View source for Talk:Chess piece relative value

{{notice|{{Graph:PageViews|365}}|heading=Daily page views |center=y |image=Open data small color.png}}
{{WikiProject banner shell|class=B|
{{WikiProject Chess|importance=High|portal=yes}}
}}

==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).
--[[User:Camembert|Camembert]]

I did some research, and I believe that the standard values were first formulated by the Modenese School in the 18th century (although some parts were already discussed by Pietro Carrera in 1617). I added this information with reference to their books. 
([[User:Sersunzo|Sersunzo]] ([[User talk:Sersunzo|talk]]) 18:15, 14 July 2010 (UTC)).

: Thanks, I think that is good material.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|<sup>(You talkin' to me?)</sup>]], 18:29, 14 July 2010 (UTC)

==Leveling effect==
In the paragraph about the shortcomings of piece values I added a few sentences that discuss the 'leveling effect' (as it was called by Ralph Betza, who, as far as I could find out, was the first to discuss it). There already is a reference to Betza's writings on piece values in the external-links section. Some of the examples for 'redundancy' at the end of the article in fact seem just an illustration of this leveling effect, where extra Queens do not nearly benefit the side that already has a Queen as much as it benefits the side with the lighter pieces, as the latter now hinder two opponent Queens. It can be easily established with the aid of computer programs that can play chess with fairy pieces that adding a piece that is similar in value to a queen, but moves differently, conveys a similar disadvantage to the side that then has two super-pieces, even though there is no 'redundancy' through having two pieces with similar moves. It thus seems to me that this redundancy concept is nothing but a red herring, and I propose to delete the mentioning of it. [[User:H.G.Muller|H.G.Muller]] ([[User talk:H.G.Muller|talk]]) 07:17, 6 October 2018 (UTC)

:{{Ping|H.G.Muller}} Kaufman is a little bit equivocal about how the concept of redundancy he mentions should work in [https://web.archive.org/web/20060629013845/http://mywebpages.comcast.net/danheisman/Articles/evaluation_of_material_imbalance.htm his article], but I think this comes from his wording and not his idea. On the bishop pair, his article reads:

{{Blockquote|Why is the bishop pair so valuable? One explanation is that the bishop is really a more valuable piece than the knight due to its greater average mobility, but unless you have both bishops the opponent can play so as to take advantage of the fact that the bishop can only attack squares of one color. In my opinion, another reason is that any other pair of pieces suffers from redundancy. Two knights, two rooks, bishop and knight, or major plus minor piece are all capable of guarding the same squares, and therefore there is apt to be some duplication of function.

With two bishops traveling on opposite colored squares there is no possibility of any duplication of function. So, in theory, rather than giving a bonus to two bishops, we should penalize every other combination of pieces, but it is obviously much easier to reward the bishop pair. It is partly for similar reasons we say to trade pieces when you are ahead; if you have two knights against one (with other pieces balanced), the exchange of knights means that you are trading a partially redundant knight for one that is not redundant.}}

:The last sentence notwithstanding, I think the first paragraph makes it clear that redundancy is supposed to apply between nonhomogeneous piece pairs as well. So two queens would be redundant, and so would a queen and a chancellor. Indeed on an 8×8 board they are even worse than on the bigger Capablanca chess 10×8 board because they keep getting in each others' way; no matter where they are, their ranges overlap significantly. (Which also means that weaker enemy pieces will find it easier to harass both of them at once, further reducing their value by the levelling effect. But I think the small size of the board should make them less valuable than the sum of their individual values already even if there are no weaker pieces around to harrass them.) Also, later on he mentions "redundancy of major pieces", which includes redundancies between rooks and queens (since this is about having a major piece to deploy on an open file). I think what Kaufman had in mind in the last sentence of this quote is that trading pieces lowers the amount of redundancy, because there are then fewer pieces around to perform the same functions of guarding the same squares, although his wording was imprecise. I'd assume that he was only thinking about inter-knight redundancy. (Pawns are special because of their endgame role, which comes from their possible promotion. That's why the guideline is "when you are ahead, trade pieces, not pawns", and the opposite for when you are behind. There is also the point that without captures, each square from the 3rd row onwards can only be guarded by two pawns, unless it is on a rook file, in which case the number is one; this cannot be improved without help from the opponent. Furthermore, once a pawn has moved past a square, it cannot come back and guard the same squares again unless it promotes later. So pawns already have low redundancy among themselves due to their move, which also explains why doubling your opponent's pawns harms him, because it increases his inter-pawn redundancy from a small value.) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 07:58, 27 March 2019 (UTC)

:{{Ping|H.G.Muller}} The statement, "This effect causes 3 queens to badly lose against 7 knights, even though the added piece values predict that the knights player is two knights short of equality", is dubious. 

:I played SF12 against itself in several randomly generated 7 knights versus 3 queens positions giving the 7 knights the advantage of first move and the queens won every time, usually within five moves. I also set up a position where none of the knights was attacked by any queen and all of the queens were attacked by at least three knights (again with the knights having first move and their king not in check) and the result was mate in ten for the queens.

:Is the whole theory dubious?
:[[User:Martin Rattigan|Martin Rattigan]] ([[User talk:Martin Rattigan|talk]]) 15:47, 24 June 2021 (UTC)
::{{ping|Martin Rattigan}} It's 7N vs 3Q ''when both start behind a wall of pawns'', as in the typical opening position. Like [https://www.chessvariants.com/rules/charge-of-the-light-brigade this]. Obviously, a position with no pawns will favour the queens. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 19:55, 23 April 2023 (UTC)

==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. --[[User:Camembert|Camembert]]

: The idea of giving weak pawn structures negative scores is expressed [http://www.cs.ucf.edu/~dmarino/CompChess.ppt here], [http://www.chessbrain.net/beowulf/theory.html 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.  [[User:Siroxo| ]]&mdash;[[User:Siroxo|<span style="color:#627562;">siro</span>]][[User talk:Siroxo|<span style="color:#627562;">''&chi;''</span>]][[Special:Contributions/Siroxo|<span style="color:#627562;">o</span>]]

::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). --[[User:Camembert|Camembert]]

:::I think substracting the equivalent of half a pawn for doubled or isolated pawns is way too much. [[Bubba73]]--[[User:Bubba73|Bubba73]] 01:40, 19 May 2005 (UTC)

:::: Probably so.  It sounds about right for pawns both doubled and isolated.  [[User:Baccyak4H|Baccyak4H]] 18:33, 24 October 2006 (UTC)

::::::(I'd say that a factor would be whether or not the opponent can block both your doubled pawns with one of his.  That would render them effectively no better than a single pawn. [[User:WHPratt|WHPratt]] ([[User talk:WHPratt|talk]]) 15:34, 9 February 2010 (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.  [[User:Bubba73|Bubba73]] [[User talk: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.  [[User:Baccyak4H|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.  [[User:Bubba73|Bubba73]] [[User talk: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.  [[User:Baccyak4H|Baccyak4H]] 19:34, 24 October 2006 (UTC)

----------

See [http://www.chessvariants.com/d.betza/pieceval/p3-01.html 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. [[User:Andreas Kaufmann|Andreas Kaufmann]] 04:09, 10 Jun 2005 (UTC)

==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. --[[User:Camembert|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.  --[[User:BadSanta|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. --[[User:Camembert|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.  [[User:Siroxo| ]]&mdash;[[User:Siroxo|<span style="color:#627562;">siro</span>]][[User talk:Siroxo|<span style="color:#627562;">''&chi;''</span>]][[Special:Contributions/Siroxo|<span style="color:#627562;">o</span>]]

::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.--[[User:Camembert|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, [http://www.ccs.neu.edu/groups/honors-program/freshsem/19951996/rsuchak/], [http://www.trismegistos.com/IconicityInLanguage/Articles/Katsenelinboigen/KATS1.HTM].  This site [http://www.playjava.com/chess_pieces.html] 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]]?  [[User:Siroxo| ]]&mdash;[[User:Siroxo|<span style="color:#627562;">siro</span>]][[User talk:Siroxo|<span style="color:#627562;">''&chi;''</span>]][[Special:Contributions/Siroxo|<span style="color:#627562;">o</span>]] 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 :) --[[User:Camembert|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. --[[User:Camembert|Camembert]] 15:46, 29 Jan 2005 (UTC)

----------
<s>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. </s>  (In the endgame, the king as a piece is worth 3-1/2 to 4.) [[Bubba73]]--[[User: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).  --[[User:BadSanta|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.

