Dagaz: In the wilds of notations

Spit in the eyes of someone who will say that you can hug the immense!
...
Zeal overcomes everything!

Kozma Prutkov " Thoughts and Aphorisms "

People constantly invent something. After the invention of chess , several thousand more similar games were developed. Initially, according to the old habit left from the time of composing ancient myths, chimeras were created, combining the qualities of two or more chess pieces, but later the authors' imagination got stronger and began to produce more interesting variants. In order not to get entangled in all this zoo, some kind of system was needed, the ability to classify new figures. And she arose. Actually, I know two of them . Unfortunately, both of them do not work.

A variety of chess options have always been the focus of attention of the chess community. In specialized publications you can find descriptions of new games, analyzes of games, as well as articles on the history of chess. Attempts to systematize the rules have never been considered as something extraordinary. Rather, it is a vital necessity. The basis of such classifications was the division of all chess pieces into two large classes: leapers and riders .
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Leaper -s are jumping figures (for example, a chess "Horse" is (1,2) -leaper ), moving by the number of fields indicated in brackets, not paying attention to the figures along the way. Figures moving one field can also be considered leaper -s ( Ferz from Shatranj is (1,1) -leaper ), but since they move to a neighboring field, only 0 figures can jump over (everything is legal). With a great desire, to the same class can be attributed, and chess " Pawn ", but usually do not. Most Orthodox do not even consider it a figure.

Rooks , elephants and queens fall into another category of pieces. These are rider s - figures moving in a straight line through an arbitrary number of empty fields (Rook - (1,0) -rider ). There are "jumping" rider- s, such as Nightrider (derived from a chess knight), but they, along their own path, can only move along empty fields. The proposed classification was considered reasonable and convenient until there were figures that do not fit into it. So appeared the Hopper- s and Locust- s. This did not solve the problem, since there were hundreds of figures that are neither.

Parlett's movement notation

The first large-scale attempt, to restore order in this zoo, made, apparently, David Parlett . In his book, The Oxford History of Board Games , he used the notation of his own invention to classify the various pieces used in numerous variations of chess games.

• King: 1 *
• Queen: n *
• Elephant: nX
• Rook: n +
• Horse: ~ 1/2
• Pawn: o1>, c1X>, oi2>

What can be said about this notation? First of all, it is not very obvious and (which is much worse) is not at all universal. Yes, we have provided a special symbol for “jumping” figures and for taking when “jumping”, as in checkers ( cn (^ 2X>), o1X> ), but we completely forgot about such an important class of figures as Hoppers .

As a result, all sorts of "guns" (for example, from Xiangqi and Janggi ) remained "behind" our description. Moreover, even chess pieces are described inaccurately. Yes, for the pawn, the possibility of “jumping” through an empty field from the initial position ( oi2> ) is described, but where is the description of the capture on the aisle ? Where is the castling notation performed by the King? If any possibility is difficult to describe, it does not mean that it is not necessary to describe it!

Ralph Betza's funny notation

Ralph Betza - personality, in the world of chess, also known. In addition to the serious hobby of classic chess, he is known as a developer of more than 40 highly original variations of this game, such as " Chess with different armies " or " The Way of the Knight ". Acutely aware of the need for a classification system for chess pieces, Ralph proposed his own version of the notation . The system proposed by him has become, in fact, the generally accepted standard used to describe the capabilities of chess pieces.

• King: K = WF
• Queen: Q = RB
• Elephant: B = FF
• Rook: R = WW
• Horse: N
• Pawn: mfWcfF

All this is fine, but the “Pawn” should be able to walk through one field from the starting position! Need more modifiers for Betza notation!

• Pawn: mfWcfFimfW2

It does not describe the " taking on the aisle, " but we will not be too petty. Of course, this notation is not universal! Here is what the author writes about this:

The notation is not universal or perfect yet. It can be used to make it so that it’s possible to make it. My notation has no way to describe such a piece.

However, such horrors as “Elephant” with “variable turn geometry” are not required at all to put Betza notation to a standstill. There are a lot of other funny figures that have been used in numerous versions of Shogi for centuries. Begin, of course, should be with Chu Shogi and her "Lion":


This figure makes as if two moves (both on the same field in any direction, as the "King"). Thus, the “Lion” can eat two figures per turn or perform an even more cunning acrobatic number - eat the figure next to it and, by the second move, return to its place. Such a move, in various “Shogi variants”, is of such fundamental importance that it is given a proper name - igui . And this is not the most exotic application of the “second move” concept:


These are three figures from Ko Shogi . Cavalry (騎 総 kisō) is very similar to the figure of "Lion", but uses the move of the chess "Horse", while moving in the "same" direction. Winged horse (天馬 temba) - a stronger figure, continuing to move in any direction accessible to the “Horse”. Twelve-mile fog (五里 霧) looks simpler, moving twice like Alibaba ( AD ), but after each turn, it can “kill” the enemy figure that happened to be next to him with igui . If these examples are not enough, there will be more:


Roaming assault (招 揺 shōyō) - "War chariot", moving in five (or less) fields in a straight line, killing all the enemy pieces that fall into the path. Thunderclap (霹靂 hekireki) makes all the same five orthogonal moves, but randomly changing direction! And do not think that this is found only in Ko Shogi! Dai dai shogi , Tenjiku shogi , Taikyoku shogi - all these games use similar figures. HG Muller , the developer of the wonderful WinBoard / XBoard chess program, offered another fun modifier to solve this problem.

