Comments/Ratings for a Single Item

I am in general against spreading misinformation; there already is so much of that on the internet, no one is longing for us to add more to it. The problem with posted piece values is that they are very often not rooted in reality, but spring purely from the imagination of the author. I don't see what value that would add to an article. Every reader should be able to make unfounded guesses without any help. And it is especially bad if people post values that contradict a large body of evidence.

If I were to edit the article on orthodox Chess, claiming that the piece values are P=1, minor=2, R=4 and Q=8, based on the theory that piece values are inversely proportional to the number of those pieces you have in a game... Should it be allowed to stand? Should it go accompanied by an explanation of how these were calculated? Or by a disclaimer like "virtually everyone in the world agrees that these values are very much off, but I present these here anyway for no other reason that I could calculate them through a method that did not require any experimental evidence"?

My brother always says:  "if you don't have anything to say, then don't do that here!". Information should flow from where there is knowledge to where there is none. It is only useful to publish information that is better / more reliable than what the reader already has. Sadly, for piece values that will usually not be the case.

The main thrust of that gives no value to human intuition when there is not yet consensus or quite conclusive enough evidence (in the eyes of the beholder). Indeed, I personally think you sometimes rely on intuition when it comes to your methods for establishing or estimating piece values - that could arguably lead to misinformation unknowingly, despite your best intentions to be thorough.

I think it is easier to determine relative values than to determine precise, absolute values. Piece values are only a guide for evaluating positions, and they do not themselves determine who wins or loses. So, if you stick to relative values, you should be good, but when you attempt to give precise, numeric values to pieces, that will be far more speculative and prone to error.

It's easier, yes. A problem can surface if ever in a game you have the choice of making 2 for 1 or 3 for 1... trades. Then, for example, in chess it would not help you that you knew that P<N<=B<R<Q, if you want to know with some degree of confidence (or at least an intuitive feeling) that N+P is normally close to worth a R, or whether it's N+2P that is is normally much closer to worth a R - that is with all other affected features of the position at hand being in some kind of balance after making such a trade.

In fact it's usually N+2P, maybe during any phase of a game (if that is also to be taken into account). A (more advanced/different?) tip I've read is that (if I recall right) B+2P are usually worth R, and N+2P are a shade less than a R. Already H.G. might argue that computer studies (not just his) put single N = single B in (8x8) chess - however he might say that things are different for such (3 for 1) trades, because more units are involved, so no loss of face for anyone necessarily in such a case, for those who intrepidly try to assign (or offer to fine-tune) fairly precise piece values. In my case, for chess variants rules pages I've made, I add the caveat that my suggested values are tentative, hopefully wakening any adult who still has a child-like faith in the written word (I'd personally make an exception for a given version of bible, but perhaps even then mistranslations might have happened in some cases).

I add the caveat that my suggested values are tentative

That should be fine. I usually ignore estimates of piece values anyway, because I don't expect them to be gospel truth, and when playing a game, I rely more on my own ability to understand and compare different pieces. But piece values could be of more interest to someone who is trying to get a program to play a game better. As someone who is programming engines to play Chess variants well, it makes sense that HG would have a keen interest in this. I recall when Steve Evans and I were working on a better Shogi ZRF together, and one thing we did, which I think was more his idea than mine, was to add code to adjust the values Zillions-of-Games assigned to different pieces.

Agreed! But I am all for publishing piece values obtained through applying your experimental method. That and other tactical or strategic tips the author has found. For example I have observed that it is wrong to move a joker, in all my apothecary games, if there are pawns still ahead because they can move forward attacking the joker while the poor sucker cannot run, as it imitates a pawn. Conversely if there are no pawns ahead moving the joker to the center can be very fruitful as it can imitate anything making it temporarily the most powerful piece on the board.

The problem with intuition is that it is notoriously unreliable. Humans suffer from an effect called 'observational bias', because one tends to remember the exceptional better than the common. This is probably the reason that GMs/world champions have grossly overestimated the tactical value of a King (as ~4 Pawns): in games where the King plays an important role it can indeed be very strong, but there are plenty of cases where a King is of no use at all (because it cannot catch up with a passed Pawn). These tend to be dismissed, as "the King played no role here, so we could not see how stong it really is".  While in fact you could see how weak it was by its lack of ability to play a role. In practice two non-royal Kings are conclusively defeated by the Bishop pair, (in combination with balanced other material, and in particular sufficiently many Pawns). In games between computer programs that most humans could not beat at all. Of course none of these GMs ever played such a game even once.