--[[User:Bubba73|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.

--[[User:Bubba73|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|BadSanta]]

:: I reformulated the text on king value, so hopefully now it makes sense. [[User:Andreas Kaufmann|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. [[User:Neilc|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... [[User:Andreas Kaufmann|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!  --[[User:BadSanta|BadSanta]]

This King=200 claim was complete bulshit, and it is good that it is removed. I have been writing chess programs sinse the early eighties, and assigning a large value to the King is in fact not sufficient to make a program obey the rules for check. No matter how large the value assigned to King, it would just reply to checks with counter checks, being convinced that trading Kings is a good deal. Chess programs need to be explicitly programmed to not have the game go on after a King gets captured, and communicate that to the place that handled the previous position, so that it can be seen there that an illegal move was done, end be judged whether it is dealing with a checkmate or a stalemate.[[User:H.G.Muller|H.G.Muller]] ([[User talk:H.G.Muller|talk]]) 07:28, 6 October 2018 (UTC)

== 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? -- [[User:Gestrin|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. [[User:Bubba73|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? -- [[User:Gestrin|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.  [[User:Bubba73|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.  [[User:Bubba73|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. -- [[User:Gestrin|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. [[User:Bubba73|Bubba73]] 18:44, September 3, 2005 (UTC)

== 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.--[[User:Sonjaaa|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.  [[User:216.227.38.10|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.

[[User:AceVentura|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.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 04:07, 7 March 2006 (UTC)

:::It can be easily tested how much the color binding depresses the value of the bishop, by measuring the value of 'augmented bishops', which differ from an orthodox bishop only by being allowed a backward step to an empty square, which would bring them to the other square shade. From such tests it turns out that there is hardly any effect on the value of pairs of such pieces, (like 1/6 Pawn per bishop), and that the little value increase there is is almost equal to the effect on similarly augmented knights. (In other words, if one player starts with augmented bishops instead of normal ones, and the otherplayer with augmented knights instead of normal knights, matches will end in scores very close to 50%.) So any discounting of the value comes about entirely through the pair bonus. One could say that without color binding the Bishop would have been worth 3.50, (half the value of the pair), but that a lone Bishop, where the color binding starts manifesting itself, must be discounted by 1/4 Pawn (making it appear as if the Bishop that completed the pair was worth 3.75). That amounts to a discount of only 7%, very much less than the 39% needed to equalize bishop and knight starting from an 'ideal value' based on the average mobility.[[User:H.G.Muller|H.G.Muller]] ([[User talk:H.G.Muller|talk]]) 08:12, 6 October 2018 (UTC)

:Attempts to calculate piece values '''ab initio''', in proportion to some square-averaged mobility usually fail badly, because they (1) do not take into account that in practical play you would avoid to put the piece on squares with poor mobility, (2) moves have synergy, so that value increases faster than linear, making a queen worth more than rook plus a bishop, and (3) there are som overall properties depending on the entire combination of moves, (speed, color binding, mating potential) which would discriminate between pieces of equal mobility. I have empirically measured (i.e. by playing games) the value of many different fairy pieces, and for fully symmetrical short-range leapers with N moves the formula 1.1*(30 + 5/8*N)*N seems a reasonably good approximation for their value in centi-Pawns. (Unless the piece is somehow 'sick', e.g. by having only forward moves, or having a severe form of higher-order color binding.) Furthermore, forward moves seem to contribute twice as much to value as backward or sideway moves, and captures seem to contribute twice as much as non-captures. Sliders are more difficult to fathom. A major effect here seems to be that moves to orthogonally adjacent squares are worth an extra bonus on top of the value of the moves itself. This contributes to the unexpectedly large value of the Archbishop (BN), and to the value difference of Rook and Bishop (which is sizable even on a cylinder board, where they have practically equal average mobility).[[User:H.G.Muller|H.G.Muller]] ([[User talk:H.G.Muller|talk]]) 08:12, 6 October 2018 (UTC)

== Removed material ==

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

<blockquote>
In some [[computer chess]] programs, the king is assigned an artificial value such as 200 points &ndash; 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.
<br>
<br>
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 pawn]]s and [[backward pawn]]s, 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. </blockquote>

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]].  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 23:01, 8 July 2006 (UTC)

~~Hi.  I changed "if the pawn on a6 was" to "if the...were".  Was is wrong because the condition is contrary to fact.  Also, "values changes" is embarrassing.  I haven't changed that.~~

== 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 [http://www.gothicchess.com/80.pdf ''80-Square Chess''], for more information.

Because, well, [[WP:NOT|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 variant]]s. [[User:Just to clarify|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.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 16:40, 3 October 2006 (UTC)

== 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.  [[User:Bubba73|Bubba73]] [[User talk: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. [[User:Matt Yeager|<b style="color:#DF0001;">Matt Yeager</b>]] [[Special:Random|<b style="font-size:medium; color:#B46611;">♫</b>]] <span style="color:#00AA88;">([[User_talk:Matt Yeager|<span style="color:#00AA88;">Talk?</span>]])</span> 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? [[User:Bubba73|Bubba73]] [[User talk: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. [[User:Matt Yeager|<b style="color:#DF0001;">Matt Yeager</b>]] [[Special:Random|<b style="font-size:medium; color:#B46611;">♫</b>]] <span style="color:#00AA88;">([[User_talk:Matt Yeager|<span style="color:#00AA88;">Talk?</span>]])</span> 07:26, 21 March 2007 (UTC)

:::: That looks OK to me.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 15:15, 21 March 2007 (UTC)

::::: Still okay, after what I just did? [[User:Matt Yeager|<b style="color:#DF0001;">Matt Yeager</b>]] [[Special:Random|<b style="font-size:medium; color:#B46611;">♫</b>]] <span style="color:#00AA88;">([[User_talk:Matt Yeager|<span style="color:#00AA88;">Talk?</span>]])</span> 20:21, 21 March 2007 (UTC)

:::::: Yes.  I think that the article needed the reorganization you did to it.  Good job, improving the article.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 20:28, 21 March 2007 (UTC)

== 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. [[User:Quale|Quale]] 00:18, 19 May 2007 (UTC)

== 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? <s> 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? </s>  [[User:Bubba73|Bubba73]] [[User talk: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.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 05:49, 12 December 2007 (UTC)

==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: {{Fact|date=September 2007}}
* pawn = 1
* knight = 3.25
* bishop = 3.3
* rook = 5
* queen = 9 [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 05:56, 12 December 2007 (UTC)

: And I never found anything on the USCF website saying that.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 19:49, 31 March 2008 (UTC)

== 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.  [[User:Bubba73|Bubba73]] [[User talk: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 [http://en.wikipedia.org/w/index.php?title=Chess_piece_point_value&diff=180572365&oldid=180523979 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.  [[User:Quale|Quale]] ([[User talk: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.  [[User:Bubba73|Bubba73]] [[User talk: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. [[User:Quale|Quale]] ([[User talk: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.  [[User:Bubba73|Bubba73]] [[User talk: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).  [[User:Quale|Quale]] ([[User talk: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.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 13:56, 24 January 2008 (UTC)

