They do have value, you just don't know what they are.
Help! Why don't fairy chess pieces have values?
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In an attempt to access the papers that are being discussed here (for curiosity), I found some links:
Taylor's paper:
https://www.tandfonline.com/doi/abs/10.1080/14786447608639029
Trice's paper:
https://content.iospress.com/articles/icga-journal/icg27203
These websites charge 50.00 and 27.50 respectively. Based on what I've read here so far, I say that I myself have better purposes for that money.
Anyone on the Discord Server for his variant has access to all of his papers for free.
https://triceschess.com/annotations/80.pdf
Annotated games with a diagram and notes for every move:
http://triceschess.com/annotations/game_notes_01.pdf
http://triceschess.com/annotations/game_notes_02.pdf
http://triceschess.com/annotations/capablanca_problems.pdf
Has it not become common knowledge that a non-royal king is on par a knight in face value. Plus minus a minuscule smidgen
Can anyone name a game where anyone sits down to play with that non-existent king?
Knightmate
Variant where the role of the king and knight is exchanged: players win by checkmating the knight, and the kings are regular pieces subject to capture.
Metamachy was pretty popular on the Jocly server when it still existed, and is frequently played as corresponcence chess on chessvariants.com. It involves a piece called Prince, that moves and captures as King. It also has a strictly forward non-capturing double step, but that cannot check either, so the safe-checking theory predicts a value zero for it.
Regular Shogi involves pieces called the Gold and Silver General, which have a subset of the moves of a King. So the safe checking theory also predicts these have zero value. Shogi players know better... How many people play Shogi? Wasn't that something like 50 million? How does that compare to the number of people that play Trice's Chess? But of course this will be dismissed as totally irrelevant, because most of these Shogi players are Japanese. 
Of course all that talk on how many people use it is the thing that is truly irrelevant, and only brought up as a distraction. Predicting an insane value for a piece that no one ever uses disqualifies a theory just as much as predicting zero value for the Rook.
I chatted with Ed Trice this morning and asked him what he thought of H.G. Muller. Here is his exact words:
“Tell him I said ‘Hello’ from America. Haven’t chatted with him in a while. My opinion of him? He’s brilliant. He’s a physicist as I recall. I thought he worked at CERN at one point in his career. He wrote some chess programs way back when I was still in grade school. Also 10x8 programs that were rated just about 2300 as their 8x8 predecessors. Yeah we disagree about piece weights but we never had ‘battles’ over it like you describe. I like him as a programming comrade and my advice to you is stop arguing with him. He’s helped me with programming ideas more than I helped him, so do me a favor and leave him alone. And simmer down yourself there’s no reason to get upset over stuff like what you described. Play whatever variants you like and don’t engage with people trying to say which variant is better or best or whatever. It doesn’t matter. Remember you’re representing our playing community so your antics and fighting will reflect poorly if you keep it up. So smoke the ‘Peace Pipe’ with H.G. and make sure you tell him I said hello.”
That’s a good enough endorsement for me.
I offer my Peace Pipe to H.G. Sorry I got so upset.
Well, Ed Trice is a wise man. I never worked at CERN, btw; what they do there is another field ('high-energy physics'), with needs experiments so huge that teams consisting of hundreds of people are needed to perform them. I am too much of a maverick for that kind of work. My field was atomic & molecular physics, where you can do experiments with equipment that fits in a room, with just 3 or 4 people. The experiment for which the Nobel prize is now awarded already had an unusually large number of investigators as authors in the paper that reported it; this was because it was a EU-funded cooperation between three laboratories (two French, one Dutch). I and one of my students participated on behalf of the Dutch. And 8 people doesn't sound as crowded as it actually was, as the three authors that had been responsible for the development of the laser we used had mostly completed their work even before we arrived. The laser was set up in a separate room anyway, the beam coming through a small hole in the wall so the visitors from other labs could use it without bringing in dust. Being with five on our part of the experiment allowed us to take shifts in operating the equipment, while we could sent out others to fetch pizza.
Well pizza is strong motivation as a reward mechanism for any experiment so no wonder your lab had good results
I really thought after pushing the pawn from h4 to h5 hitting the chancellor and archbishop simultaneously that I would win this game. My opponent escaped and later won!
