Ratings & Comments

I agree that the way XBetza handles multi-leg moves is not very intuitive. I don't think it is too late to switch to a more intuitive notation, as long as it doesn't allow specification of moves that would not be possible to specify in XBetza. Because then it would be quite easy to just equip the Interactive Diagram (or XBoard) with a simple pre-processor, which just converts the more human-friendly notation to XBetza before interpreting the latter.

E.g. how about writing multi-leg moves always within parentheses, using a hyphen as leg separator, and requiring all atoms should be 'compatible'? Where compatibility means they should either all be multiples of K steps, or of the same oblique leap. The Griffin would then be F(F-fsR), and the pre-processor would act on anything between parentheses, run through the legs to see whether range-toggling is needed. Depending on that it then translates the hyphen to a or ya. So that it ends up with the modifier string yafs, after which it then writes the leading atom F to get the equivalent XBetza. (I guess we could also use square brackets and commas, to stay closer to Betza's original suggestion: F[F,fsR].)

As to your specific questions: the Snake is easy: vWvyafsW. This is just the Manticore with all its moves prefixed with a v. The Ship, however is hard. This is not so much the fault of the notation, but caused by the fact that moves with different initial steps bend in different directions, and you have to indicate which (while for the Snake all moves bent in both directions). The only way to do it is to separate the left-bending from the right-bending move, i.e. the diagonal from the anti-diagonal first steps. This in itself is cumbersome, as there are no shorthands like v or s for diametrically opposed diagonal moves. So you have to write out all directions, and being diagonals, each direction requires two letters. E.g. a Ferz moving along an anti-diagonal is flbrF, and in the Ship you want those to bend to the right (i.e. fr) in the next leg. So you get flbryafrF for these two paths. And then you have to write the other two paths in the same way, changing all l into r and vice versa. This is how I did it in my Diagram for Tamerlane II. (Note that flbr[F,frR] as it would look in the proposed more intuitive system would not be much less cumbersome...)

@Bn Em: your trick for the Ship with the z is clever, but makes the description even less intuitive. When I made the Tamerlane II diagram this alternative use of z did not exist, though. I am not sure if defining a meaning for z and q without first using an s would be helpful. But, come to think of it, s is a dummy on a diagonal atom, as lF is the two left moves, and rF the two right moves, so together these are a full Ferz. But such a dummy s could be used to define the symmetry breaking as used by following z or q. I guess it would be most useful to define it such that it causes the diagonal atom to be interpreted as an oblique one with the longest leap in the sideway direction (i.e. as sN would have been interpreted). Then the Ship would be FsyafqF.

I have no idea why yafqF does what it does. Without a preceding s or oblique leg it triggers the code for the old Betza meaning, which lays out the entire path for the circular piece, with a special mode flag to indicate it can be terminated at any square along the path. But the preceding leg must utterly confuse it...

Thank you HG and Bn for your answer, it's fascinating, although I can't understand everything.

I have tried the strings you said for the Ship. Not all of them work. Maybe I haven't caught what you meant.

flbryafrFfrblyaflF: doesn't work. It skips the F-square

smpyasW: it works, but I really don't have the skills to understand why (it looks like "sympa" a French equivalent of "cool" or "great" that you say when something is nice)

FvmpasyazW: doesn't work. Strange pattern: B+incomplete Manticore

flbryafrFfrblyaflF: doesn't work. It skips the F-square

That is correct. But then you simply add it explicitly: FflbryafrFfrblyaflF.

All the bent trajectories you can specify with XBetza skip the first square (or actually the entire first leg if it is more than a single square, or even all non-final legs if they have more than two legs). All legs mentioned in a description are compulsary, and must contain at least one step if they are sliding.

This was a choice; it could have been defined such that slider continuation legs can make 0 to infinite steps, rather than 1 to infinite (like the initial or only leg can). But what would you do then for a piece where you don't want that? E.g. a Griffon that cannot move to the F squares, even though it can be blocked there? It is much easier to add the F moves to a piece that not naturally has those, than it would be to prevent it from stopping on the first square of its path. So asR is a hook mover that must turn a corner, and cannot move like a simple Rook. If you would want it to move as a simple Rook as well, as the Hook Mover from the large Shogi variants can, just write RasR.

smpyasW […] looks like "sympa"

Well the ship is certainly a sympathic piece ;‌)

FvmpasyazW: doesn't work. Strange pattern: B+incomplete Manticore

Sounds like a Crooked Rook (=Girlscout) move to me, which would make sense in the old/non‐continuation‐leg interpretation of z. It gives me a Ship when I try it; maybe try refreshing your Cache? (Ctrl–Shift–R)

BTW, I now made it such that FsyafqF for the Ship works too. (Refresh cache!)