== Value or values? ==

I believe this page should be moved to "chess piece point values" since it is about systems of values, not about the values individually (which would be nonsensical). [[Special:Contributions/91.107.140.122|91.107.140.122]] ([[User talk:91.107.140.122|talk]]) 20:24, 11 September 2008 (UTC)

: Maybe.  It is about the relative value of each piece.  Several systems are discussed.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 20:48, 11 September 2008 (UTC)

: Perhaps "chess piece relative values".  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 21:32, 11 September 2008 (UTC)

::We almost invariably use single nouns instead of plural for Wikipedia article names, for instance [[Cat]] instead of [[Cats]] even though we talk about "cats" not "cat" both inside and outside of that article. [[User:Matt Yeager|<b><span style="color:#DF0001;">Matt Yeager</span></b>]] [[Special:Random|<b><span style="font-size:medium; color:#B46611;">♫</span></b>]] [[User_talk:Matt Yeager|<span style="color:#00AA88;">(Talk?)</span>]] 04:37, 12 September 2008 (UTC)

::: OK.  What do you think about "chess piece relative value"? Or "chess piece value"?  I am in favor of changing or removing "point". [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 04:43, 12 September 2008 (UTC)

== Alternate valuations section too long? ==
Hey, I'm just wondering to what extent we want to list every valuation that was ever suggested. What I mean is that, for instance, there are so many valuations that all look the same (Evans, Euwe, Fischer, "early Soviet chess program", another popular chess system for example are pretty much all the same). I'm just thinking it's either too crowded for little reason, or the format clearly needs reworking.

Actually, I'm thinking of two alternate ways of presenting all this:
* Citing people who made such propositions and outlining the main "features" (main disparities, for example). This can surely be done in a few lines of text;
* To sum up every method in a table. The way I see it, there could be six columns: Author, pawn, knight, bishop, rook, queen, source/reference. Maybe put a little star besides the ones that have been "normalized" so that pawns are worth one or something, and that's it.

Because seriously... some stuff just isn't worth mentioning with such emphasis.
[[User:Seigneur101|Seigneur101]] ([[User talk:Seigneur101|talk]]) 02:54, 24 April 2009 (UTC)

: Well, we were trying to get every point of view.  None of them are the correct one.  A table would work well for most of them, but there are exceptions such as Kauffman's system and Berliner's system. Maybe a column for a note to give additional info. [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 03:41, 24 April 2009 (UTC)

: As far as Euwe, Evans, Fisher and the early Soviet program looking the same, they are all different in some way.  I think there are no two listed that are exactly the same. [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 04:11, 24 April 2009 (UTC)

:: I know that not one's the same... but do I really care if one gives 9 points for the Queen, the other 10 points, and then there's a third one that gives 3.4 for the knight rather than 3.5? These differences are immaterial [in an actual chess game], which in some way, makes them "all the same". Anyway, I don't think the point of the section should be to list exhaustively all the possibilities that ever rose in the past. Since there's one valuation that's always used (1-3-3-5-9), the details of all the others seem somewhat superfluous. Basically, the section wants to show that "there are or have been alternatives which looked approximately like that", not "here's an exhaustive list of all the valuations we could find, hope we didn't miss one".

:: That was my first reaction when I saw the article, and I can't seem to shed that feeling away.

:: [[User:Seigneur101|Seigneur101]] ([[User talk:Seigneur101|talk]]) 15:25, 24 April 2009 (UTC)

::: 1/3/3/5/9 isn't always used, either now or in the past.  There is nothing that singles it out as being the correct one.  It is used because it is simple, with no fractions.  We are supposed to represent all significant points-of-view [[wp:POV]].  I wouldn't say that the difference between 9 points and 10 points for the queen is immaterial.  Would you exchange a queen for two rooks?  A queen for three minor pieces?  It may depend on how much value you place on the queen.  A similar thing applies to a rook versus a minor piece and two pawns, or a rook and pawn versus two minor pieces.  I do agree with your suggestion of a table for the alternate and historical evaluations.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 16:41, 24 April 2009 (UTC)

::::Well, obviously we don't agree on everything. First, I don't consider listing every model that ever came up in history is "all '''significant''' points-of-view". The NPOV policy, roughly stated, says that different points of view should receive "proportional coverage" if you will to that which is to be found in reality. A quick check-up on Google for chess pieces values gave me four sites where they went 1-3-3-5-9, and only one that gave 2.7 for the knights (instead of three). I checked the latest version of Chessmaster, and they give 1-3-3-5-9 to the Chessmaster personality. This is my main point: I honestly believe that this article gives too much weight to alternate valuations, and this is why I'm suggesting we sum them up in a table that could take half a page max, and then people can choose to go see the sources if they see fit.

::::Second of all, you're being very dogmatic when you say that "[i]t may depend on how much value you place on the queen", regarding whether I'd exchange her or not for two rooks. What you're saying (to some extent; I'm sure there's a grey zone here) is that you can simply check the value of the proposed/supposed value of pieces to know whether you should exchange or not. I believe that those two things (whether you should exchange and the supposed value of pieces) depend both of a same thing, which is the actual ''intrinsic'' value of the pieces. For instance, I wouldn't mind taking a rook for a knight and a pawn, but I most certainly wouldn't take a rook and two pawns for two bishops, particularly in the endgame. This decision is based on what I perceive is the intrinsic value of the pieces at the time of my decision (and not the supposed value of the pieces, say 1-3-3-5-9). I don't think these are meant to be used as actual rules (well, maybe as rules of thumb), but mainly trying to convey the intrinsic value of the pieces the best way they can. In that optic, of course you're going to get a thousand different valuations from everyone; what else would you expect? However, common census is to use the 1-3-3-5-9 rule whenever you want a quick and reliable material checkup of a position, regardless of the position (notice that interfaces such as BlitzIn/Dasher, Babaschess, Thief, Nemesis, etc. all give material evaluations using the 1-3-3-5-9 rule).

::::I'm not saying it's the best. It's just that, just like you said, it's the most common one, for whatever reason. And currently, apart from the sections title, I don't find that the article reflects that.

::::Finally, since you seem to agree that summing everything up in a table is a good idea, I'm not sure why we're having this conversation.

::::[[User:Seigneur101|Seigneur101]] ([[User talk:Seigneur101|talk]]) 19:53, 24 April 2009 (UTC)

::::: Check the books referenced and you will find that quite a few systems have been proposed and used over the years.  There is the section for the standard 1/3/3/5/9 system and then sections for historical and alternate systems.  Those probably need to be in two tables, one for historical ones before 1900 or so.  The way the Berliner system is, it won't fit into a simple table along with the others.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 20:48, 24 April 2009 (UTC)