Other forms of intuition often result from application of simplistic logic, rather than observation. It is 'intuitively obvious' that a BN is worth several Pawns less than RN, as B is worth several Pawns less than R, and it is their only difference. Alas, it is not true. They are almost equivalent. It ignores the effect that some moves can cooperate better than others, and in games BN + Pawn would score convincingly better than RN (and on average even beat Q).

We should also keep in mind that piece values are just an approximation. It is not a law of nature that the strength of an army can be obtained by adding a value of individual pieces, and that the win probability can be calculated from the difference between the thus obtained army strength. And indeed, closer study shows that it is not true at all. The win probability depends on how well pieces in the army cooperate, and complement each other, and how effective they are against what the opponent has.

For example, A=BN and C=RN are more effective against a Queen than against a combination of lighter material (say R+N+2P) that in itself would perfectly balance a Queen. Because all squares attacked by the latter, even though very similar to the number of squares attacked by a single Q, are no-go areas for a C or A, even when they are protected, while they would not have to shy away from a Q attack in similar situations. This causes Q+C+A < R+B+C+A, in Capablanca Chess, even though Q > R+B as usual. The extra C and A on the Q side are effectively weaker pieces than their counterparts on the R+B side, so much that it reverses the advantage. An extreme manifestation of this effect is that 7 Knights easily beat 3 Queens on an 8x8 board. Something that cannot be explained by any value for N/Q that would make sense in a context with more mixed FIDE material.

Your claim that B+2P ~ R and N+2P < R, which I don't doubt, cannot be used to conclude that B > N because of these subtleties. Piece values are not defined as how well the pieces do against a Rook, but by how well they do against a mix of opponent pieces such as these typically occur in end-games. And I have no doubt that the average performance of the Bishop suffers from the fact that there are many cases where B+2P ~ B+P, while N+2P would have done much better (namely when the Bishops are on unlike shades).

Note that the claim lone B ~ N was not based on what I would call a 'computer study'. I have no doubt a computer was used in the process, but just as an aid for quickly searching a huge database of human GM games. Not by playing computers against each other. The fact that a computer was used thus in no way had any effect on the conclusion. In the Kaufman study the claim was detailed further by stating that the B-N difference correlated with the number of Pawns, and exact equality only occurred when each player had about 5 Pawns; for fewer Pawns the Bishop performed better, for more Pawns the Knight. It is also common knowledge that Knights typically perform poorer in end-games where there are Pawns on different wings than when all Pawns are close together. This is of course also something that transcends piece values, which are defined as the best estimate for the chances without knowing the location of the pieces. Piece values are not the only terms that contribute to the heuristic evaluation of individual positions.

But to come back to the main topic: I don't think it would be a good idea to dismis any form of a quality standard on published piece values because "people should know that they should not believe what they read". That is an argument that could be used for publishing any form of fake news. It is already bad enough that this is the case, and we should not make it even more true by adding to the nonsense. There can also be piece values that have a more solid basis, and I think readers should have the right to distinguish the one from the other. So as far as I am concerned people can publish anything, as long as they clearly state how they arrived at those values. Like "personal experience based on N games I played with these pieces" or "based on counting their average number of moves on an NxN board" or whatever. If there is a non-trivial calculation scheme involved, it is fine to publish that as a separate article, and then refer to that.

One problem with computer studies of chess [variants] is that there has been no peer review by many mathematicians, and grandmasters of chess might be thrown in. For the scientific method to work in a trustworthy way, at least according to the high priests of science etc., you need that.

There are things already about computer studies that give me red flags personally (although I am no scientist/math wizard). The claimed margin of error could be wrong, for one thing. The armies or initial position chosen for each side of a given study could make a hugely underestimated difference. The (2300 FIDE at best!?) engine(s) used have been relatively weak so far, as far as I know - chess endgames take 2700+ human opponent players to play optimally sometimes.

I'm not sure why I should not believe such computer studies in general should be just dismissed as a pile of rubbish, if people more knowledgeable were to insist on rigourous proof for studies being correct at this point in time, if you want to play hardball about publishing standards. Such standards are reserved for scientific journals in the real world anyway, not for hobbyists who do not have (much, if any) money or life and death issues at stake.