Explanation: q in a continuation leg stands for l or r that would bend the path in same direction as before / initially. So fq can mean either 45-degrees left or right. Now the s at the start of the multi-leg part defines 'sideways' as the initial direction (which for diagonal atoms would otherwise be ambiguous). So the move toward the lower right bends to the right (if you imagine it to start to the right), so it bends 45-degree right again for the second leg, which makes that move straight down. The move to the upper right, however, had to bend left if it startes horizontally to the right. So the leg after that one bends left, making it move straight up.

Bright! Thank you

I see Betza's notation as a convenient and intuitive way of describing the moves of a chess piece. I believe XBetza's notation has another goal, that of being able to be understood by an AI for the cases not covered by the basic notation.

In principle there is no limit to what an AI can understand; it is just a matter of how much effort you put in creating it. And I subscribe to the goal of making move description convenient and intuitive, even for moves that are intrinsically more complex, such as the Griffon, Falcon or Chu-Shogi Lion. So think it is worth it to put a great deal of effort in achieving that goal.

But for any system of notation it seems important that it is unambiguous, and covers sufficiently many cases. Betza himself has suggested the t[F,R] notation for Griffon, but this is not unambiguous, as an 'Acute Griffon', which would continue inward instead of outward, making a 135-degree turn, (or the piece that can continue in all four Rook directions), would be written the same. Furthermore, the leading t seems redundant here: the 'then' meaning could be implied by the presence of the brackets. I think Betza suggested also other uses for the brackets, like z[F,W] for a slider that alternats W and F steps in a crooked way, but this distinction could also have been made by using other separators than comma for that, e.g. [W/F]. Once non-alphanumeric characters are allowed in the notation, lots of options are available.

I hope you agree that it hardly matters for the intuitive understanding whether one would write F&R, F-R, [F-R] or [F,R]. But now suppose that we want to slam extra W moves on a Griffon... I don't like WF&R so much, because intuitively you would parse this as (WF)&R, as punctuation usually separates 'words'. While it is intended to mean W(F&R). This is why I think it would be better to require some sort of parentheses around the complex moves. And to stay as closely as possible to Betza's legacy, these can be brackets. With W[F-R] there is little doubt that the W is a separate move.

The ambiguity problem has to be solved by putting some directional specification on the continuation legs, to distingush outward from inward, or even between several possible outward directions (such as in the case of the Ship). In your example you suggested a new prefix character ($, as we have run out of letters) for indicating 'outward'. This has the advantage that we can keep using the original directional modifiers in the meaning they have in the absolute frame of reference. This works well for the Ship, where you can write F&$vR to make the extra v pick out the vertical of the two outward Rook paths.

But I wonder whether introducing a whole new system for indicating relative directions is worth it. For one, the use of an absolute direction to disambiguate equivalent relative directions only rarely works; the Ship is a favorable case. It would for instance not work on a 'Chiral Griffon', which would bend always in the same relative direction (left or right), to give a rotation-symmetric rather than reflection-symmetric move pattern. And how would you know that in N&$R 'outward' would mean 'in the direction of the long component'? Some are v and others s so you cannot use those to indicate it. And if you define the meaning of 'outward' on oblique moves as in their long direction, how would you describe a piece that would continue like a Rook in the short direction of the knight move? It seems that we would have to create a whole new system for describing relative directions, or groups of directions, similar to the existing Betza system for absolute (initial) directions, but using puntuation characters instead of the familiar fbvlrs. That would involve a lot of new characters, but perhaps these could be chosen in a somewhat intuitive way, so they would not be too hard to remember (like ! for outward, ^ for inward, < for turn left, > for turn right, _ for < or > and | for ! or ^). But it still seems a hassle, which can be exploited only very rarely.

So I think there is a lot of merit in sticking to the existing Betza scheme for indicating directions, but interpret them as relative directions on continuation legs. Then instead of needing a new symbol like $ or ! for 'outward', we can simply use f for outward. In a sense the Betza directional modifiers have always been relative: for simple moves they are relative compared to the way the player is looking. We also say fmWfcF for black Pawns! (And in a 4-player game even v and s have player-dependent meaning.) Is F&fR really any less intuitive than F&$R ? You would lose the possibility to disambiguate the two outward Rook moves by use of an absolute direction, but you now have a simple way to write a (right-handed) Chiral Griffon: F&frR. One always has to compromise: what makes one piece easier to describe, will make some other piece that behaves in the opposit way more difficult to describe. I think it would be a mistake to judge a description system solely on how well it does on a single piece that you happen to use, but is not very common, and even less representative for the general problem.

