Talk:Chess piece point value

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Contents

[edit] History

I've removed the assertion that these piece values were first introduced to help in computer chess; it isn't true. Many books from before the computer era include similar points systems; one example, if I recall correctly, is Howard Staunton's Chess Player's Handbook (1847). --Camembert

[edit] Pawn structure values

Can we cite a writer who advocates these half-pawn deductions for doubled, isolated and backward pawns? They seem very simplistic (the degree of difficulty doubled pawns, for example, present is very much dependent on the position; in some cases they may actually constitute an advantage), and I know many chess players would disagree with them, or at least say that you can't generalise about such things, but if we can at least quote somebody reputable saying these are sensible deductions, then lets do so. --Camembert

The idea of giving weak pawn structures negative scores is expressed here, and here, both advocate a similar approach (although one assigns pawns a value of 100, and deducts 50 for doubled pawns). After reading a little more now, there are many interesting other things such as +.1 of a pawn's worth for each possible move on the board, penalties for the king being in an unsafe position, or bonuses for a knight's proximity to the center. Maybe that kinda stuff doesn't belong in this article though, I'm not sure. —siroχo
I see now that you're dealing mainly with computer chess. I was coming at it from the point of view of a human player, for whom such definite values are of limited practical use, of course. I'll try to tweak the article to reflect that. I wonder if it's a subject better suited to the computer chess article, however (there's already a little there in the "Leaf evaluation" section). --Camembert
I think substracting the equivalent of half a pawn for doubled or isolated pawns is way too much. Bubba73--Bubba73 01:40, 19 May 2005 (UTC)
Probably so. It sounds about right for pawns both doubled and isolated. Baccyak4H 18:33, 24 October 2006 (UTC)
Yes, if you subtract 1/2 point for a pawn being doubled and 1/2 point for a pawn being isolated, then a pair of pawns that are doubled and isolated, they would be worthless. Shannon used that in his paper, but he was just giving an illustration. Bubba73 (talk), 18:49, 24 October 2006 (UTC)
Hmm, I wasn't clear with what I meant. I agree that 1/2 pawn penalty is too much for either doubled or isolated pawns (in general). But I said that it sounds about right if the two pawns were both. That is, the two would be worth 1.5 points (approximately, in general). In general I do not think they would be worth only 1 point; while their mobility is halved and their ability to protect each other completely gone, they still control the same number of squares and usually count as fully two pawns for purposes of determining whether the opponent has a pawn majority or not. Baccyak4H 19:03, 24 October 2006 (UTC)
Your 1.5 for a pair of isolated and doubled pawns is probably about right. I don't remember seeing that anywhere though. Bubba73 (talk), 19:13, 24 October 2006 (UTC)
You probably didn't. It's just adding my two cents about the half pawn penalties apparently in the two references above; I do not intend to change the article in any way to reflect any of this. Baccyak4H 19:34, 24 October 2006 (UTC)

See Point Count Chess from Ralph Betza article (he is a chess master and an inventor of many chess variants). It says:

The basic premise is that every positional advantage is worth one-third of a Pawn. For example, if you get the Bishop-pair but get a doubled Pawn, it is an even trade; but if you get a doubled isolated Pawn on an open file, you have lost two points.

So it is not a half-pawn, but a third of a pawn. I changed the text accordingly. Andreas Kaufmann 04:09, 10 Jun 2005 (UTC)

[edit] King Value

Can we have a few examples of the "many" chess engines which assign the value of 200 to the king? It seems a bit of an odd thing to do to me, and in fact, intuitively, I don't see how it can work: if you treat the king like any other piece, albeit one of immensely high value, then the computer won't stop calculating at checkmate. In some cases, it may actually willfully be checkmated because it can see that on the next move it can capture its opponent's king, thus levelling material. So you have to tell the computer that checkmate ends the game; if you get checkmated, you lose. But if you do that, why do you have to assign the king any value at all? I don't see the logic in it. But I've never programmed a chess engine, and maybe I'm missing something; as I say, if we can give examples of some engines which actually do this, then fair enough. --Camembert

Please understand that I respect the query you are making and I believe we should be reasonably patient (if required) in waiting for a reply from the/a knowledgeable person. However, I must point-out that the current state of this article is nearly unacceptable since it variously states the value of a king in chess to be BOTH infinity and 200 points- diplomatic and contextual wording, notwithstanding. So, as soon as you determine which value is correct, the incorrect value needs to be deleted entirely. --BadSanta