Bro thinks a rook is weaker that a bishop
The theory that rook is not exactly 5, maybe there is something to it. I'd rather give 4.8 than 4.75
Nordlandia schreef:
The theory that rook is not exactly 5, maybe there is something to it. I'd rather give 4.8 than 4.75
In the computer games I played the initial value of the Rook indeed was around 4.75 instead of 5. Later I discovered that all orthogonally moving pieces (e.g. Wazir) test below their expected value if you start them on the back rank behind a closed rank of Pawns. But their value increases by a quarter Pawn if you start them between or in front of the Pawns.
I suppose this is related to the 'open file bonus' that some engines award to Rooks that control open files. In the end-game most files are open, or the Rook is already in front of its Pawns. So it seems the open-file bonus becomes an integral part of the Rook's value there.
When we are at it. How much would you estimate the difference between Archbishop in case the archbishop is enhanced by a wazir and the chancellor an ferz.
One of the major drawbacks of these pieces is not full coverage at close range.
Intuitively I would think that the difference goes up. Their common moves are now N+K, and both the remaining part of the Rook-like and Bishop-like slide cause 8 more orthogonal contacts. So the fact remains that Rook moves are worth more than Bishop moves (probably also because the former make orthogonal contacts).
I did test RF (7) and BW (5.25), and these have about the same difference as R and B.
I guess chess.com takes the compound value
In that case they could checkmate a king by themselves
Letchworthshire schreef:
"I meant 0 papers published about chess values.
Taylor has 1 paper published on piece values.
Trice has 1 paper published on piece values.
Yet you belittle both of them.
Why?
"
Why? Because the presented theory predicts an obviously wrong value for the non-royal King, (namely 0), of course. Not to mention all the Shogi Generals...
Nothing personal. But having a publication in a peer-reviewed journal is not the same as elevation to sainthood. Such publications merely serve to present your experimental results or theoretical ideas to the scientific community, so they get the opportunity to criticise or corroborate those, and in the end consensus will be reached on what is the truth. The peer review is supposed to weed out the biggest nonsense, but it is far from fail-proof. Especially if there only is one referee. (For prestigeous journals like Science there are three, which are not only supposed to assess the scientific soundness, but also the importance, and if only one is not happy the paper is rejected.) Experimental results cannot be verified, and implications of a theory other than what the authors mention might escape their attention. Referees are not expected to completely duplicate the research effort; they just glance at the paper, judge originality, and are prepared to accept claims that are not obviously contradicting known facts on good faith.
Some referees scrutinize submissions better than others; Trice was lucky they did not send the paper to me for refereeing. (Yes, I have refereed papers for the ICGA Journal!) It probably would have been rejected, if he had not been able to adapt it such as to get a plausible value for the non-royal King.
Of course 'luck' in this case is a dubious asset; if a referee allows you to present nonsense to the community, the community will act as thousands of additional referees, and some of those are bound to recognize the flaws, and expose them in public. Journals like Physical Review Letters even have a special 'Comments' section where they publish criticism on papers they published before (again refereed for validity, of course).
The save checking theory is rather primitive by modern standards (now that far more complex calculations can be done with the aid of computers in a matter of seconds), but for 1876 it was probably 'state of the art'. I already pointed out most of the effects it does not account for, and those for which it does account in a wrong way (i.e. the safe checks). That it was published doesn't make these flaws disappear, and does not make it immune for criticism.
I can very easily write a paper about piece values, e.g. about the algorithm of the Interactive Diagram guestimates them. This does take into account most of the effects I mentioned, so it is a far more refined algorithm than Taylor's or Trice's, and would thus be considered sufficiently novel to warrant publication. (It also gets too low an Archbishop value, b.t.w.) The referee would very likely not reject it, as it never predicts obviously wrong values like zero. Even if you were to be the referee, arguments for rejecting it as you presented here so far (such as "You should not publish this, because I beat a chess program this author once wrote") would fall on deaf ears with the editors, after they had a big laugh. But why should I? No one is interested in piece values anymore; all strong chess engines use trained neural networks for evaluation nowadays. How many citations did the Trice paper get?