How about

{| class="wikitable"
|+Alternate systems, with pawn = 1
! [[Image:Chess nlt45.svg]] !! [[Image:Chess blt45.svg]] !! [[Image:Chess rlt45.svg]] !! [[Image:Chess qlt45.svg]] ||[[Image:Chess kdt45.svg]]||Source|| Date || Comment
|-
|3.1||3.3||5||7.9||2.2||Sarratt?||1813||(rounded) pawns vary from 0.7 to 1.3
|-
|3.05||3.5||5.48||9.94|| ||Philidor||1817||also given by Staunton in 1847
|-
|3½||3½||5½||10|| ||Euwe||1944||
|-
|3½||3½||5||8½||4||Lasker||1947||kingside rooks and bishops are valued more, queenside ones less
|-
|3||3+||5||9|| ||Horowitz||1951||The bishop is "3 plus small fraction"
|-
|3¼||3½||5||10|| ||Evans||1958||Earlier in the book Evans gave 3¼ for the bishop
|-
|3||3¼||5||9|| ||Fischer||1972||
|-
|3¼||3¼||5||9¾|| ||Kaufman||1999||Add ½ point for the bishop pair
|-
|3.2||3.33||5.1||8.8|| ||Berliner||1999||plus adjustments for openness of position, rank & file
|-
|3½||3½||5||9½|| || || ||early Soviet chess program {{harvcol|Soltis|2004|p=6}}
|-
|3||3||4½||9|| || || ||another popular system {{harvcol|Soltis|2004|p=6}}
|-
|2.4||4||6.4||10.4||3||Gik|| ||based on average mobility; Soltis pointed out problems
|}
with the king value and date filled in only if appropriate.  Assume 1 for the pawn.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 21:27, 24 April 2009 (UTC)

:Wow... that's excellent -- pretty much what I had in mind. [[User:Seigneur101|Seigneur101]] ([[User talk:Seigneur101|talk]]) 04:17, 10 May 2009 (UTC)

:: OK, I've been working on it along and along.  Still some work to do and some of the discussion will need to remain in that section, but the values will be tabulated.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|(talk)]], 04:23, 10 May 2009 (UTC)

::: The table is nice.  
:::The note on Lasker's evaluation says that "kingside rooks and bishops are valued more, queenside ones less."  Curious.  The article doesn't address the issue of K-side vs Q-side.  It would be interesting whether this idea is based upon proximity to the opposing K, or rather defensive value towards one's own K.  (One would think that this would be more of an issue for the slow-moving knights.)
:::I note that a white K starts on a dark square, and would occupy another dark square after castling either way, which means that the opponent's KB (confined to dark squares) is better equipped to attack him early on.  The same applies in reverse for the black K and the white KB.
:::But any advantage to the K-side R would be temporary, as either R can get to the other flank rather swiftly, and their functions are usually coordinated as soon as possible.
:::Am I overlooking some important issue?  In any event, I'd guess that any K-side advantage wouyld be truly minimal and would wash out early. [[User:WHPratt|WHPratt]] ([[User talk:WHPratt|talk]]) 16:33, 22 November 2010 (UTC)

:::: The kingside bishop is probably more valuable because it can attack the opponent's f2/f7 square (it was nice when we used descriptive notation because that would be called just KB2) and h2/h7.  I think you are right about the kingside rook advantage being only temporary.  Usually players castle on the kingside so the kingside rook usually gets on an open file sooner, but otherwise they are indistinguishable.  (And it can be more valuable foe defense after 0-0.) [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 17:31, 22 November 2010 (UTC)

== Princess and empress ==

On the queen=9, rook=5, bishop=3, knight=3, pawn=1 scale, how can we define the values of the princess and empress?? (See [[fairy chess piece]] for what these are.) [[User:Georgia guy|Georgia guy]] ([[User talk:Georgia guy|talk]]) 20:43, 29 April 2010 (UTC)

: I'm certainly no expert on that, but the value is approximately proportional to the average mobility (except for the bishop because it is restricted to one color).  I estimate that an empress (R+N) would be 8 to 8.5, more likely 8.5.  I don't think it would be quite as good as a queen.  For a princess (B+N), probably 5.5 to 6.5.  It isn't restricted to one color the way the bishop is, but it might not be as good as having a bishop and a knight.  MY guess is closer to 5.5 than 6.5.  Just my 2 cents - take with a grain of salt.  [[User:Bubba73|Bubba73]] [[User talk:Bubba73|<sup>(You talkin' to me?)</sup>]], 02:26, 30 April 2010 (UTC)

::My guesses are 9 and 7! Because having one piece gives the opponent one target instead of two. And also because these pieces move in 12 directions and have a lot of forking power. These are reasons why the queen is stronger than a separate rook and bishop by about a pawn.
::I give the empress 5+3+1=9 (rook+knight+forking and single piece bonus). I think the empress and the queen are almost exactly equal in the opening and middlegame, as the knight and bishop are almost exactly equal. In the endgame, the queen may increase in value more, but the fact that the empress always wins against a pawn (when the queen doesn't) makes me even more certain that they are equal in value, with their own advantages and disadvantages.
::As for the princess, surely it must receive bonuses for the same reason. It is obviously stronger than a rook. (And I don't think colourboundedness is such an issue, especially for riders like the bishop. In cylindrical chess the bishop is as strong as a rook, even though it's still colourbound!) So I give the princess 3+3+1=7 (knight+bishop+forking and single piece bonus). [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 03:03, 11 December 2013 (UTC)

::: But having two pieces in one has some disadvantages: two individual pieces can double attack, discovered attack, and one can protect/support the other.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 03:14, 11 December 2013 (UTC)
:::: But it also has some advantages: the queen has much forking power going forward, while the rook doesn't have any and the bishop only has the minimum possible. (The empress gets more of this, naturally.) And also the queen can move in 8 directions, while the rook and bishop have only 4. The fact that the queen is commonly held to be worth more than the sum of its components seems to mean that the advantages here outweigh the disadvantages. Or at least, that's how I'm interpreting it. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 08:10, 11 December 2013 (UTC)
:::: P.S. The fact that [[Almost Chess|Sort of Almost Chess]] has been invented and thus passed the "not-skewed-towards-one-side" test (one side has an empress, the other has a usual queen) seems to indicate to me that the difference between empress and queen is similar to that between bishop and knight, where the absolute difference in value is smaller than the fluctuations in value caused by the specific position. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 08:14, 11 December 2013 (UTC)

::::: Rooks can fork.  Rooks and bishops aren't nearly as good at forking as knights and queens, though.  But I still think a queen is a half point to 1 point more valuable than a R+N combination.  A queen can move along a diagonal to get between pawns and then attack like a rook.  A R+N combination isn't so good at doing that.  And a queen and bishop on the same diagonal can be very powerful, whereas there is no equivalent with a R+N combination.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 20:47, 11 December 2013 (UTC)
::::::Yes, rooks can fork, but not forwards. Surely that restriction has some meaning because enemy pieces are in front of you, and therefore until you get deep into the enemy camp you won't have much backward- or sideways-forking opportunity. You have R and B (4 directions), N and Q (R+B) (8 directions), then surely B+N and R+N (12 directions) must benefit from great forking power?
::::::Well, an empress (I don't like that name really; it implies that it's more powerful than a queen, which I don't believe it is) can move like a knight and cut past pawn barriers in closed positions, before wrecking havoc in the enemy camp, which a queen can't do because it can't get there! I can see situations that would favour the queen, and situations that would favour the empress; so I still think they are like the knight and bishop, approximately equal in value, so much so that the specific position impacts their value more than their intrinsic power. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 02:47, 12 December 2013 (UTC)

::::::FWIW, [[Chancellor (chess)]] says "...this piece is at best equal to and perhaps weaker than the queen, especially in the endgame."  and [[Archbishop (chess)]] says "Ralph Betza (inventor of chess with different armies, in which the archbishop was used in one of the armies) rated the archbishop as about seven points..." [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 03:20, 12 December 2013 (UTC)
:::::::Well, the chancellor article also says "the chancellor...has a great ability to give perpetual check and save a draw in an otherwise lost [end]game", and gives Betza's valuation as nine points. So I guess even in the endgame it might not be that bad. The queen and chancellor are good at giving perpetual checks; if they fail against a stronger force (e.g. two rooks), they lose rather quickly. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 03:28, 12 December 2013 (UTC)