Well, what it's meant to say is that while the value of the king is infinite, for practical reasons it is often assigned the value of 200 points when programming playing engines. As I say above, I'm not sure why it's assigned that value (or even if it's assigned it at all), but that's what the previous author wrote. Sorry for not making that clearer at first; hopefully it's a bit better now. --Camembert

I guess it varies from source to source. In most things i've read online the king is given some value, 200 was a common one, which is why I used it. You can look at any of a variety of sources to find out about giving the king a value, almost every computer chess paper or article I've read has said something of the sort. —siroχo

I guess I'll have to take your word on the 200 points for the king thing. Maybe it would be useful to cite one or two specific papers which use that value? Maybe not, just a thought.--Camembert

I think the 200 points actually might come from a very early chess program designed by Claude Shannon as given by these two papers, [1], [2]. This site [3] alludes to "early computer chess programs". You may be right that some of the stuff in this article belongs in the computer chess article. Perhaps this article should just be merged with Chess piece and computer chess? —siroχo 22:23, Nov 19, 2004 (UTC)

Perhaps also with chess strategy and tactics, where some of this article's content has already been added. I'll leave it to you if you want to merge some more - I'm feeling a bit lazy :) --Camembert

Incidentally, not that I want to bang on about this, but I was browsing through the Oxford Companion to Chess (1992) earlier today, and stumbled across the following in the "value of pieces" entry:

Computers need values for chess purposes. One set is P=2, B=7, N=8, R=14, Q=27. The king has two values: for general purposes 8, but for exchanges 1,000 (so that the computer never tries to exchange it).

They don't give a source. Can't say I understand it still (don't think I will until we have an article that goes into the details of chess computer programming), just thought I'd mention it for curiosity value. --Camembert 15:46, 29 Jan 2005 (UTC)

I believe that the value of 200 for the king must be based on its value as a piece, based on pawn=100, and before the endgame. Programs usually use that because it is easier to work with integers than fractions. Therefore I think the 200 in the article should be changed to 2. (In the endgame, the king as a piece is worth 3-1/2 to 4.) Bubba73--Bubba73 01:40, 19 May 2005 (UTC)

Please take the time to read the above discussion about the king's relative value. Various editors and chess experts have sources for the estimated value of 200 points for the king (where the pawn is valued at exactly 1.0 point). --BadSanta

Actually that's not quite true. I checked computer chess and there it talks about assigning a value of 200 for the purposes of the game tree evaluation. It does not reflect any actual valuation, i.e. it isn't worth 200 pawns. Any value significantly higher than the sum of value of the other pieces (39) would do. It could be a 1000 for those purposes. I now agree with leaving it at 200, with a reference to computer chess to make it clearer, but I think my paragraph about Larry Evans should stay in, so I restored it.

And if the 200 figure comes from the very early program, as someone stated, then it probably was a more-or-less arbitrary figure so that the value of all pieces (200+39 = 239) will still fit in one byte of memory.

--Bubba73 03:21, 19 May 2005 (UTC)

This paper by Shannon is undoubtedly the smoking gun: http://www.pi.infn.it/%7Ecarosi/chess/shannon.txt

“The formula is given only for illustrative purposes. Checkmate has been artificially included here by giving the king the large value 200 (anything greater than the maximum of all other terms would do).”

And if that isn’t clear enough, David Levy, in his book “Computer Gamesmanship”, on page 111, he is discussing Shannon’s paper: “The king is given an arbitary high value because loss of the king means loss of the game. The values 9, 5, 3, 3, and 1 for the other pieces are the rule-of-thumb values which chess players learn early … “

So there you have it. The value of 200 for the king is artificial, arbitrary, and for illustrative purposes. It has nothing to do with a king being the material equivalent of 200 pawns or 40 rooks or 22 queens plus 2 pawns, etc. It is a value that is assigned to checkmate, not to the king as a piece. Since it is possible to queen all 8 pawns, the maximum amount of material possible is 103 points. You need some value for a checkmate that is higher than that, and 200 was the next convienent round number. The reason for having a checkmate position valued more than the largest possible sum of the other pieces is so that the program will give up all of the material it has to in order to prevent mate, as well as sacrifice all of the material it needs to if it achieves checkmate.

The whole paragraph about the 200 points for the king should be removed from this article. It is properly discussed in computer chess, and essentially the same statements are already there. However, even there, it is completely misleading. I propose that this paragraph be removed from this article, since it isn’t at all relative, and that the similar material in computer chess be revised to correct it.