There also is a more fundamental issue: writing the Griffon as F&fR or [F-fR] assumes the move can also be terminated without making all its legs, after just the F step. It might be subjective whether this is intuitive or not; it seems to me that this is mainly inspired by the case at hand (i.e. bent slider). Problem is there are many other cases where you would not want this. E.g. lame leapers like the Mao also need a multi-leg description to indicate where they can be blocked. But if W&fF or [W-fF] also allows making a W move, how can we describe the Mao then? And if fcF&fmF would also allow plain capturing diagonally forward (fcF), how would we describe the Checker? We do need a way to describe complex paths that cannot be terminated half-way. One way would be to forbid incomplete moves, so that these have to be described as separate moves when they are desired. (Advantage: no new notation needed. Disadvantage: move descriptions get longer.) The alternative is to introduce a different symbol for continuations that are only optional. E.g. [F~fR] could mean a Griffon that can make F moves, as the fR continuation is optional. While [F-fR] could not make the F move, although it can be blocked on the F square, as the fR continuation is mandatory. Actually I sort of like this latter solution, even though it requires introduction of a new symbol.

I would also like to have some feedback from other people, on what they would consider intuitively clear in these matters.

I think mpsyasW is pretty clear, but perhaps not very intuitive. What if doubling a direction made it absolute instead of relative? Then the ship could be something like FyafvvF or FyavvsF. It's not clear to me how exactly combinations of directions should be interpreted.

I think mpsyasW is pretty clear, but perhaps not very intuitive.

Well, I think it is a justified complaint that it is not easy to see that there is a Rook move hidden in there. The bracket notation [smpW-sR] would make that more explicit. The notation of a full Griffin based on this idea would be [mpW-sR], and would automatically visit the F squares, as these are now reached by the first sideway Rook step. But it literally requires some 'out of the box' thinking to detour the trajectory over an auxiliary square (sW), and subsequently make that square fully transparent by giving it mode mp. And this obscures the fact that in reality the first square visited by the piece (in the sence that it can move to it or be blocked there) is an F square. That distracts greatly from the intuitiveness.

Doubling of directional modifiers is a bit tricky, as sometimes it is needed to prevent such modifiers from combining to the intermediate direction. E.g. if we want to describe a Knight that lacks the two backward-most moves, we must specify an s and an f direction on it. But we cannot just write fsN, as this means flNfrN, and fl and fr describe individual N moves. To prevent that we write ffssN.

Thanks HG.

"I hope you agree that it hardly matters for the intuitive understanding whether one would write F&R, F-R, [F-R] or [F,R]. " >> Yes,of course;

"With W[F-R] there is little doubt that the W is a separate move" >> I fully agree

"And how would you know that in N&$R 'outward' would mean 'in the direction of the long component'? " >> Not sure what you mean by long. The "R" part? I don't see what the problem is, it is not easy by messages. "Outward" for me means the move is always in the direction of going away from the starting square both in x and y. If after the first leg, the second leg starts by going to a square that is closer to starting square either in x or y than the intermediate square (between the two legs), then it is not outward on that definition.

"Is F&fR really any less intuitive than F&$R ?" >> no no it is not. Don't misunderstand me.I was just using these 2 characters & and $ just for the example and to avoid to select 2 true letters and thus choose the wrong ones. You can replace them by any letter or character.

" I think it would be a mistake to judge a description system solely on how well it does on a single piece that you happen to use, but is not very common, and even less representative for the general problem" >> I fully agree. This is a must.

"how can we describe the Mao then?" >> Again I agree with you, I don't know.

I was not proposing a new system, I was just trying to answer your question to me by making a thought to fuel the discussion, but of course I don't pretend to have solve this very difficult issue. I do rely on you and other skilled people in that matter.

I also have the feeling that maybe it would necessary to introduce more symbols.

Well, I think it is a justified complaint that it is not easy to see that there is a Rook move hidden in there. The bracket notation [smpW-sR] would make that more explicit. The notation of a full Griffin based on this idea would be [mpW-sR], and would automatically visit the F squares, as these are now reached by the first sideway Rook step. But it literally requires some 'out of the box' thinking to detour the trajectory over an auxiliary square (sW), and subsequently make that square fully transparent by giving it mode mp. And this obscures the fact that in reality the first square visited by the piece (in the sense that it can move to it or be blocked there) is an F square. That distracts greatly from the intuitiveness.

