Comments/Ratings for a Single Item

Short-range pieces go down in value compared to sliders, but Chieftain Chess has mostly (only) short-range pieces. Which suffer similarly. The orthodox Knight isn't so hot on 16x12 either. Speed no doubt is an asset in games with conventional Pawns, as it increases the area from which you are able to stop a passer. The Knight is better at that than the Man. OTOH, when a Man catches up with a passer, it annihilates it. A Knight can only stop its advance, remaining bound to doing so forever.

Of course having other types of Pawns would totally upset these evaluations. E.g. with Metamachy Pawns, which can always move 2 steps ahead, a Man would be pretty inept at stopping them, greatly affecting the relative value of Knight and Man.

As to the Pawn definition: Part of the problem is that 'Pawns' are a family rather than a class of pieces. In Berolina Chess the Berolina Pawns obviously are Pawns. So when they appear in another variant as 'guest pieces' in low numbers, we still think of them as Pawns. In Mini-Shogi you only start with a single Pawn. But no one doubts it is a Pawn, because it is the same piece as in regular Shogi, where you start with 9. I wouldn't call a 'Steward' a Pawn, especially not when you start with only two, embedded in the Pawn rank. It is just a weak piece, and starting on the Pawn rank IMO doesn't have any significance. It is weak enough to fit my definition, though, in a variant where you started with many of them. The Cavalier already is more worrisome, although a Mao is only worth half a Knight in a FIDE context. But part of the value of a FIDE Pawn (some 40%) comes from its ability to promote, and a Mao would promote much more easily. A Horseman should still be pretty weak; it adds a quarter non-capturing Knight to a normal Pawn.

Some other examples:

Cavalier in Grand Cavalier Chess

Horseman in Wildebeast9

Fwiw, I had calculated a really low value for a single Guard (Man) on a 16x12 Board (1.33 chess pawns), and 2.31 for a Knight for that board size, for example (with the other pieces being of even greater value), though as usual my ways of calculating values are primitive/suspect, for some/many people I suspect. :) Naturally though, for a given board size, 2 or more Guards would be worth more than (2+)x the value of a single guard.

Ooops, sorry, yes, same thing

I would hesitate to qualify the Man in Chieftain Chess as a Pawn. It is more equal in value to the other pieces than to their value difference. But it is certainly true that you start with very many of them. Accepting that it would be Pawn is tantamount to dropping any requirement on value, and consider their large number the only defining characteristic.

I'd note it's possible that a Guard (Man) might qualify for at least some people as both as a major piece and as a 'pawn' (if it is used numerously in the armies in the setup of a given CV, as in the case of the Chieftain Chess CV invented by Joe Joyce that I linked to earlier in this thread).

https://www.chessvariants.com/rules/chieftain-chess

Regarding the table I created on the 27th of December last year, I actually agree with Mr. Pacey's suggestion about me classifying the rook as 'light'. I think that that the class of 'light major', should be occupied by the gold general and the mann, whilst the rook moves up to the category of 'medium major'.

I posted the following link earlier, in case you missed it, which comes close: Maos (instead of Knights) as promotable 'pawns' (not able to promote to Amazons, though):

https://www.chessvariants.com/dpieces.dir/cavalier/index.html

This is probably a question that can be solved by philosophes. Just for fun. A chess variant where all pawns would be replaced by knights. Knights that can be promoted to an Amazon. Possible no? Maybe better on a large board. OK. Then, is the Knight a Pawn?

I would define a Pawn as a piece of which you start with many, and has a value so low that they act merely as 'change' when other pieces of unequal type are traded.

Irreversibility or promotability IMO are not requirements. E.g. when a chess variant fills the second rank of the setup with pieces that move and capture like an inverted Y (fWbF), I think most people would consider those 'Pawns'.