--Bubba73 14:55, 19 May 2005 (UTC)

For the most part, I find your research, information and conclusions sound up until your final paragraph. However, we must NOT remove the estimated point value of the king from an article entitled "chess piece point value" where indisputably, the king is the most important piece of all.
It is critically important that human players as well as computer AI players have the information that the king is more valuable than all of the other pieces added together and it makes sense (esp. for computers) to define this greater value via a number. Although the complexities in estimating a material value for the king are messy and unweildy, going well beyond merely calculating attack values and positional values, to omit this vital information for the sake of simplicity and neatness would render the big picture less than complete. --BadSanta
I reformulated the text on king value, so hopefully now it makes sense. Andreas Kaufmann 03:58, 10 Jun 2005 (UTC)
I think we should just remove the 200 point claim from articles that don't deal specifically with computer chess programs. The fact that some programs assign 200 points to the king is irrelevant to a human player of the game -- the point is merely that the king is the most valuable piece on the board, which can be made without reference to some magic "200" constant. Neilc 04:25, 10 Jun 2005 (UTC)
Agreed. I removed "200" statement from Chess strategy and tactics article. However this article seems to be talking also about piece values for computer chess programs... Andreas Kaufmann 04:40, 10 Jun 2005 (UTC)

It seems that the computer values and human values for every chess piece are interchangeable UNTIL the complex and problemmatical case of the king is mentioned. People say variously it is of infinite value, beyond an exact value or impossible to value while computer programs do not overreact or underreact in gameplay with a value of appr. 200 points. For some time, this issue has caused contention amongst experts at Wikipedia who approached it from contrasting viewpoints. Finally, our patient communications with one another have resulted in the right information being put into its proper place with a balanced treatment of the facts. Thanks to all! --BadSanta

[edit] Piece Values

I think it's worth pointing out that in addition to the book by Larry Evans (which I haven't read), Max Euwe and Hans Kramer use a very similar value system in Vol. 1 of their "The Middlegame" (I should note that I have the "Algebraic Edition," which is a recent reprinting), the only difference being that they value both the knight and the bishop at 3 1/2. Is this worth mentioning in the article? Also, aside from its lasting popularity, what evidence is there to suggest that the "traditional" value system is more accurate? -- Gestrin 16:25, 3 September 2005 (UTC)

I think it is worth mentioning Euwe and Kramer. In Evans' book, he first says that both B and N are 3.5. Later he says that the B is actually 3.75. I have no problem with a B usually being 1/4 point more than a N, but I think that 3.5 or 3.75 is overvaluing the minor pieces.
For your second question, although pawns increase in value in the endgame, the traditional system seems to be more accurate. For instance, equal value of material normally is a draw and a 1-point advantage is usually enough to win. In Evan's system of Q=10, that would equal two rooks, but two rooks are better. 2R vs. Q+P is an even match. With a B at 3.75, B+P should be an even match for a R, but it is really more like B+2P vs. a R. Bubba73 16:47, September 3, 2005 (UTC)
I see what you mean. I have to correct myself here: I've consulted the book, and Kramer and Euwe in fact value the rook at 5 1/2, not 5, so their system holds up in both Q vs. 2R and B+(2)P vs. R. I agree that, in the Evans system, there seems to be a definite imbalance. I think it's probably worth elucidating this in the article. Any thoughts? -- Gestrin 17:02, 3 September 2005 (UTC)
I'm not so sure about a rook being 5.5, unless there were adjustments to other pieces. For instance, in my experience is that in the middlegame B+N or 2B are almost always better than R+P. I'm not sure about 2N vs. R+P, I don't remember having that situation. But I think alternate evaluations should definuitely be mentioned. Also, the value of pawns changes greatly in the endgame, and depends on where they are, etc. I think that generally a lone 4 pawns win versus a rook. Bubba73 18:00, September 3, 2005 (UTC)
PS - with Euwe's 3.5 for minor pieces and 5.5 for the R, that makes two minor bieces better than a R+P, and I believe is true. All valuation systems are guidelines, and I don't think any simple fixed system can account for all combinations. Bubba73 18:16, September 3, 2005 (UTC)
Yes, that's definitely true. At the least it seems like this system is more accurate in more situations than Evans' system. -- Gestrin 18:22, 3 September 2005 (UTC)
As I reflect on it, I think that the Euwe system is more accurate than the traditional system for the middlegame, but then the book was about the middlegame. But after the middlegame the gods placed the endgame! Of course, these values are generalizations and positional factors can be more important - open vs. closed position, good vs. bad bishop, rooks on open files and on the 7th rank, etc. Bubba73 18:44, September 3, 2005 (UTC)

[edit] calculating values for fairy pieces?

