian study which concluded that in the games of Carlsen and Anand a knight was worth less than 2.5 pawns, this is clearly nonsense. Perhaps they only sacrifice a piece for pawns when there is substantial positional compensation not detected by the methodology. I know that when I did my own study of master games back in 1999, I consistently found that in human practice a knight was worth on average a bit more than three pawns, which is the consensus of chess literature. I suggest that all chess engines should define a knight as something like 325 centipawns so that output will have a constant meaning for all engines.

[Dann Corbit]

You are an excellent chess teacher and have very good ability to explain.
You should write hundreds of chess books.

In a similar way, it is a tragedy that Bruce Moreland never wrote a book on chess programming. His site explained things so clearly and cleverly that it was a must read for programmers who wanted to write a chess engine.

I just did a check and found that you have written quite a few books.
I am going to buy some of them.

[bob]

You are an excellent chess teacher and have very good ability to explain.
You should write hundreds of chess books.

In a similar way, it is a tragedy that Bruce Moreland never wrote a book on chess programming. His site explained things so clearly and cleverly that it was a must read for programmers who wanted to write a chess engine.

I just did a check and found that you have written quite a few books.
I am going to buy some of them.

Someone posted a link to copies of the old computer chess reports. You should look thru them. Guess who was the principal writer?

I used to look forward to those things coming out.