That is true, it wasn't easy to understand the bent moves at first for me for that reason, and also because it's not immediately obvious that 'a' actually applies only to the move at the end of the sequence of modifiers rather than being a connector between two different moves, and that every leg before the last is mandatory.

What about using the brackets alone to indicate that all the moves contained within are part of a sequence? [FfR] [smpWsR] You could differentiate between mandatory and optional continuations using a separator or with different symbols, such as [F+fR] and {FfR} meaning F followed by a mandatory R.

And then perhaps the whole sequence could be modified too, so what if you could do p[FfR] to get a gryphon that must jump (a grao)? And v[FfR] might work for the ship, if it's not ambiguous somehow.

Not sure what you mean by long. The "R" part? I don't see what the problem is, it is not easy by messages. "Outward" for me means the move is always in the direction of going away from the starting square both in x and y. If after the first leg, the second leg starts by going to a square that is closer to starting square either in x or y than the intermediate square (between the two legs), then it is not outward on that definition.

If the N moves goes from e1 to f3 (i.e. both increasing in the x and y dimension) then both f3 -> f8 and f3 -> h3 are R moves that neither decrease x nor y. So both fit your definition. But they are not equivalent. Probably f3 -> f8 has the best claim on being called 'outward'. One could argue that the other one is unnatural, because it crosses its counterpart that moves from e1 -> g2 -> g8, and therefore is unlikely to ever occur in any game. So that there also is no need to have any notation for it.

Anyway, I brought this up in order to show that just having one new symbol, meaning 'outward', is not enough, but that we would likely need a complete system for indicating all 8 relative directions. Which seemed worse than just using the existing system used for indicating the 8 directions relative to the player. As these new symbols would only be encountered in multi-leg moves, which are quite rare themselves, so that people would not be familiar with those, but likely think "what kind of a freaky symbol is that???".

The price for this is that these symbols would no longer be available for indicating absolute directions, though.

The Ship just happens to be one of these very rare nasty cases, because the equivalent moves of the Ferz alternately bent to the left and the right. It hardly ever happens that referring to an absolute direction is of any help. I can think of many solutions, but most of those require introducing new symbols or new meanings of existing symbols that would virtually never be used, and thus unknown to the casual user of Betza notation. I think the best way is to accept that compactnes and intuitiveness here are conflicting demands, and thus go for the somewhat cumbersome description [frblF~flR][flbrF~frR], to explicitly indicate on which starting steps there is a right bend, and on which a left bend.

A more practical problem is that the difference between tilde and hyphen is hardly visible in this font...

What about using the brackets alone to indicate that all the moves contained within are part of a sequence? [FfR] [smpWsR]

Well, for practical reasons I would prefer to have some separator between the legs. (Then I can just use the JavaScript split method to split the move in the parts between the hyphens, while otherwise this should be judged by the case of every individual letter.) I think that once you allow the brackets, allowing other non-alphabetic characters as well is no longer a problem.

The idea of considering a certain grouped sequence of directional modifiers plus atoms as a 'crooked atom', and allowing the whole group to be prefixed, does have merit, however. Otherwise you would have to specify a separate move for each leg the mount could be in to make a hopper. E.g. for the Grao you would need [pF-fsR][F~fspR] (i.e. mount either at the F square or in the Rook path). Then p[F~fsR] is a lot simpler. The Interactive Diagram internally already uses this method for moves like zB and qN: it creates a complete description of the maximum-length path as a sequence of 1-step legs, with in each leg a special mode flag to indicate the move can also terminate there. And it does allow the entire path to be used as a hopper, in order to allow zpB or zgB. I could easily extend that to allow user-defined paths.

And you are right: the entire Griffon move is essentially an oblique slider, like the Nightrider. So it does make sense to allow indicating the individual trajectories by the same direction system as the trajectories of the Nightrider (or Knight). So the Ship would be the 'Narrow Griffon', like vN is the Narrow Knight.

Well, for practical reasons I would prefer to have some separator between the legs. (Then I can just use the JavaScript split method to split the move in the parts between the hyphens, while otherwise this should be judged by the case of every individual letter.) I think that once you allow the brackets, allowing other non-alphabetic characters as well is no longer a problem.

In that case, perhaps it would be good to have two different separators to distinguish between optional and required continuations. For example, the griffon could be F&fR, and the mao W+fF (or whatever other symbols would be preferable)