Is there some sort of formula that came up with these numbers for the various pieces? Can we apply it to various fairy pieces? See the discussion on that article's talk page.--Sonjaaa 23:03, 17 October 2005 (UTC)

I think the values are mainly derrived from experience, of how they compare in actual games. However, except for the bishop, the values are approximately proportional to their average mobility. Bishops are an exception, because they are confined to squares of one color. 216.227.38.10 00:42, 26 December 2005 (UTC)

The bit about bishops having their relative piece values discounted by half due to being colorbound is very popular and widespread misinformation.

In fact, the reason knights have appr. the same value as bishops in chess, although purely in terms of movement a light-spaced OR dark-spaced bishop can reach far more squares on an ideal, otherwise-empty board is that in practice, the board is never empty. It can get close to empty in a very tight endgame but is 50% full at the start of the game. So, the bishops, being of unlimited range, must be discounted to a realistic value compared to the knights, being of limited, 1-leap range for which getting blocked in the full extent of movement (except by friendly pieces) is not a problem.

AceVentura

The bishops are not discounted by a full half (because they reach only half the squares). The fact that they are a long-range piece partially compensates for that. Also, how they do in actual positions should be taken into effect ("a knight on the rim is pretty grim"). On an empty board, averaged over all of the squares, the bishop has an average mobility of 8.625 squares and the knight has an average mobility of 5.25 squares. That is a "discount" of 39%. If you consider maximum mobility, it is 13 versus 8, a very similar 38.5% "discount". But you're right about actual positions need to be taken into account. Bubba73 (talk), 04:07, 7 March 2006 (UTC)

[edit] Removed material

I removed the following (much of which I wrote or revised):

In some computer chess programs, the king is assigned an artificial value such as 200 points – an arbitrary value higher than the sum of all other pieces plus positional factors. This ensures that the computer will value checkmate over all exchanges or sacrifices. See the discussion about Shannon's chess program at Claude Elwood Shannon for a more complete description.

In evaluating a position, computer programs will typically make further adjustments to this score according to various positional factors. For example, 1/3 of a point may be subtracted for doubled pawns, isolated pawns and backward pawns, fractions of points may be added for possession of open files, and so on. For most humans, such positional evaluation is done without reference to a numerical score.

because it is about positional factors and evaluation functions in chess programs, and not directly about the topic of the article. This is basically covered in computer chess, Claude Elwood Shannon, and evaluation function. Bubba73 (talk), 23:01, 8 July 2006 (UTC)

[edit] More removed material

I have removed the following:

In 1999, chess programmer Ed Trice derived equations to compute values for chess piece on boards of any size for his innovative game known as Gothic Chess. The forumlae apply equally well for standard chess, and are an extension of the work of Henry Taylor from 1876. Trice's paper was published by the International Computer Games Association Journal in 2004. See 80-Square Chess, for more information.

Because, well, Wikipedia is not a soapbox, and because such discussion belongs on the page for Capablanca chess or Gothic chess because it is only of interest for people interested in Chess variants. Just to clarify 15:48, 3 October 2006 (UTC)

I didn't add that paragraph, and I don't object to it being removed. However, it does state that it applies to standard chess, and that is the only tie-in to this article. However, it doesn't state any results for standard chess. Bubba73 (talk), 16:40, 3 October 2006 (UTC)

[edit] material from Alburt and Krogius

I restored the material from grandmasters Lev Alburt and Nikolay Krogius again. It is cited in their book, which is referenced. It is not my opinion, it is their opinion. Bubba73 (talk), 00:41, 20 March 2007 (UTC)

But just because it's their opinion, should it be placed on the article? Is their opinion really that notable, especially when it flies in the face of everything else? I think if we include it, let's just put their values in the same section as everybody else's self-made values. Matt Yeager ♫ (Talk?) 00:44, 20 March 2007 (UTC)
The others are static evaluations. The material from Alburt and Krogius is specifically about how the valuations change in the endgame. What do you think about either "Changing valuations in the endgame" below "alternate valuations" or making it a subset of the latter? Bubba73 (talk), 00:52, 20 March 2007 (UTC)
A subset might work nicely. Good thinking. I've done it... how do you like it? I think we can work the Evans and Fischer stuff into the main area, as well, but another task for another day. Matt Yeager ♫ (Talk?) 07:26, 21 March 2007 (UTC)
That looks OK to me. Bubba73 (talk), 15:15, 21 March 2007 (UTC)
Still okay, after what I just did? Matt Yeager ♫ (Talk?) 20:21, 21 March 2007 (UTC)
Yes. I think that the article needed the reorganization you did to it. Good job, improving the article. Bubba73 (talk), 20:28, 21 March 2007 (UTC)