Large Shogi variants tend to have multiple piece types of very low value. (But the Asian Pawn is significantly weaker than a Shatranj Pawn too.) E.g. a Shogi Knight (fN), Stone General (fF), or Go-Between (vW). People don't consider those Pawns, though, (even though they of course all promote in Shogi, and the first two are irreversible), because you only start with a pair of them.

That's a very good try at a definition, H.G.

I'd thought of something similar, in that I gave great weight to 'pawns' (in the context of a given CV) being most numerous in the setup of that given CV. Then I recalled Napoleonic Chess, which used a small number of Steward Pawns and a (only relatively) small number of Berolina Pawns, on top of the more numerous type of pawns, for each side's army.

I'd note that I haven't seen Steward Pawns as the most numerous piece type in any CV I've seen so far, unlike for Berolina Pawns.

Napoleonic Chess is the reason why I tried using a tentative definition of a 'pawn' being either numerous AND/OR promotable. Promotability being included as a criteria would allow for Napoleonic Chess, except I then thought, what if in Napoleonic Chess the Steward Pawns were replaced by Ultima Pawns (also known as Pincer Pawn), which are not promotable (on top of that there is shogi, e.g. with its small number of promotable knights)? So, I'm afraid we both might still be at square one when it comes to defining what a CV 'pawn' is. Unless, in the context of Napoleonic Chess alone, you wouldn't consider Steward or Berolina types as 'pawns' for that particular CV.

https://www.chessvariants.com/large.dir/contest/napoleonic.html

https://www.chessvariants.com/play/pbm/play.php?game%3DNapoleonic+Chess%26settings%3DNormal

I would define a Pawn as a piece of which you start with many, and has a value so low that they act merely as 'change' when other pieces of unequal type are traded.

Irreversibility or promotability IMO are not requirements. E.g. when a chess variant fills the second rank of the setup with pieces that move and capture like an inverted Y (fWbF), I think most people would consider those 'Pawns'.

Large Shogi variants tend to have multiple piece types of very low value. (But the Asian Pawn is significantly weaker than a Shatranj Pawn too.) E.g. a Shogi Knight (fN), Stone General (fF), or Go-Between (vW). People don't consider those Pawns, though, (even though they of course all promote in Shogi, and the first two are irreversible), because you only start with a pair of them.

That's a good idea to abandon absolutes in this case, H.G.

I'm wondering if there might also be an approach that abandons absolutes when it comes to declaring what a fairy chess 'pawn' class might be. I'm rather stumped on how define such a class, with or without absolutes. Perhaps it is a hopeless task, in that a given CV can use a piece as a fairy chess non-pawn or 'pawn' depending on the setup that is selected by the inventor for the CV, for example (e.g. Joe Joyce's Chieftain Chess uses guards numerously in the setup).

There might be endless criteria for what could qualify as a fairy chess 'pawn', though somehow I doubt that should be the case. Have you given much thought to what might be classed as a fairy chess 'pawn'?

The case of a Rook on a circular board is similar to a Silver General on a rectangular board: there are virtually no forced wins, and the few that exist are very short. If one would consider such piece 'major' for that reason, then 'major' basically becomes a useless concept. The only reason for distinguishing majors from minors in chess theory is to imply the prospects of winning the game. That there could be an extremely small number of exceptions (which are even less likely to occur in practice than their number suggests) is not very important. Checkmating a bare King is not the only concern inchess (variants). One also wants to recognize more complex elementary wins, e.g. 2 minors vs bare King, or a strong major vs a much weaker defender, such as Queen vs Rook. The latter is generally won, but there are some draws, where the Rook can deliver a perpetual, and you cannot escape it without losing the Queen.

So a more practical approach would be to abandon absolutism, and allow a small number of exceptions (say a few percent of the positions). The Rook on a circular / cylinder board then is a minor, the Woody Rook on 8x8 a major. Just a slightly imperfect one.

For cases that are really intermediate, such as the Evil Wolf, (or in fact the orthodox Pawn), we must admit that they are neither major nor minor, and that the winning prospects cannot be judged by material balance alone.

