Shatranj with Different Armies. Possibly a worthwhile idea... Only possibly, since Shatranj is such a bad game. I will digest this more and post further thoughts, but my first observation is that "The Japanese Jostlers" show a different icon for the Pawn, although the text claims it isn't a Shogi Pawn. Please clarify. Furthermore, I think Shatranj with Different Armies should follow CwDA in the core tenant that the Pawns and Kings don't change between armies. If you have armies with wild pawns, to me that is not "Shatranj with Different Armies" but something else.

The Checkmating Applet cannot do bent riders like Osprey. But it can do a truncated leaping version, like DC. And a pair of these does have mating potential, on 10x10. In the theory of 3-vs-1 mates discussed on the Applet page the Osprey would classify as 'potent', since it can switch its attack from c1 to a1 in a singly move (e.g. f2-f4 or f2-d2). This means it can execute mates in combination with almost anything else that is not bound to the same color.

In fact an Osprey can drive a bare King into a corner together with almost anything on any size board: positioned on an edge it can dynamically confine a King in a corner with the help of its own King. With moves to spare, which can be used to invoke the additional piece.

The observations that certain pieces become effectively neutral in color on petrification, and that a petrified Go Away is identical to a Mummy, are almost true. However, if one were to actually make such reductions during play, information would be lost as far as counting repetitions of positions goes.

Unrelated but worth mentioning while I'm here: in my Nemoroth implementation, there are really two Leaf Pile piece types, normal and "digesting." A normal Leaf Pile becomes a digesting Leaf Pile upon engulfing a piece, and a digesting Leaf Pile reverts back to normal when it moves of its own accord (i.e. not as a result of a Go Away's scream). It's rather important to keep track of this state, or you won't remember whether the Leaf Pile is supposed to leave behind a Mummy. This is an unfortunate omission from the otherwise fine scheme in the "Nemoroth Notation" article by John Lawson -- I would suggest using a "d" prefix to indicate digestion, such as in "dL."

Indeed, the digestion is most conveniently indicated through changing the piece type to a visibly different one. It is no crime in chess variants to have invisible game state (e.g. castling rights in orthodox Chess), but I think this would just invite errors in the Leaf Pile case.

It is true that 'collapsing' game-theoretically identical piece types into one would affect the repetition rule. But this seems an advantage rather than a disadvantage. What would be the use of prolonging play by allowing another set of repetitions of game states that are considered artificially different (e.g. because two Mummies got swapped)? In the end repeating the sequence of moves will swap the pieces back, with the same result. In my experience pieces almost never get swapped in games without drops. (Jocly considers pieces of the same type distinguishable when testing for repetitions, in deviation of FIDE rules, and it only started to cause problems when I implemented Shogi variants.)

BTW, I am pondering about how to make a more compact description of the rules of this excellent game. A formulation that seems to go a long way would be:

Pieces can change location either by 'Moving', or by being pushed (by a Go Away). In general, Moving is only allowed to empty, unpolluted squares. But there is no restriction on squares pieces can be pushed to; the pushed pieces will coexist there with any previous occupants. Exceptions are the Zombie (which can Move to any square, and then destroys all pieces that were there before), and the Leaf Pile (which can Move to unpolluted squares containing only mobile pieces). Zombies cannot coexist with Ichor, and the two agents destroy each other. Leaf Piles digest all pieces that try to coexist with them; when two Leaf Piles meet the stationary one is digested. Removal of pieces due to failure to coexist happens automatically at the end of any turn.

About the UI issues with Go-Away pushing order: wouldn't it be a natural interface to highlight all adjacent pieces after ordering a push by clicking the Go Away twice (as already has to be done now), and then allow the user to 'click them away' one by one?

And some thoughts about compulsion:

Replacing a Ghast compulsion by a lesser one (at greater distance) was explicity declared to be legal. The other two types of compulsion do not exist in grades. (Although they could, depending on the age of the Ichor or the number of pieces in a crowded square.) It was not specified whether it was legal to replace one type of compulsion by another. E.g. when a piece is pushed from an ichorous square onto a Ghast square, is the compulsion addressed? And when the reverse happens? What if a piece gets pushed to an ichorous Ghast square? Can you resolve that by pushing it to an empty square closer to the Ghast? Or would you have to address all pre-existing compulsions on the same piece simultaneously?

I would be inclined to require that, with the exception of getting a lesser Ghast compulsion, the piece should be free of all compulsions after the move in order to count that move as legal.