[edit] Staunton

I expanded Staunton's valuation of the pieces a bit from a Project Gutenberg text. Unfortunately I might not have it quite right—the Gutenberg text is a 1930 reprint of an 1870 original with additional material from unnamed "Modern Authorities". I think it unlikely that the piece values material from pages 30–31 of that text were altered from Staunton's work, but I can't be sure. Quale 00:18, 19 May 2007 (UTC)

[edit] seeking sources

There are citation requests for the value of the bishop given by Fischer and the values given by the USCF. I don't know of any source for the USCF statement - it may be bogus. Does anyone know where that came from? I've read the Fischer value of the bishop, but I don't remember where. It might be in 60 Memorable Games or something. Does anyone know? Bubba73 (talk), 20:15, 11 December 2007 (UTC)

The "values used by the USCF" paragraph was added by an anon user on Sept 30, 2007. I could find no reference for this and I think that a request for a citation was never answered. In addition, this is the only chess edit by this IP user. I propose that it be deleted, unless someone can find a reference. Bubba73 (talk), 05:49, 12 December 2007 (UTC)

[edit] USCF values

Well, since it has been unsourced for over two months, I deleted it (see aboove):

The values used by the United States Chess Federation are: [citation needed]

  • pawn = 1
  • knight = 3.25
  • bishop = 3.3
  • rook = 5
  • queen = 9 Bubba73 (talk), 05:56, 12 December 2007 (UTC)
And I never found anything on the USCF website saying that. Bubba73 (talk), 19:49, 31 March 2008 (UTC)

[edit] added and removed material today

I think I understand what the text that was added and removed today means. In the early program, they put a value of 200 points on the king and then did not have to program in the rules about moving into check and checkmate. Since 200 points is higher than the sum of all other material, this would be an easy way to have the program avoid checkmate at all costs (and also avoid moving into check). However, by the requirement to move (not exactly what zugzwang means, this method will not work correctly for stalemate positions - the program would avoid getting itself stalemated. Bubba73 (talk), 02:40, 24 January 2008 (UTC)

  • I think it is true that some early programs did use a king value of 200 for the reason that the editor and you give. Move generation is simpler if you don't have to consider check. Stalemate would seem to require special treatment to recognize or the program would make an illegal move when stalemated. I also don't see how zugzwang plays into this, since the computer would do the same thing a human would do—play the move that loses the least material or resign. Compare with this earlier edit I think trying to express the same idea which I reverted entirely. The part of the new edit I kept seems much better to me and is a good addition to the article. If you or the original editor think it should be adjusted, go ahead. Detailed considerations of computer chess and move generation articles probably belong somewhere else, and I found the stalemate bit very confusing without more context. Quale (talk) 03:04, 24 January 2008 (UTC)
As I said, that is not really a correct use of "zugzwqng" - I think the editor really means the requirement to move. Bubba73 (talk), 03:12, 24 January 2008 (UTC)
Sorry, I wasn't disagreeing with you re: zugzwang. My use of "I also don't see" was meant to indicate agreement, but I didn't word it well. As far as I understand it, requirement to move isn't really addressed in computer chess at all. It comes up in the well known horizon effect, and quiescence searches and threat something or other extensions are used to mitigate the problem. Quale (talk) 03:57, 24 January 2008 (UTC)
As long as the horizon effect doesn't come into play, giving the king a high value and allowing it to be captured and moved like a regular piece is a quick and dirty way to have it avoid checkmate at all costs, and it also means that you don't have to program in checkmate and not moving into check directly - with the provisio that it loses if it move into check. But it also avoids stalemate. Bubba73 (talk), 04:02, 24 January 2008 (UTC)
OK, I think I might understand what you and the original editor were getting at. Because a stalemate looks very bad to the computer (at least −200 points instead of the correct evaluation of +0), it will do really dumb things including sacrificing the queen and all other pieces to avoid it. In other words, the computer would lose in order to avoid a draw (since it doesn't recognize stalemate as a draw). Quale (talk) 05:25, 24 January 2008 (UTC)
Yes, if you are using the simple to program method of loss of the king is more points than all of the other material combined, then stalemate would look like a loss, and that would make it avoid being stalemated, and it would think that if it stalemated the other king it would be a win. Of course, they probably did that to be expediant. Also, the value isn't "artibrary" - it has to be higher than the max possible sum other material and positional factors. Bubba73 (talk), 13:56, 24 January 2008 (UTC)