Pawn Structure Classification Codes

I'm currently working on a new classification of chess openings. I post here a summary of the beginning of my book Coherent Mathematical Classification of Chess Openings, Pawn Structures and PSCC Codes in preparation. Any comments, remarks, suggestions etc. are welcome!

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1. Pawn height

The pawn height of a white (resp. black) pawn on the board with coordinates (x,y) is y-2 (resp. 7-y). It's the vertical distance from its original position. By definition, the height of a taken or promoted pawn is equal to 6. The total height h of a chess position is the sum of heights of all 16 white and black pawns. So, the maximal height of a pawnless endgame is equal to 16x6=96. The height is also naturally divided in white and black parts h=h1+h2 where h1, h2 =< 48. Heights 32 and 64 approximately divide chess games into 3 parts: opening, middle game and endgame.

2. PSCC codes

Pawn Structure Classification Codes are written as follows. The PSCC code of the initial position IP or a game without pawn mouvements is I. Otherwise, the general form of a PSSC code is

[6*][5*][4*][3*][2*][1*}[0*]

where * stands for words in capital and small letters containing A,...,H (resp. a,...,h). These letters describe advanced pawns, capital for white and small for black, and corresponding number is equal to their height. For example, the Sicilian: Alapin opening 1. e4 e5 2. c3 has height 5 and PSCC code 2Ec1C. Files without pawns are described by the expression 6* or 0* depending on the height. For instance, Scandinavian game 1. e4 d5 2. exd5 Qxd5 has height 12=6+6 and PSCC code 6Ed. Doubled pawns are indicated by an additional * symbol. Let's take Ruy Lopez: Exchange variation 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Bxc6 dxc6 as an example. Its height is 6=2+4 and it is described by PSCC code 2Ee1ac*0d (here * indicates that the pawn on c6 is doubled). By erasing all letters in a PSCC code we obtain the numerical code (NC) of the position. Notice that PSCC codes describe chess positions while chess games correspond to sequences of such codes.

2. Oriented graph G of pawn structures

Admissible pawn structures are vertices of this graph. Consider two vertices
S1 and S2. They are connected by an arrow if there is a position P2 with structure S2 that can be obtained from a position P1 with structure S1 in 1 ply. The graph G is a ramified tree with the unique root I and the unique treetop 6ABCDEFGHabcdefgh
of height 96=48+48. How many branches (arrows) go from the root to the stratum
of height 1, i.e. what is the number of pawn structures of level 1? There are 8 structures of height 1+0: 1A,...,1H as well as 8 structures of height 0+1: 1a,...,1h.

4. Ramified core of G

Let's consider the set of all master games. We say that a given pawn structure belong to the ramified k-core if it appears in, at least, k>1 games. In this book we will indicate PSCC codes for 100-core games (k=100). The number of games will be taken from the chess.com database. Aproximative numerical evaluations of chess positions are deduced from the chessOK database and chess.com explorer.

5. Games of height 0 and transitions

The PSCC code of such games is I. The initial position itself will be denoted IP. We indicate all transitions to positions belonging to the ramified 100-core of master

games.

I: IP  [A00, +0.1/+0.15]

   --->(1.a3) 1A Anderssen's opening [A00, +0.0], h=1+0.

   --->(1.b3) 1B NLA [A01, -0.05/-0.00], h=1+0.
   --->(1.c3) 1C Saragossa opening [A00, -0.05], h=1+0.

   --->(1.d3) 1D Mieses opening [A00, -0.05/-0.00], h=1+0.
   --->(1.e3) 1E Van't Kruijs opening [A00, +0.05], h=1+0.

   --->(1.g3) 1G Benko's opening [A00, +0.0], h=1+0.
   --->(1.b4) 2B Sokolsky opening [A00, -0.2 ], h=2+0.

   --->(2.c4) 2C English opening [A10, +0.05/+0.1], h=2+0.

   --->(2.d4) 2D QP [A40, +0.1/+0.15], h=2+0.

   --->(2.e4) 2E KP [B00, +0.1/+0.15], h=2+0.
   --->(2.f4) 2F Bird's opening [A02, -0.1/-0.05], h=2+0.

   --->(2.g4) 2G Grob opening {A00, -0.4/-0.3], h=2+0.

I: 1.Nc3 Dunst [A00, +0.0/+0.1] --> 1g, 2c, 2d, 2e Reversed Nimzo.

