Comments/Ratings for a Single Item

@ 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.

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.

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.

@ 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)?

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.

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'?

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.

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

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 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

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'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

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.

Ooops, sorry, yes, same thing

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.

Some other examples:

Cavalier in Grand Cavalier Chess

Horseman in Wildebeast9

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.

One possible way to find out if a piece was a member of the pawn family, is to imagine if they would look down at other pawns at dinner e.g. Berolina Pawn: Hey, FIDE Pawn, it sure is nice to see you. FIDE Pawn: Yeah, nice to see you too. Metamarchy Pawn: (sprints up to them) Hi you two, how's it going. FIDE Pawn: Alright, thanks- Mann: OUT OF MY WAY WEAKLINGS! (All pawns silently glare at Mann)