@ H.G.:

I had thought I could transfer what it means for a piece to be a major one in orthodox chess to games of chess variants in general, but in light of your previous post in this thread about fortress draws, with at least some types of fairy pieces, being possible, I'll have to change my mind, if I hope to find a relatively simple and clear definition of what a major piece is for the field of chess variants in general.

Your notion (expressed elsewhere) of 'mating potential' (which I more or less understand, I think, without fully expressing it in words) might seem to do the trick, i.e. let's try saying a piece type would be a major one if it (a priori) has (any) mating potential (that is, for the situation of the single piece + K vs. lone K).

Then, even though the percent of mates a Silver General can deliver that you gave is a low percentage, since it (a priori) has mating potential, it might be considered a major piece, after all - nice if we want to have a simple and clear definition of what is a major piece.

There are still possible problems, though. A rook (kind of?) has mating potential on a Circular Chess board, even, but it only can (quickly) deliver mate in a very low number of kinds of positions that are generally unforceable. Might we still consider it a major piece on a circular board since it has mating potential, even though it forces mate in a very tiny percentage of cases? If not, what might an (arbitrary) cutoff percentage for a given piece type be that should not be considered major (for a given board size and shape, I should have noted from the start)?

So, you are right. The Gold is a major piece, at least on normal boards.

OK, so we agree that the only issue is fortress draws, where you can avoid loss of the piece indefinitely, but cannot make any progress towards a win. The Woody Rook (WD) has that problem:

In this position it is 'dynamically trapped' in the corner by the bare King, which will approach along the diagonal and eventually capture it when it stays stationary. And it can stay on the same diagonal as the WD (without approaching) when the latter moves, to renew the threat. Yet 96.9% of all positions with the strong side to move is a forced win. (The Checkmating Applet reports 70.6% wins when the bare King has the first move, but the remaining 29% includes all positions where that first move captures a King or unprotected Woody Rook.) So althoug the possibility to hang on to the WD doesn't guarantee a win, it is still useful to think of the WD as a major piece, as it is really exceptional that it cannot force mate.

This would be quite different for the Evil Wolf from the large Shogi variants, which is a Gold without the backward step (fsWfF). If the bare King can get behind that, it is safe. Still 16.7% of the positions where the bare King has the move are forced wins. In practical games the bare King would likely be close to its own back rank, and you would avoid frivolously advancing an unidirectional piece like the Evil Wolf, and tend to assign it a defensive function in your own camp. So in practice K + EW might still almost always be a forced win. In any case it would be quite wrong to think of the Evil Wolf as a minor.

Although a Silver can force mate in 4 in some postions, these make up less than 0.1%. So considering the Silver a minor seems quite justified.

I should also note that the value of short range pieces (and thus possibly their classification as medium or light pieces) decreases on larger board sizes. Debatably, I think the numerical value of a (single) Guard can be drastically lower on a very large board size, e.g. on 16x12.

@ H.G.:

I'd initially (and carelessly/quickly) thought that if the (lone) K can make it to (or starts on) the first rank of the side with the Gold, then the side with the Gold cannot force mate with the help of its K, as the Gold can only make one (orthogonal) step in its rear direction. However, I now realize the Gold can simply move to its first rank, and then move sideways to check the lone K sideways. So, you are right. The Gold is a major piece, at least on normal boards.

How do you define 'forced captured', then? I would say the only problem with a Gold general is that in a minority of the positions the bare King can force its capture. It doesn't always capture it on the first move, though.

This is a bit different for the Woody Rook. With that, there exist fortress draws, where the bare King cannot force its capture, but can perpetually chase it with the threat of capture.

But I agree that there is a spectrum between major and minor, depending on the fraction of won positions. We should laso take into account that a large fraction of the possible positions is unnatural; we tend to keep our pieces in safe places. So in practice the important thing might be whether a piece can always force mate when it starts protected by its own King.