I: 1.Nc3 Nf6 Dunst [A00, +0.1] --> 2d QP: Indian, 2e Alekhine.

I: 1.Nf3 Réti [A04, +0.1/+0.2] --> 1b Réti: QF, 1c Réti: Slav, 1d Réti: Pirc, 1e, 1g
Réti: KF, 2b Réti: Polish, 2c Réti: Sicilian, 2d, 2f Réti: Dutch.

I: 1.Nf3 Nc6 Réti: Black Mustang [A04, +0.2/+0.3] --> 1G Benko, 2C Anglo-Lithuanian, 2D Mikenas, 2E QP: Nimzo.

 I: 1.Nf3 Nf6 Réti: Symm [A05, +0.1/+0.2] --> 1B Réti: NLA, 1D Mieses, 1E Réti: Quiet,

1G Réti: KIA, 2B Sokolsky: Zukertort, 2C Anglo-Indian: KK,  2D Indian: KK.

Abbreviations:

IP = Initial Position

KF = Kingside Fianchetto

KIA = King's Indian Attack

KK = King's Knight

KP = King's Pawn

NLA = Nimzo-Larsen Attack

QF = Queenside Fianchetto

QP = Queen's Pawn

----------------------- to be continued ---------------------

Nice

Heya Billy, thanks! Btw, U are truly omnipresent in all groups and forums.

Thanks again..

Hi, I see that we have only 16 pawns, so a coding system that has 16 characters/digits would suffice.  Do we really need to shorten the thing to such a short code, which is not easy to decipher?

The genius of PGN and FEN formats was that they are readable even without computer visualization and a reference table (your classification would need one).  New In Chess also suggested some opening classification that has full words in, not Axx, Bxx, etc.  

Why would you want to make things more difficult for humans?

Hey, thanks for your comment. Well, I use exactly 16 letters A,..., H,a,...,h. Digits are necessary to describe the position (height) of each pawn. Personally, I find that these codes are easily readable after a little practice. And I seem to be a human btw.

Good work, I'm sure. Mind you don't end up as bonkers as Kmoch.

Thank U bro! I don't know who is Kmoch.

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

His book on the role of pawns, written way back in the late 1950s, is one of the most widely acclaimed texts in the history of the game. Many commentators have since declared that in spite of his real genius, he was evidently quite mad. I'll let others elaborate. 

Oh, great! I didn't know about the existence of this book.

If you order it by post beware of which edition you buy. There is currently a reprint available published by Dover but as I recall it is presented with the old English language descriptive notation system rather than with the now universal algebraic notation that displaced it in English language speaking countries in the 1970s. The Dover edition is a reprint of an older edition with the older notation, but you may not find it easy to read if you are unfamiliar with the old style. It is, however, almost certainly also published elsewhere and available in the algebraic notation that we now all use.

Playing career[edit]

Kmoch had most of his best competitive results between 1925 and 1931. He won at Debrecen 1925 with 10/13. At Budapest 1926, he shared 3rd-5th places with 9/15 behind winners Ernst Gruenfeld and Mario Monticelli. At Vienna 1928, Kmoch placed 6th with 8/13 as Richard Réti won. Then at the Trebitsch Memorial, Vienna 1928, Kmoch shared 3rd-6th places with 6/10, half a point behind Gruenfeld and Sandor Takacs. At Brno 1928, Kmoch placed 3rd with 6/9, with Réti and Friedrich Saemisch winning. Kmoch won at Ebensee 1930 with 6/7, ahead of Erich Eliskases.

Kmoch represented Austria three times in Chess Olympiads. Here are his detailed results, according to olimpbase.org. At London 1927, he played board three and scored 6.5/12 (+4 =5 -3). At Hamburg 1930, he was on board one, and scored 8/14 (+6 =4 -4), as Austria placed fourth. Then at Prague 1931, Kmoch was on board three and scored 9/15 (+4 =10 -1); overall, he scored 23.5/41 (+14 =19 -8), for 57.3 per cent.

His last good tournament result was 2nd at Baarn 1941 with 5.5/7, behind Max Euwe, and he stopped playing competitively after this.

Writing career[edit]

Kmoch had written for the magazine Wiener Schachzeitung from the early 1920s. His Die Kunst der Verteidigung (The Art of Defence) was the first chess book devoted to this subject. In 1930, Kmoch updated the Bilguer handbook, and wrote the tournament book for the Carlsbad 1929 event.