It's clear that the rules of compulsion as laid out here are not quite formal. I took my own stab at interpreting them on the itch.io page that I linked. To summarize my interpretation:

• Every compulsion defines conditions under which it is satisfied.
• Multiple occupancy compulsion is satisfied by moving off or destroying the piece entirely (plus some edge cases).
• Ichor compulsion is satisfied by moving off, being pushed to a non-ichorous square, or destroying the piece entirely (plus some edge cases).
• Ghast compulsion is satisfied by fleeing, being pushed further from the Ghast, destroying the Ghast, or destroying the piece (plus some edge cases).
• If it's your turn and one of your pieces is compelled, you must make a legal move that satisfies at least one of your pieces' compulsions.
• There is nothing wrong with adding new compulsions to your pieces, although this is only possible with either a Go Away's push or by a Wounded Fiend leaving a square containing another one of your pieces.

While typing this up I realized that there are a few omissions in my edge cases, which I will rectify when I get a chance. It really is tough to enumerate all the cases!

It strikes me as a bit inconsistent that an Ichor compulsion would not count as resolved when you push the piece onto other Ichor, while it would count as twice resolved when you push it onto a Ghast square, and then back onto the same Ichor. Of course there is a clear precedent in that you don't have to completely resolve Ghast compulsion in a single move, but there at least the severity must decrease. It would be more consistent to require all types of compulsions on the same piece to be lessened. (Which for Ichor and crowdedness would mean these have to entirely disappear.)

But perhaps this is completely moot, because players would try to avoid compelling their own pieces very strongly, even when it is not required by the rules. Still, requiring more thorough resolution of compulsion would make it easier to checkmate. I don't know if that is good or bad, though.

Fundamentally, the problem we're encountering is that Betza never gave an example of what happens when a piece is under multiple different types of compulsion. Your interpretation requires all types of compulsion to be satisfied simultaneously to count as a saving move for a piece, while my interpretation (and the one currently implemented in the Web game) requires just one type of compulsion to be satisfied.

Your example doesn't seem particularly inconsistent to me, by the way, but maybe because I'm just used to playing by my interpretation of the rules for all these years.

There is nothing 'unknown' about the set of prime numbers; it is in fact very well known that there is no such thing as a 'complete' set of them, as the set is infinite. There exist simple (albeit inefficient) algorithms to determine for any given number whether it is prime or not.

It is also a misconception that the presence of a Huygens would make a game unsolvable due to the properties of primes or any other of its properties. E.g. it is very easy to prove a game with a starting position of King + 2 Queens vs King + Huygens on an infinite board is won for the Queens. It is even possible to give a detailed algorithm for how to do this, in a number of moves that only grows logarithmically with the distance between the Huygens and the Kings. If the Huygens has the first move, this number can of course be made arbitrarily large, by moving the Huygens far away after it runs out of safe checks (because the King approached it).

All this would still be true if the Huygens was a Rook, rather than a subset of it.

I think this is unlikely. I have never seen the Edo-era description of Tenjiku Shogi, but I do know how such descriptions looked in general. They basically showed a drawing of the initial position, where each square contained a drawing of the way the piece moved, with the kanji of the piece name in the center. Sliding moves would just be radial lines, and it would be immediately clear whether the Lion Hawk also had orthogonal slides.

Only complex moves, such as the Lion, would not be obvious from the drawing, and would be described by an additional line of text. I once have seen the picture for the Teaching King (a piece from Maka Dai Dai Shogi); it had lines in 8 directions, each with 3 perpendicular line segments crossing it for indicating the multi-captures of teh Lion Dog. (And the text line then said it would move like Queen or Lion Dog.)

It appears the CVP website has been switched from http to https. Since the piece images are on my own website, which is http, the browser now refuses to display them.

In this case I can easily fix it, because the same piece set probably is somewhere on the CVP website, and if not, can be uploaded as user graphics. But the same problem will now manifest itself in other places. In particular, the 'Diagram Editor with Scalable Graphics' will be broken. This refers to a C program on my own website thar dynamically generates piece images according to specification, and now also is no longer accessible. So far Fergus did not manage to compile the same program for the CVP website, so that it could run there.

[Edit] Interesting. On my PC with FireFox all this works. Perhaps I have switched off this pedantic security feature there; I don't really remember.

Edited regarding letters: Berolina pawns changed from P to Q.

Just noticed this comment. Apparently Old Shatar actually starts with the pawns on the 2nd and 7th ranks. 1. d4 d5 is mandatory first move. Since Old Shatar did not actually have the Hia, I wanted to keep the game as close as possible to the original but, of course, add a Hia. Your idea, of course, is good. I did add a game in a comment, as an example game. I think the checkmate is very nice.

I wouldn't switch courier and knight. The charm is to respect the historical setup of Courier chess. That position for the knight, next to the rook is not unusual to my eyes.