More specifically for myself, I already balk at the idea Amazon only =Q+N in value, even on 8x8. As a chess master with the memory of a number of chess world champions' and grandmasters' views, I do not trust that single B merely = N exactly on 8x8 on average. As for Archbishop almost = Chancellor, a bit hard to trust, but that is more alien to my intuition. They both cover 16 nearby cells in a radius of 2 cells, I give you that.

[edit: if you really want, to please/amuse you and others I could always [not just sometimes] put calculations I use for my tentative estimated piece values on Rules Pages Notes - I look at the answers I get and see if my intuition agrees (so far it has, pretty much). I have yet to do such calculations for my most recent large batch of Rules Pages. For what it's worth, sometimes I also borrow some of your rules of thumb, where I lack my own formulae.]

I've edited my previous post, for any who missed that.

Well, from what you say it appears that with 'computer study' you mean statistical data from games that computers played against each other (or themselves). As I would. But as I said, the B = N observation came from the Kaufman study, which was nothing of the sort. He just filtered positions with a B-vs-N imbalance from a huge database of human GM games, selecting those that were the imbalance was stable for some number of moves (to weed out tactics in progress), and counted the number of wins, draws and losses in which these games ended. Which apparently was a 50% score.

It doesn't sound like rocket science to me, but I suppose a complete idiot could bungle even the most simple tasks. And I have met other chess-engine programmers that have done similar things for themselves. (The Kaufman study did not publish more specific things, like how the N or B would do against Rooks, or whether the difference also correlates with the presence of other pieces than Pawns, and some programmers want to make their engines aware of that too, and put a complete table of every conceivable material compustion in their engine.) And they never told me they had proven Kaufman wrong.

The problem is that implying someone is a bungling idiot that even cannot do the simplest thing right, or a fraud who intentionally publishes falsehoods, is a pretty heavy accusation. Most people would hesitate to make such an accusation without having very solid evidence that the published results were indeed wrong. "It was not checked by anyone, so it must be wrong" is not really a valid line of reasoning.

You seem to have a wrong impression of the peer-review system. The 'peers' that are asked to referee a scientific publication will NOT redo the reported work. They only judge whether the described method according to which the results were obtained is a proper procedure. If the claims are in contradiction with earlier results the referees have a hard time. They would at the very least insist that the authors of the new manuscript give an explanation for why their method would be more reliable than what people previously did, and even then they stand a large probability of rejection if that doesn't convince the referees. In a sense everyone is a peer on the internet, and could have contested what others publish there, in particular the Kaufman results. But it didn't happen, and that means much more than when he would just had to fool one or two referees. And there isn't really any need for mathematicians, people that know how to count seem sufficient. You are aware that Larry Kaufman is a GM himself?

I don't really understand your third paragraph, but I am intrigued by the term "more knowledgeable". True knowledge should of course never be dismissed. But what knowledge are you talking about, here?

I agree the Amazon result is suspect; it was only based on a couple of hundred games where the Queen and a Knight where replaced by an Amazon, and the baseline pieces were shuffled to provide more game diversity. That is a very different story than GMs not being able to convert a B-N 'advantage' into a better result in a few thousand games. The remarkable thing about computer games is that it doesn't seem to matter much what the level of play is. Errors tend to cancel out, when both players make them. Even random movers systematically win more games when you give them stronger material. (Although quantitatively they don't make the most of that, as they too easily give the strong material away.)

Rather than describing the calculations in a large number of articles, which is likely to lead to a lot of duplication, you could make a separate article of it. That could lead to a more coherent presentation, and the other pages could then just refer to that.

By more knowledgeable (than me), I mean someone who might have better qualifications for evaluating the sorts of computer studies done both by yourself and Kaufman (his is, naturally, a different type of computer study, if I may call it that). That is, someone who is a mathematician and/or a chess grandmaster, neither of which I am. Even then, Kaufman may qualify, especially if he is the former besides being a GM - however other people with equally good qualifications may disagree. A body of such people, who are known to be interested/paid (to make the evaluations of the studies/results), really, would be needed to build a consensus. I've read online somewhere long ago that some GM tried to explain the result Kaufman got, maybe unconvincingly.

Most of my calculations for estimating piece values are quite short and simple, even if highly suspect to at least some readers. An article on my assortment of quick and dirty methods of calculation (that try to presently provide for a big range of pieces and board sizes/shapes) would not cover all the piece types that are possible, I suppose, and also I have never done a CVP article/item of that sort (perhaps you could for your computer studies method, too, if it would not be too lengthy).

I've edited my last post a bit, for any who missed it.