On the idea of the distinction between major/minor/pawn and heavy/middle/light, here is a diagram.

	Heavy	Middle	Light
Major	Amazon	Queen	Rook
Minor	Nightrider	Knight	Ferz
Pawn	N/A	Sergeant	Berolina

Interesting table, Leon. It works for normal-sized square or rectangular board shapes (although I'd be shy about calling a rook a light piece myself - a Guard would qualify better), which is what most CVs are played on. However, I'd note that for Circular Chess, a lone rook cannot normally force mate. Also, on board sizes greater than 12x12, H.G. has discovered that a Champion cannot force mate, whereas on smaller square/rectangular boards it can. Also, editor Joe Joyce has used the Guard (Man) piece type numerously (like a pawn in all but name) in at least one of his CVs, and it is a major piece normally (e.g. even on 16x12). It also goes without saying that the mate must be delivered in less than e.g. 50 moves, if that's even possible for the given board size and exact position.

https://www.chessvariants.com/piececlopedia.dir/man.html

https://en.wikipedia.org/wiki/Circular_chess#Theory

https://www.chessvariants.com/piececlopedia.dir/champion.html

https://www.chessvariants.com/rules/chieftain-chess

@ H.G.: For a given board size and shape, I would count a piece type as a major piece only if it can deliver mate absolutely all of the time (with the exception that the piece cannot be forced-captured by the lone K right off the mark). In the case of a Gold General this does not apply. Just to be clear, we are talking about games that do not use drops (or other such special rules, possibly).

It seems undesirable that the meaning of heavy / light depends on other properties (such as mating potential).

How would you claasify a Gold General? It is worth less than a Knight, but still has mating portential. And you can even take away its step to the right, without spoiling the mating potential. While with only 5 moves it is hardly worth more than a Ferz. Especially if you invert it, so that most moves go backward.

On the idea of the distinction between major/minor/pawn and heavy/middle/light, here is a diagram.

It is just as valid and unambiguous in orthodox Chess. Which, after all, is just one particular chess variant. The only peculiarity is that 'heavy major' and 'light minor' there are tautologies.

Just like 'promotable piece' and Pawn are the same in orthodox Chess, but not in Shogi.

Well, it doesn't reallly matter which terms you use to classify these independent aspects of pieces. In orthodox Chess they will always be synonyms, as the Bishop and Knight fall in one group, and the Queen and Rook in the other. Weak and Strong can also be used interchangeably with major and minor. The point is that it is different in chess variants, so what will be synonyms for orthodox Chess, can describe entirely different concepts in variants.

I'd note that using 'strong minor piece' or 'weak major piece', as I did, might be seen as removing ambiguity over what is meant. However, if one prefers to use just one word/aspect, instead of two, then using 'heavy piece' and 'light piece' (rather than being 'more specific', or in other words have more categories, e.g. using heavy minor piece, light major piece, or heavy major piece, for example) might be seen as also unambiguous, as long as it's agreed by [ideally standard] convention that this is in the context of chess variants, rather than for orthodox chess.

Regarding terminology, I have seen, for orthodox chess, 'heavy' and 'light' used interchangeably with 'major' and 'minor'.

Well, it doesn't reallly matter which terms you use to classify these independent aspects of pieces. In orthodox Chess they will always be synonyms, as the Bishop and Knight fall in one group, and the Queen and Rook in the other. Weak and Strong can also be used interchangeably with major and minor. The point is that it is different in chess variants, so what will be synonyms for orthodox Chess, can describe entirely different concepts in variants.

@Jean-Louis: I know that in Xiangqi a Rook slaughters two Cannons. Piece values tend to be dominated by their end-game values, and the value of a Cannon dwindles spectacularly to nothing as the board empties. The Interactive Diagram estimates the value of a Cannon on 8x8 as less than a Knight. I think that is a lot more realistic than Zillions. (You can see all the estimates by clicking on the header of the 'move' column in the piece table of the Play-Test Applet.)