::::::: A B+N or R+N are not really "12 directions" because in 8 of those, it can move to only one specific square.  And besides forks, there are pins and skewers which the long-range pieces can do but knights can't.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 03:02, 12 December 2013 (UTC)
::::::::Well, they will always have some pinning and skewering power from the bishop or rook component. And the knight direction is useful because other pieces (except knights) can't use them, which means they can attack non-knight pieces without being attacked in turn. And since knights are great at forking despite its 8 directions being limited to one square, I think that when it comes to forking they are really 12-directional, though they aren't for pinning and skewering. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 03:13, 12 December 2013 (UTC)

Now curious on how you would value a triple-compound piece: the [[amazon (chess)|amazon]] is R+N+B. I guess 11.5, maybe 12 because it can hunt down and mate a lone king by itself? How would you value the [[nightrider (chess)|nightrider]] (which is to the knight what the queen is to the king, making an unlimited number of knight moves in one direction?) (I guess 5.) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 09:52, 11 December 2013 (UTC)

: I am not a Chess expert, but having read several different discussions on the subject of fairy piece values and designed some variant games using fairy pieces, I offer the following opinions:
: * Compound pieces are generally worth more than the sum of their parts, because each component makes it easier to line up future moves with the other(s); e.g. the Rook component of a Queen is more valuable because the Bishop component helps the Queen get into more positions where the Rook moves will be useful.  Basically, value rises faster-than-linearly with mobility.
: * Several people who have played [[Capablanca Chess]], including one who created a computer player for it, have claimed that the Archbishop (B+N) is '''much''' stronger than the sum of its parts; nearly as strong as the Chancellor (R+N) and Queen (R+B), despite the fact that Rooks are individually more valuable than Knights or Bishops.  I have never yet heard a theoretical justification for this that I believe, but have no empirical reason to doubt it.
: * Forcing checkmate with Archbishop + King vs King is possible (according to computer proof), and anecdotally is easier than forcing checkmate with Knight + Bishop + King.
: * A "cylindrical" Bishop is indeed about equal to a Rook, and I've even seen it valued slightly higher; however, this was argued to be because of its "forwardness" (being able to move towards the enemy in 2 directions rather than 1--forward moves are more valuable than sideways or backwards ones because the enemy starts in front of you), not because colorboundness is insignificant.  The [[Ferz (chess)|Ferz]] (1-space Bishop) is thought to be stronger than the [[Wazir (chess)|Wazir]] (1-space Rook) for the same reason.
: * IIRC Ralph Betza valued the Amazon at around 13 pawns, which sounds about right to me if the Queen is 9, but I wouldn't be surprised if it was even higher.  Among other advantages, it can force checkmate in an open position '''without''' the assistance of a friendly King.  [[Maharajah and the Sepoys]] seems to suggest a ridiculously high value for the Amazon, though that may not be directly applicable since it allows her mobility for evading check as well as for attacking.
: * The Nightrider is commonly valued as equal to, or slightly better than, a Rook.  IIRC Betza opined that a Rook could win in an endgame with 2(?) or fewer pawns against a Nightrider but the Nightrider won with 3 or more pawns due to its forking power.
: [[User:Antistone|Antistone]] ([[User talk:Antistone|talk]]) 06:04, 1 July 2014 (UTC)
::I'll use "princess" for BN and "empress" for RN below, both to be consistent with the OP, and also to keep with the problemist tradition (whereas "archbishop" in the problemist tradition is quite a different piece, and "chancellor" has been given to many other pieces.)
::Since my initial comment, I have revised my tentative princess value to 8 instead of 7, because it fixes important weak points of her component pieces: it does not have the bishop's colourboundedness, nor does it have the knight's somewhat slow movement when compared with the other pieces. The rook's main benefits from the conversion seems to be an additional number of forward directions that it can move in, and a slow development: but the latter is not much of a benefit IMHO because the rook's slow development means that it will stick around until the endgame, as it should, being a major piece; and the former doesn't seem to be that much of a weakness, as the natural way to use rooks seems to be to move them along the back rank to open files or support pawns' advances, in which case their move complements perfectly with this action. So their limited forwardness cooperates well with the pawns, which the bishop cannot do (although a bishop and pawn can mutually defend each other, the pawn cannot then advance, which is generally something you want to do). It's great to know that experimental results bear this out! :-) Although KBN vs. K is one of the hardest of the basic checkmates (KBB is a bit unclear for a beginner, but nowhere near as hard), so I'm not surprised that K+princess vs. K is easier than that.
::I agree with you on the value of the oB (cylindrical bishop).
::I don't think [[Maharajah and the Sepoys]] suggests that the amazon has the full 39-point value of the entire FIDE chess army of one side – after all, the game is a forced loss for the amazon. Now what would be interesting is to see what's the smallest amount of material that can force checkmate on a royal amazon. I would also suggest 13 or 14, because it gives the triple compound advantage: each component (R, N, B) can help the amazon get into a position where at least one of the other two is useful, which is nearly all the time. Therefore I think 14 is better because it gives a larger bonus because of the even greater utility of a triple-compound piece as compared to a double-compound piece. Something like the amazon rider (RBNN) would, I think, be worth about 16 or 17 points for the same reason and also because all 16 of its possible directions are unlimited in range (and would honestly be colossal overkill if we use an orthodox king, unless the defenders are also of similar strength).
::The nightrider does seem to be of about a rook in strength. It skips over every other rank or file, but has twice as many directions to move in as the rook does. It will win in the endgame against a rook if it can use its immense forking power to win a large enough material advantage: but if there are very few pieces left, it will probably lose against a rook because it cannot checkmate the enemy king and cannot assist by pushing its last pawns forward to promotion or interdicting the enemy king or pawns against advancing another rank. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 11:39, 1 July 2014 (UTC)
:::OTOH, one must consider that the amazon carpet-bombs an entire area, but the queen, princess, and empress already succeed in covering much of that 5×5 square anyway. The additional concentration of power in the amazon should not add as much of an advantage. Consider that the princess works so well (8 pawns) because both its components (knight and bishop) have weaknesses that are masked when they are united in her. But if we add a rook to the princess, the rook component benefits, but not the princess. In fact, since the double-compounds already have so much mobility, I wouldn't be surprised if the triple-compound advantage was actually zero, giving about 11 for the amazon, so that it would indeed equal the sum of its parts (5+3+3=11). [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 14:52, 30 January 2016 (UTC)
::::A value of 11 for Amazon implies that both Queen+Knight and Princess+Rook are worth ''less'' than the sum of their parts, which seems quite implausible.  I'm not aware of ANY example where a compound piece is commonly accepted to be weaker than the sum of its (non-overlapping) parts. --[[User:Antistone|Antistone]] ([[User talk:Antistone|talk]]) 05:36, 8 June 2017 (UTC)
:::::Perhaps one should however be careful of extrapolating from normal-strength pieces to very strong ones like this; the strength of the princess is quite counterintuitive, and I wouldn't rule out the possibility of the amazon being overly weak instead. I would guess 12 as a sort of compromise figure as exactly equal to Q+N, since only one of the components seems to really benefit instead of both. But of course, this is only a guess without empirical confirmation. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 05:46, 8 June 2017 (UTC)

== Hans Berliner's tables ==

Clarification needed: 
1st and 2nd tables: What thinks/says Berliner about rank 7?
3rd table "advanced pawns": There is no advanced pawns with rank 4... Value "x"? Rank 7?  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/217.110.99.238|217.110.99.238]] ([[User talk:217.110.99.238|talk]]) 15:48, 21 January 2011 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:The fourth rank is not considered "advanced".  The tables are as in his book, he gives no value for the cases with the "x".  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 17:12, 21 January 2011 (UTC)

:: Thank you Bubba73. What is then the meaning of the 4. rank in the last table "advanced pawns?" I think, I should find the book...  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/217.110.99.238|217.110.99.238]] ([[User talk:217.110.99.238|talk]]) 10:40, 31 January 2011 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