The modifier " a " means the execution of the "second move", which allows to describe the move of the "Lion" as aK (double move "The King"). As usual, additional modifiers allow you to describe more complex moves. So, for example, in the expanded notation of Betza, the move of the piece from “Checkers” looks like: fmF (fcafmF) . You can try to decipher it yourself. It is this notation that is used when describing figures in "historical" versions of Shogi:

• Cavalry: [NaffN] [xN]
• Winged horse: aN
• Twelve-mile fog: a [DA] acxK
• Roaming assault: Wa5fW
• Thunderclap: a! 5W

Do you think the Betza notation has become universal? Then try to describe, with its help, this game:


So…

If you have a problem and you want to use regular expressions ...

Understand me correctly, I'm not looking for complexity for the sake of complexity! I just do not like the fact that existing notations are non-constructive. In fact, what do we do when we discover a new type of shape? We add a new letter! For example, no need to go far. Here is what HG Muller writes about castling:

This is not the original atom atom but many extensions. As such, any repetition of it, like O2, would be pointless, like any modifier prefixes. I therefore propose to use O + number as a shorthand for (conventional) castling. (After all, casting in PGN is denoted as OO or OOO.) King moves. He ends up with a little bit of it. You can’t be empty. King would be FIDE: WFisO2

Reserving a single letter for such a private thing as castling, to me personally, seems very wasteful! Following this path, we will begin to reserve all new and new letters for all specific moves! For example, in Jetan- e "Princess", once per game, has the right to jump onto any free board field that is not under combat. This move is not similar to castling. So you need a new letter? And what to do when all the letters end? And this is not to mention the fact that at the output we have not quite obvious, not universal and, most importantly, redundant notation:

• g - Grasshopper
• p - "Cannon" from " Chinese chess "
• j - Mandatory "jumping" of the figure
• ...

Grasshopper is almost the same as the Cannon (in any case, Korean)! Why waste another letter on him? And his behavior is directly connected with “jumping over” the figures ( j )! With the Parlett notation, the same story: ' ~ ' - jumping over the figures, ' ^ ' - taking the sprung figure, but we generally forgot about the hopper- s! Returning to Fanorone . The whole problem lies in its specific way of taking:


This is not a chess and checkers take. Given the limited size of the board, such a move can be described using the ' a ' modifier for Betza notation, but the description will be very cumbersome! We'll have to describe the movement of the figure beyond the target field (with the capture of enemy figures along the way), and then the return, for the chain of each length and for all eight directions! And this is not to mention the fact that all these eight directions are not available in all the fields of Fanorona. But Fanorona is not some new-fashioned invention! In Madagascar, this game has been played since 1600.

(*)[p]|((\1[ex])*;~1(~1[ex])*) 

It looks like a complete abracadabra and is somewhat similar to regular expressions . In general, this is not an accident. Regular expressions were invented to describe finite automata , but what is a game board, with a moving figure on it, but a finite state machine? Consider the component parts in more detail:


After all these necessary clarifications, I can “decipher” my notation of the course of the figures in Fanorone:

 (*) #     (   ) [p] #     -    | #     ( (\1[ex])* #        -   ; #  ~1 #   (  ) (~1[ex])* #  ,      ) 

Here, I deliberately omit the moments related to the description of the compound course (this is a separate and rather interesting topic ). Continuing the comparison of notations, I will give my description of the moves of chess pieces. In bold, the part of the description that Parlett and Betza were not even taken up (castling and taking "on the aisle") is highlighted :

• King: * [A] ; [MA] (E [p]) {2} [A] | E ^ [M] W {2}; [MA] (W [p]) {3} [A] | W ^ [M] E {2}
• Queen: (*) ([p] \ 1) *
• Elephant: (X) ([p] \ 1) *
• Rook: (+) ([p] \ 1) *
• Horse: N, OM; E, OT; S, TR; W, RM
• Pawn: N [p]; OM [e]; [M] (N [p]) {2} ; [(te, = Pawn, x)> E] O [l> N]; [(te, = Pawn , x)> W] M [l> N]

I would like to complete this narrative with the aphorism of Kozma Prutkov :

It happens that zeal overcomes and reason