HG, do you think that a Cannon in a different context than XQ and its special board, for instance in Shako, can be worth than that? I wonder.

Zillions (I know that you don't like their estimate, and you're probably right) is estimating the Cannon just slightly below the Rook, and the Vao just below the Bishop. I also think this is overestimating. But how far?

In Shako or in Metamachy, the Cannon are still powerful pieces putting a lot of pressure on the columns they control.

@ H.G.:

Good job on the fortress position with the Amazon.

Regarding terminology, I have seen, for orthodox chess, 'heavy' and 'light' used interchangeably with 'major' and 'minor'. So, perhaps my initial suggestion of using 'strong' and 'weak' (i.e. instead of 'heavy' and 'light') in the case of strong minor pieces, and weak major pieces, would create less confusion for chess players who are transferring over to the world of chess variants.

In the following position (White should be able to obtain it, I'd guess), Black to move loses.

Well, I was just relaying what I heard from someone I trusted. The EGT builder did not resolve the issue, as with Queen (and white to move) it already 99% of the positions are wins; it is apparently very hard to reach the fortress position before you are slaughtered. So I configured Fairy-Max to use an Amazon instead of a Queen, and fed it the position you indicate. I even made a special version of Fairy-Max that doesn't use null moves, to make sure it would not miss any zugzwangs.

It was not impressed... It plays 1... Ng6!, and after 2. Zxg6? it would be stalemate! The score doesn't go up from the initial evaluation (based on the material advantage), no matter how deep I let it search.

So I guess my trust was justified. The fortress is a bit more elaborate (i.e. must use more positions) than against a Queen, but it does not crumble.

Then you are just using wrong terminology, confusing major / minor with heavy / light. A Cannon is a quite weak piece, BTW. In Xiangqi it is initially worth more than a Horse, but due to the inability to jump a Horse is worth only half a Knight. And a Cannon is certainly not worth 2 Horses, in Xiangqi.

I actually disagree with my previous idea that on the ability for forcing checkmates. Whilst it is useful for looking at pieces that are the compounds of regular chess pieces, such as the princess, empress, amazon and queen as well as basic (1,1) or (1,0) riders, other, more 'exotic' pieces need a different classification system. The mann and the gold general are pieces I would call minor, despite their ability to force checkmate in a piece + k v. k (simplified endings), as they can only move to squares that are orthogonally or diagonally adjacent. The cannon (or pao) is a major piece though, despite its inability to force mate in an simplified ending, due to its mobility and ability to attack far away squares from behind a wall of pawns, which is also why the nightrider is major.

@ H.G.:

Regarding the K+Q vs. K+B+N fortress position, are you sure an Amazon can be substituted for a Q and the result still should be a draw? In the following position (White should be able to obtain it, I'd guess), Black to move loses. If White only had a queen Black could retreat his bishop into the corner in the diagram, but with an Amazon, White mates with 2.Amazon-h6#:

I edited my last post in this thread a bit extensively, for any who missed it.

On a seperate issue, I was going to suggest that a Pawn in chess variants might be defined as a usually (fairly weak, slow-moving [along a straight line], and) numerically common piece and/or that can promote. Already with Shogi there are many pieces that can promote (besides Shogi pawns), including some pretty weak ones (such as a Shogi knight). To be honest, I'm not sure how to define a class of 'pawns' in chess variants, except that everyone seems to know a pawn when they see one. :) Perhaps having at least one of the above-mentioned qualities usually suffices, but then again some game(s) may include only one or two units of an otherwise atypical type of 'pawn' in its setup, possibly borrowed from other game(s) that use it more. I haven't seen many games yet where a pawn starts on the first 'rank' of an army; one not-so-obvious function of pawns in the setup of many games is to help initially obstruct the more mobile/powerful units of each army from immediately capturing or harassing one another in some way.