::: Good catch.  The table is actually for "pawn advances", i.e. he must mean a pawn advance from that rank.  He says "A pawn's value doesn't increase much until it reaches the fifth rank, and then it increases its base value according to the table below which shows the gains... These multipliers are to be applied to the base value of the pawn" (which differs according to the rank).  Of course, you might use this sort of valuation in a computer program, but people don't think in terms of "I'll advance that pawn and increase its value by 10%".  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 17:05, 31 January 2011 (UTC)

==Citations==
What the hell are wrong with the citations on this page?  Someone should look into this, they're all f**ked up.<small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:116.236.175.178|116.236.175.178]] ([[User talk:116.236.175.178|talk]] • [[Special:Contributions/116.236.175.178|contribs]]) </span></small><!-- Template:Unsigned -->

: They work for me - click on them and they take you to the reference data.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 20:54, 7 May 2011 (UTC)

== Added the king to the table ==

Like in the endgame the king has a value about 3 pawns,  <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:WorldofTanks|WorldofTanks]] ([[User talk:WorldofTanks|talk]] • [[Special:Contributions/WorldofTanks|contribs]]) 12:23, 13 July 2011 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

: That table is for the "standard valuations".  So few references give a value for the king that I don't think that is standard. [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 15:16, 13 July 2011 (UTC)

::It's more of a 4 really in the endgame. In the opening it is much weaker because it has to worry about check; maybe 2.5 or 3 at the most? [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 09:58, 11 December 2013 (UTC)
:::(no, I don't think so now: I think in the opening the royal king is worth 1.5 to 2, and it only becomes 4 in the endgame when checkmate is less of a threat. I think the non-royal king is still just 2 to 2.5 in the opening because it takes time to develop, but it can reach 4 in the middlegame already if centralized.) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 02:59, 17 December 2013 (UTC)
::: From what I've read, about 2 points early in the game, getting to about 4 in the endgame.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 03:58, 17 December 2013 (UTC)
::::OK, that's about what I estimated – always a good sign! (Heh.)
::::It then makes me wonder how much being royal (if it is captured, its owner loses the game) impacts the piece's value. A royal king can't sit in the centre and use its concentrated stepping power, because it's not going to live very long there; but a non-royal king can! (Or maybe not, since in this position it is surely stronger than a knight or bishop, and thus it is afraid of being traded off? Compare this to the alibaba ([[dabbaba (chess)|dabbaba]] + [[alfil (chess)|alfil]]), which is surely weaker than a knight or bishop, but is very strong in the centre and therefore the opponent has to choose between allowing it to remain in its powerful position or losing material!)
::::What if you have two kings? Under the Japanese interpretation (seen, for example, in [[chu shogi]], a sort of Japanese Grand Chess), you can ignore check if you have two kings: but at the same time you might not want to, because if your second king is captured you're back to having to worry about check! Then again, there you get a second king through promotion and thus only in the endgame if at all; maybe analyzing my rule modification to [[Double Chess]] (using the Japanese interpretation of check with multiple kings) would give some idea on what happens in the opening when pieces are more plentiful and checkmate is more of a danger? [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 08:12, 17 December 2013 (UTC)

== Use in the rules ==

We recently had a [[tournament]] at the high school I attend. The time limit was one hour for the game, but that was based in real time. We didn't use the [[game clock]].

At the end of the hour, and only in draws under that rule, we used the standard scoring system to break ties. Whoever had more points on the board moved on. If there was a tie, it was treated like any other draw and they replayed the match.

The tournament never reached a point where the rule was enforced, and I don't expect it to catch on, but hey, the system found a way into a rule book.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/67.142.177.20|67.142.177.20]] ([[User talk:67.142.177.20|talk]]) 22:09, 28 February 2014 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

: What rulebook has that "rule"?  There is no such rule.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 01:00, 1 March 2014 (UTC)

::Some competitions incorporate a rule that long-running games can be resolved by adjudication, wherein some agreed-upon expert can decide who's winning, if either player, and thus award the points. However, these judges take the entire position and dynamics into account, not just the value of the remaining pieces. The procedure described above would be an extremely low-level application of this idea.[[User:WHPratt|WHPratt]] ([[User talk:WHPratt|talk]]) 17:55, 1 March 2014 (UTC)

::: Yea, just grab a pawn and hold on.  Don't move until the time runs out! [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 02:55, 2 March 2014 (UTC)

:::: 1.d4 d5 2.c4 dxc4 3. any, then Black just sits there until the time is up and wins the game.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 03:06, 2 March 2014 (UTC)

:::Not to mention that this system will end up somewhat altering the gameplay strategies: it doesn't let you sacrifice to create stalemates when swindling opportunities arise, because your opponent will end up having more "points" on the board. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 02:25, 2 March 2014 (UTC)

::::This is the guy that posted that to begin with, and you can check the IP address for verification. It's important to note that this was an intramural high school tournament with no official standing in the eyes of any governing body. Therefore, we could pretty much do whatever we wanted to. Where I went, most of the students (myself included) have some sort of mental "disability" and really didn't have the patience to just sit there for an hour. In the final (I was a spectator and, at times, substitute official), I had to tell the guy playing black to stop bouncing. A redemption bracket match featured 7 replays just because one guy kept forgetting that checkmate requires your opponent to be in check. I think I would have been the only one there who would think to use that to my advantage, and I decided not to sign up. If it was a tournament among students on the autism spectrum, it might work again. But if Magnus Carlsen and Viswanathan Anand played for the world championship under these rules, expect a return of Jesus Christ, our Lord and Savior.[[Special:Contributions/67.142.163.20|67.142.163.20]] ([[User talk:67.142.163.20|talk]]) 13:48, 22 July 2014 (UTC)

== King value of 1,000,000,000 points ==

The article claims that some computer programs value the king at 1,000,000,000 points. Says who?  Since programs usually use centipawns, that's 100 billion centipawns, a value that won't fit in a 32-bit unsigned integer.  I think this claim is an exaggeration, which is to say false.  One million would be plausible, since there's absolutely no point in using a billion here.  No possible material advantage combined with any conceivable position evaluation advantage could come within six orders of magnitude of a billion.  [[User:Quale|Quale]] ([[User talk:Quale|talk]]) 19:53, 22 November 2014 (UTC)
:I am rather sceptical that they actually use a positive integer value for the king. By that logic, wouldn't it seem perfectly fine to a computer to answer check with check, or to exchange kings? [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 08:40, 3 March 2016 (UTC)

:: It is probably built into the rules that the kings can't get close enough to exchange.  Putting a high value on the capture of the king is an easy way for it to have the goal of checkmate, as if it were capturing the king.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 16:32, 3 March 2016 (UTC)
:::Yes, but it would not prevent them from answering mate with a mate, right? (As if Black could play ...Qe1# after Kramnik's famous mate-in-one blunder, even after the White Qh7#). So all the rules about check and mate need to be programmed in. (Otherwise most stalemates become wins since the stalemated player would have to commit suicide.) This kind of defeats the purpose of trying to simplify things by giving the king a large numerical point value. Now, I could believe that a forced mating sequence counts for large numerical points (so that sacrifices are OK), but not the king itself. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 02:01, 4 March 2016 (UTC)

:::: You are probably right about that.  It would see that if it can checkmate on the next move, it would "even out".  Simple (and early) programs probably don't take that into account. [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 02:54, 4 March 2016 (UTC)
:::::Presumably the Black player of [http://streathambrixtonchess.blogspot.com/2008/03/ultimate-ultimate-blunder.html this game] had the same misunderstanding, or I cannot find an explanation for his blindness. ^_^ (Surely this is the best of the ultimate blunders!) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 15:02, 6 March 2016 (UTC)