In 1929 and 1934, Kmoch served as Alexander Alekhine's second in his world championship matches against Efim Bogoljubov. Kmoch and his Jewish wife Trudy lived in the Netherlands from 1932 to 1947. Kmoch also served as Alekhine's second in the 1935 title match against Max Euwe, and he wrote a book on the match. In 1941, he wrote a book on the best games of Akiba Rubinstein.

After World War II ended, Kmoch and his wife moved to the United States, settling in New York City. Kmoch served as the Secretary and manager of the Manhattan Chess Club, and directed tournaments. He also wrote for Chess Review, then one of the leading American chess magazines.

In 1959, he wrote his most famous book, Pawn Power in Chess (German: Die Kunst der Bauernführung), which is notorious for its use of neologisms ("ram", "lever", "sweeper", "sealer", "quartgrip", "monochromy", etc.).^[1]

A neologism (/niːˈɒlədʒɪzəm/; from Greek νέο- néo-, "new" and λόγος lógos, "speech, utterance") is the name for a relatively new or isolated term, word, or phrase that may be in the process of entering common use, but that has not yet been fully accepted into mainstream language.^[1] Neologisms are often directly attributable to a specific person, publication, period, or event.

Huhh?

P2tP: Thanks for these references! Great that someone (Andrew Soltis) worked on pawn structure links. Though, it seems, that he wasn't preoccupied by classification. Anyway, I prefer do it myself as a useful exercise.

What about a naming system that identifies patterns of pawns instead of specifying the location of every single pawn?

For example:

• FA means French Advance, which means the center pawns are like in a French Advance:

• FFA means flipped French Advance (e.g KID):

• abc (lowercase) means the a, b and c files do not have pawns on them.
• !abc (lowercase) means that there are doubled pawns on the a, b and c-file.
• !!abc is similar to !abc, but with tripled pawns instead of doubled pawns.
• #abc (lowercase) means that there are "overextended" pawns (pawns past your half of the board) on the a, b and c-files.
• DB means that the DSB is blocked in with d6/e3.
• LB is similar to DB, but with the LSB instead.
• DF means that the pawn at g6/b3 suggests that the DSB is going to get fianchettoed (specifically - open g/b-files don't count).
• LF is similar to DF, but with the LSB instead (specifically - open g/b-files don't count).

Attributes belonging to White are put into square brackets, and attributes belonging to Black are put into round brackets. The square brackets go before the round brackets. The attributes are separated by dashes.

For example, this Nimzo-Indian Saemisch would be classified as [b-!c]-(LB-LF):

The Sicilian Dragon would be classified as [d]-(c-DB-DF):

Whaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa?

Iamunknown2: U are partially right, the naming is good for games with few moves. Classification codes are necessary for more complicated openings.

I modified the section 5 clearly indicating transitions from the initial position.

I: IP  [A00, +0.11/+0.14]

   --->(1.a3) 1A Anderssen's opening [A00, +0.00/+0.01], h=1+0.

   --->(1.b3) 1B NLA [A01, -0.07/+0.00], h=1+0.
   --->(1.c3) 1C Saragossa opening [A00, -0.07/+0.00], h=1+0.

   --->(1.d3) 1D Mieses opening [A00, -0.10/-0.04], h=1+0.
   --->(1.e3) 1E Van't Kruijs opening [A00, +0.04/+0.08], h=1+0.

   --->(1.g3) 1G Benko's opening [A00, -0.05/+0.04], h=1+0.
   --->(1.b4) 2B Sokolsky opening [A00, -0.25/-0.18 ], h=2+0.

   --->(2.c4) 2C English opening [A10, +0.05/+0.10], h=2+0.

   --->(2.d4) 2D QP  [A40, +0.1/+0.15], h=2+0.

   --->(2.e4) 2E KP [B00, +0.1/+0.15], h=2+0.
   --->(2.f4) 2F Bird's opening [A02, -0.1/-0.05], h=2+0.

   --->(2.g4) 2G Grob opening [A00, -0.4/-0.3], h=2+0.

Please let me know if you disagree with numerical evaluations, e.g. I estimated Nimzo-Larsen attack between -0.07 and +0.00 by comparing chessOK data with chess.com explorer / Stockfish evaluations starting from d=20.