Nonetheless, numerical commonness and/or promoting ability would perhaps be most indicative of being pawn-like; I'd note that in some variants, pawns may have the option of remaining pawns without promoting even upon reaching a promotion rank, and even if they no longer can legally move - this idea was once debated for inclusion in orthodox chess, as in certain rare cases a stalemate might result the next move if a pawn didn't have to promote upon reaching the 8th rank(!).

https://en.wikipedia.org/wiki/Promotion_(chess)#History_of_the_rule

In the following game (Cavalier Chess), non-leaping Ns (commonly known as Chinese Chess Ns, or Maos) are used instead of multiple pawns in the setup, and by the game's rules specially given the ability to promote (compulsory) upon reaching the last rank, and the new piece selected depends on which file on the 8th rank the promoting piece reached - perhaps a border-line case of pieces that at least some might consider to be pawns:

https://www.chessvariants.com/dpieces.dir/cavalier/index.html

Some types of 'pawns' don't have the ability to promote, even, and can possibly make long-distance moves, too. In the following game (Ultima), the 'pawns' are also known as 'pincer pawns' - at least in this game they are the most numerous type of piece in the setup, and move along a straight line (some other game[s], such as Latrunculi XXI, refer to the piece type by another name - it's as a soldier in that game, which starts all of them on the first rank of the setup incidentally[!] - although there are some special rules that make soldiers' capturing abilities at times somewhat greater than in the case of the simpler rules used for Ultima pawns):

https://www.chessvariants.com/other.dir/ultima.html

https://www.chessvariants.com/rules/latrunculi-petteia-xxi

I saw last night that Wikipedia's entry for [orthodox] chess terms distinguishes a major from a minor piece in chess in that a major piece+K can force mate vs. lone K (both a R and Q can do so in under 50 moves in the case of chess, I'd add) - a definition I was aware of already for majors/minors in chess.

https://en.wikipedia.org/wiki/Glossary_of_chess#M

A fortress draw is a position where the superficially much stronger side can make no progress towards a win, even though there is no threat of him losing anything. E.g. in KQKBN there is the following fortress (which would even hold up to an Amazon):

I guess the simplest fortress is the KPK defense:

just asking but what's a fortress draw

There is a discussion on the meaning of major / minor in the article of the Checkmating Applet for 2 vs 1 checkmates. Pretty much the same as what you say here. Note that the checkmate must be forcible from the majority of the possible positions; help-mates don't count. So the Silver General (FfW) is a minor, even though there are checkmate positions because it attacks two orthogonally adjacent squares. The Gold General van force checkmate on 8x8, but in a minority of the positions KGK is still a draw, when the bare King can attack the Gold from its 'blind side', and drive it to the edge that way. This can be seen as 'deep tactics' that lose the the piece; of course any position where a piece X is forcibly lost isn't really a K+X vs K end-game, and should be excluded from the statistics.

More tricky is the case where there is a fortress draw. such as with the Dragon Fly vRsD on 8x8. There is a 'safe edge' there which the piece cannot cover. If the bare King can reach that, the game is a draw, even though you still have the Dragon Fly. If you can cut off the bare King from that edge, you can force checkmate. So this is an intermediate case ('medior'?).

I tend to use the term 'super-piece' for Queen-class pieces.

Sorry, I have just noticed that my idea on minor/major distinction is the same as yours, Mr. Pacey.

Thank you Mr. Pacey. My own personal system for classifying pieces works in this way: if you had only that piece (with no promoting) and a king, would you be able to force checkmate against a lone king, and if you could then it is a major piece, if not it would be a minor piece. Under this classification, a man is a major piece, whilst the nightrider is a minor piece. (On the subject of nightriders I think that a nightrider/rose compound and a piece I call the 'fusilier' (which is to the nightrider as the cannon is to thee rook) are interesting ideas.

I cannot seem to edit my last post, and then at that point post it, right now (I can edit & then post this present post, though[!]).

edit: the problem went away somehow when I tried shorter words - weird...