== On fairy pieces ==

Given that the princess (B+N) and empress (R+N) are the two fairy pieces everyone invents and [[List of chess variants#Chess with empress and/or princess pieces|puts in their chess variants]] (including Capablanca), I wonder if there have yet been enough variants made that people have said anything about their values in reliable sources. It seems more likely than for any other fairy pieces (although if we're talking about historical variants too, there most certainly are historical values for shatranj). I would personally put the princess at 8 pawns and the empress at 9 pawns, assuming both are living on an 8×8 board, but that is only my OR. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 14:22, 15 January 2016 (UTC)
:Oh, the list there also includes one with an amazon (Q+N): I would personally rate that as 12. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 14:30, 15 January 2016 (UTC)

== External links modified ==

Hello fellow Wikipedians,

I have just modified {{plural:4|one external link|4 external links}} on [[Chess piece relative value]]. Please take a moment to review [https://en.wikipedia.org/w/index.php?diff=prev&oldid=750719223 my edit]. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit [[User:Cyberpower678/FaQs#InternetArchiveBot|this simple FaQ]] for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20060629013845/http://mywebpages.comcast.net:80/danheisman/Articles/evaluation_of_material_imbalance.htm to http://mywebpages.comcast.net/danheisman/Articles/evaluation_of_material_imbalance.htm
*Added archive https://web.archive.org/web/20040802224948/http://chess.about.com:80/library/ble23pvl.htm to http://chess.about.com/library/ble23pvl.htm
*Added archive https://web.archive.org/web/20040803054716/http://chess.about.com:80/library/ble23zws.htm to http://chess.about.com/library/ble23zws.htm
*Added archive https://web.archive.org/web/20160314214435/http://www.danheisman.com/Articles/evaluation_of_material_imbalance.htm to http://www.danheisman.com/Articles/evaluation_of_material_imbalance.htm

When you have finished reviewing my changes, please set the ''checked'' parameter below to '''true''' or '''failed''' to let others know (documentation at {{tlx|Sourcecheck}}).

{{sourcecheck|checked=false}}

Cheers.—[[User:InternetArchiveBot|'''<span style="color:darkgrey;font-family:monospace">InternetArchiveBot</span>''']] <span style="color:green;font-family:Rockwell">([[User talk:InternetArchiveBot|Report bug]])</span> 12:50, 21 November 2016 (UTC)

== Chess piece potential value. ==

I am the author of "True Chess: The American Revolution" and I was looking to making what I call "The Formula" known to all who would search wikipedia for answers concerning chess piece values. In my book I reveal "The Formula" and I show how it all makes sense. I demonstrate how the value of the squares and the value of the pieces come together. I demonstrate in irrefutable fashion how chess is an expression of Pi. All who are interested in knowing the value of the pieces should have access to this information. I am new to editing and I don't look forward to making another attempt at it. The potential value of the pieces are pawns = .942  knights = 2.512  bishops = 4.082  rooks = 4.396  queens = 8.478  kings have a fighting strength value of 2.512. The squares = .314 each times 64 = 20.096  One queen, one rook, one bishop, one knight, and one pawn = 20.410.
The difference between 20.410 and 20.096 is .314   Please contact me and help me add this information to the Chess piece relative value page or help me create the Chess piece potential value page. Don't do it for me do it for the people who are seeking information.[[User:MyDiametrical|MyDiametrical]] ([[User talk:MyDiametrical|talk]]) 18:18, 12 June 2017 (UTC)

# I don't believe that there are such precise values.
# I don't think it involves pi.
# You have to avoid putting [[wp:OR]] in Wikipedia articles.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 20:26, 12 June 2017 (UTC)
# I demonstrate in undeniable fashion how chess is in fact an expression of Pi. My book makes it plain and simple for all to understand. "true Chess" is available at Amazon Books. Let's leave preconceived notions behind and deal with facts and information. "I don't think" has no place here. Explain how the formula is incorrect. It cannot be done.[[User:MyDiametrical|MyDiametrical]] ([[User talk:MyDiametrical|talk]]) 16:16, 20 July 2017 (UTC)

You are not new to editing here, as you have been trying to add this information since October 2015. If you have reliable sources (other than a self-published book), please feel free to add the information. --<span style="#111111">‖ [[User:Ebyabe|Ebyabe]] <sup>[[User talk:Ebyabe|talk]]</sup> - <small>[[Special:Contributions/Ebyabe|<span style="cursor:help;">''Attract and Repel''</span>]]</small></span> ‖ 17:06, 20 July 2017 (UTC)


Apart from the religious-sounding decision to express everything as a multiple of 0.314 (which is meaningless, since only the value ''ratios'' matter--and which, incidentally, does ''not'' equal pi), it seems you're just counting the maximum squares a piece can reach within 1 move under ideal circumstances.  This is a common starting point for people trying to measure piece value, but vast amounts of empirical evidence show it to be a rather poor estimate of practical value.  This is not surprising, since it ignores significant information about the pieces--for instance, your system assigns the same value to a special rook that can jump over pieces as to a normal rook that can be blocked, where clearly the jumping rook is strictly more powerful and therefore must have a higher value.

Most sophisticated methods for calculating piece value seem to rely principally on some sort of weighted average of the number of squares that can be reached under a '''range''' of different circumstances (rather than simply taking the maximum).  This usually gives values pretty close to the empirical values, but it's still far from perfect agreement, and additional corrective rules are often applied to fine-tune values. [[User:Antistone|Antistone]] ([[User talk:Antistone|talk]]) 08:04, 30 November 2017 (UTC)

== Transferred use ==

Could it be possible to transfer this analogy to other games, such as [[Battleships (game)|Battleships]] ?
[[Special:Contributions/80.43.1.195|80.43.1.195]] ([[User talk:80.43.1.195|talk]]) 19:37, 20 March 2021 (UTC)

== Stockfish valuations ==

We need a reference for the Stockfish valuations.  I couldn't find it.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 01:06, 11 March 2019 (UTC)

: The Stockfish valuations have been explained in a footnote, but we still need a reference for them.  Also, they are dubious.  For the endgame a pawn is 213 and a knight is 865, i.e. a knight is 4.06 pawns.  But two pawns usually win against a knight.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 23:25, 17 March 2019 (UTC)
::The fact that the number of pawns on the board is not considered is to me already a major red flag. A late endgame situation with no other material on each side will depress the value of a minor piece, especially as it is a knight, because it can at most hope to draw (except for the odd case of Stamma's mate in N vs P). K+8P vs K+N+6P should give the knight's side a strong advantage, as the defending king is just going to be too slow to deal with all the forking threats. A value of 4 pawns for the knight seems only reasonable in the very early opening or perhaps in a closed position with all the pawns on the board; in the very late endgame it should be around 2{{frac|1|4}} at most when almost all the pawns disappear. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 06:23, 18 March 2019 (UTC)