I should have mentioned that the distinction between major and minor pieces in chess variants is not always clear-cut. In chess a major piece (R or Q) is a piece that when aided just by the K can mate a lone K. In the case of fairy pieces, some such pieces could have the numerical value of at least a rook, but do not have mating potential, like a rook does in chess - an example would be a Nightrider piece (NN). Perhaps a NN should be called a strong minor piece. On the other hand, some fairy pieces that could have the numerical value of a chess minor piece (B or N) happen to have mating potential, like a rook does - an example would be a Dabbabah-Wazir compound piece (a Q is an example of a compound piece, acting as R or B). The DW compound piece was called a 'Woody Rook' by Ralph Betza, when he included it in his classic game Chess With Different Armies (CWDA for short). Perhaps a DW should be called a weak major piece. Finally, I'd note that the Amazon fairy piece (QN compound piece) is so powerful in terms of mating potential that she can mate a lone K all by herself, without the help of her K.

One term that I have seen used, at least informally(?) is 'superpiece'. An Amazon or a Q would definitely qualify, but I personally do not yet know if a R or even a NN would qualify (I'd guess not in both cases). One last thing: I have seen K and Q referred to as the royal pieces in chess, but in chess variant terms that is incorrect - the K is the (usually sole) Royal piece in many chess-like games, as in such a winning goal is to checkmate a Royal piece. However, games like Anti-King Chess, where both sides have a K and Anti-King, can mess with this otherwise tidy view of things.

https://www.chessvariants.com/piececlopedia.dir/knightrider.html

https://www.chessvariants.com/piececlopedia.dir/dabbabah.html

https://www.chessvariants.com/piececlopedia.dir/wazir.html

https://www.chessvariants.com/piececlopedia.dir/amazon.html

https://www.chessvariants.com/unequal.dir/cwda.html

https://www.chessvariants.com/diffobjective.dir/anti-king-chess.html

I've added to my last post with edits, for any who missed those.

Estimating fairy piece values is a major topic for chess variant players and theoreticians alike; it would be hard to play a chess variant game well without knowing/guessing what kind of trade(s) are more or less okay to make from a materialistic point of view alone.

Some people have tried to develop formulae to make estimates that would apply well to even a large number of board sizes and/or shapes. Special rules for some chess variants can make estimating piece values even harder than usual. For rectangular/square boards especially, there have also been efforts made to statistically analyse the results of engine vs. engine games with fairy pieces included in one or both armies (if two sides play, as usually the case). Personally I take even such more scientific efforts with a grain of salt, e.g. the composition and/or initial setup of the armies can affect the results somewhat, just maybe. However, I am not a thought-leader on such a statistical approach. :) Here's is a link to one effort to estimate piece values, by someone who made a big contribution to the development of chess variants (this can also be taken with a grain of salt, as formulae are not foolproof):

https://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values.html

Incidentally, even the values for chess are not completely agreed upon. Some such as myself use Euwe's values of P=1, N=B=3.5, R=5.5, Q=10 on 8x8; however, 2 Bishops are generally worth a bit more than two Ns (or N and B), and almost all chess Grandmasters still slightly prefer a lone B to a lone N on average - to express that, I personally change N to be something like = 3.49, if I tried to be more exact (but still it's a guess). Once again, computer statistical work has been tried with chess piece values (this time using games of pretty strong human players), and curiously finds N=B exactly (though I don't know what's thought the margin of error).

For what it's worth, here's the wiki on fairy pieces, which among other things mentions classification:

https://en.wikipedia.org/wiki/Fairy_chess_piece

Classification is a thankless task to attempt, as the list just grows... Here's one (by no means complete) attempt on this website:

https://www.chessvariants.com/piececlopedia.dir/taxonomy.html

So, everyone knows the piece values of orthodox chess, okay. 1 for a pawn, 3 for a knight and for a bishop, 5 for a rook and 9 for a queen. But what about the values of FAIRY chess pieces? And are they major, minor, royal or pawn? And why?