:: Well the valuations are referenced because the footnote links to the code.  But it also gives a rook as 6.47 pawns in the endgame.  Three pawns often win against a rook, depending on how far advanced they are. (I had one of those and won with the pawns.)  And four pawns generally beat a rook.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 17:30, 18 March 2019 (UTC)
:::Yes, they do, but piece values are usually intended to be valid for average situations without significant positional advantages affecting one or the other type of piece and a material balance of rook versus enough pawns with no other material is never going to occur in such an average situation – especially since the value of the pawn is affected more significantly by positional concerns than that of any other piece. Piece values are influenced by what else is on the board and the values of large swarms of identical pieces are not always predictable by multiplying the value of one of that piece type by how many of them you have. To take an extreme example, [https://www.chessvariants.com/rules/charge-of-the-light-brigade 3Q+8P is slaughtered by 7N+8P] because the queens have no room to avoid being harrassed by all the knights, but we cannot conclude from this that Q is closer to being worth 2 minors rather than 3 on average. When we say "rook = 5 points", it doesn't mean that an average position with the material imbalance of R vs 5P will give equal chances for both sides. An army with all its pawns deleted will slaughter one with only its queen deleted from the initial position, not just mildly outclass it as one would expect from comparing a queen to eight pawns. No, we can only compare against sets of pawns for minor pieces (e.g. piece vs 3 pawns); when we say that rook = 5 and queen = 9, we are actually thinking of comparisons like R vs minor (the exchange), 2 minors vs R, R + minor vs Q, 2R vs Q, 3 minors vs Q, and how many pawns it takes to balance them; and not comparing them against swarms of pawns, whose total values will not equal 5 or 9 times that of the average pawn, but will be very dependent on the exact shape of the swarm and how well-placed the enemy pieces are at dealing with them. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 03:10, 19 March 2019 (UTC)
:::P.S. I wrote the above half-remembering that I'd seen similar statements and examples, and indeed, now that I've looked it up, I see my memory is heavily indebted to [https://www.chessvariants.com/index/listcomments.php?id=35556 this comment on piece values] by [[User:H.G.Muller|H.G.Muller]] on ''[[The Chess Variant Pages]]''. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 03:31, 19 March 2019 (UTC)

:::: Yes, the valuations are a lot more useful in comparing differences in N/B/R/Q in typical positions rather than those unusual situations, or a piece versus a number of pawns (although I've had some of those).  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 04:32, 19 March 2019 (UTC)
:::::Yes indeed; OTOH, I really don't see how the Stockfish valuations as quoted could possibly be relevant for anything other than unusual situations... [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 05:19, 19 March 2019 (UTC)

Presenting Stockfish's "raw" material values as being representative of how pieces are typically evaluated by this engine is a case of improper original research, because it assumes without justification that the effect that the presence or absence of a piece has on other (positional) evaluation terms is zero on average. One could, for one thing, change the effective material evaluation just by uniformly shifting the values of [[piece-square table]]s. As another illustration, if the engine gives a bonus for having the bishop pair but doesn't penalize its absence (and by the same amount), then that means a bishop is on average valued more than its baseline value.<br /> Unless someone comes up with evidence that Stockfish's authors have been going out of their way to neutralize the bias material has on other evaluation terms (and there is no reason to do so from a performance standpoint), I will remove the Stockfish figures. -- [[User:Dissident|Dissident]] ([[User talk:Dissident|Talk]]) 22:06, 19 December 2021 (UTC)

== Changes in standard valuations section ==

I have added a citation needed flag to the sentence describing Betza's 'leveling effect'. So far as I know he uses the term only to mean that a defended lower value piece is not generally worried by an attack by a higher valued piece, but usually a defended higher value piece if attacked by a lower valued piece must move (and similar considerations). This is not the meaning ascribed.

I've also removed the comment about three queens losing badly to seven knights because firstly there was no citation and I don't see it in Betza's page and secondly it's false; the queens win 90% of the time usually very quickly.   
--[[User:Martin Rattigan|Martin Rattigan]] ([[User talk:Martin Rattigan|talk]]) 22:09, 12 May 2022 (UTC)
:3Q lose badly to 7N ''when both start behind a closed wall of pawns''. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 16:27, 28 December 2023 (UTC)

== "Lasker's" Alternative valuations ==
The alternative valuations table says "Lasker adjusts some of these depending on the starting positions".  However, it's not clear which Lasker, Emanuel or Edward, is being referred to.  Both Laskers are mentioned in the article.  On the one hand, since the previous reference to Lasker (and the only other one in that table) refers to Emanuel, one would suspect that the "Lasker adjusts" statement refers to Emanuel.  On the other hand, the date for this valuation is given as 1947, at which time Emanuel was dead but Edward was still alive.  This would tend to point to Edward for this valuation.  

Which is it? [[User:Riordanmr|Riordanmr]] ([[User talk:Riordanmr|talk]]) 20:52, 8 August 2022 (UTC)

: It must be Emanuel since he is the one in the reference.  [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 21:20, 8 August 2022 (UTC)

:: I think that you are right that it's Emanuel.  Digging deeper, I see that a reference in that section mentions (Emanuel) Lasker's Manual of Chess, and gives it a publication date of 1947.  There are quite a few dates of publication floating around for this book.  I believe that the facts of the matter are that German edition was published in 1925 and the English in 1932.  However, I will do some more research before making any fixes to the article.  [[User:Riordanmr|Riordanmr]] ([[User talk:Riordanmr|talk]]) 19:14, 4 September 2022 (UTC)

== Fractions vs Decimals? ==

[https://en.wikipedia.org/w/index.php?title=Chess_piece_relative_value&diff=prev&oldid=1144666196 This edit] created '''decimals''', with the edit summary: "Merged fractions into a unitary decimal system...}

[https://en.wikipedia.org/w/index.php?title=Chess_piece_relative_value&diff=prev&oldid=1144686211 This edit] reverted to '''fractions''', with this edit summary: "Not an improvement"

I reverted the last one, but I'd like to see what others think.

What do we really want? I don't know if there is any standard way, and I've seen both used. The UCSF shows a [https://www.uscfsales.com/blog/know-your-chess-pieces-value-to-triumph.html decimal system]. -- [[User:Valjean|Valjean]] ([[User talk:Valjean|talk]]) ('''''[[Help:Notifications|PING me]]''''') 02:19, 15 March 2023 (UTC)

* '''Decimals''' -- [[User:Valjean|Valjean]] ([[User talk:Valjean|talk]]) ('''''[[Help:Notifications|PING me]]''''') 02:19, 15 March 2023 (UTC)
* '''Follow the sources'''  It is generally good advice for Wikipedia articles to follow the sources, and this definitely applies here.  Some sources have used decimal values, others fractional.  Sources that used fractions should not be given here in decimal.  The original sources could easily have used decimal if they thought it better, but if they used fractions then it is not Wikipedia's place to second guess or misrepresent their choice.  Also 5.25 is not the same as {{frac|5|1|4}} since 5.25 suggests a much greater precision than was probably intended.  It's likely that authors using {{frac|5|1|4}} were not making any statement that the precise value was 5.2500000 and not 5.24 or 5.26, so replacing the author's expression with a decimal misrepresents their intent.  Computer values are often given in decimal and it is likely in those cases that the decimal values indicate the precision intended.  In the same way, the article should not use {{frac|3|1|10}} if the source says 3.1.  [[User:Quale|Quale]] ([[User talk:Quale|talk]]) 06:14, 15 March 2023 (UTC)

== Discussion ==

The endgame value of a pawn  maybe different than one because of possible  promotion to other pieces. [[Special:Contributions/194.153.110.5|194.153.110.5]] ([[User talk:194.153.110.5|talk]]) 16:04, 28 December 2023 (UTC)
:It depends on the particular pawn. The values are intended as averages, not for cases like draws in KQ vs KP. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 16:25, 28 December 2023 (UTC)

: Pawns do increase in value in the endgame.  A few methods take that into account. [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 17:05, 28 December 2023 (UTC)

== Non-credible youtube user ==

His channel isn't even primarily focused on chess. This is essentially the same naive mobility-based analysis as that by Gik, with all the same caveats as pointed out by Soltis. Youtube is not a credible source for anything, it's a self-publishing site where anyone can say anything they want. [[User:MaxBrowne2|MaxBrowne2]] ([[User talk:MaxBrowne2|talk]]) 23:11, 24 March 2024 (UTC)