Toward coherent mathematical classification of openings

At the invitatiton of Open Encyclopedia of Chess Openings

http://finaltheoryofchess.game-server.cc/mediawiki/index.php/Main_Page

Gary Danelishen, I started to work on new classification based on pawn structures here:

http://finaltheoryofchess.game-server.cc/mediawiki/index.php/Pawn_Structure_Classification_Codes

The advantage of this new classification is that you see immediately all openings with the same or similar pawn structures as well as all possible and imaginable transitions!

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Well, that's my personal program to make a bit of order in opening classifications.

First of all, chess positions are naturally stratified by pawn stems. If all pawns are present in their original columns, there is stratification by pawn structures. Let's say, King's Indian Attack 1.Nf3 d5 2.g3 is characterized by pawns on g3 and d5 (Nf3 is reversible move). I call all openings with this pawn structure 3g|5d-hierarchy etc.

http://www.chess.com/forum/view/chess-openings/kia-and-hierarchy-of-3g5d-openings

If some pawns are exchanged or doubled, I indicate it saying that it's, let's say, x|y2x-gambit if white don't have pawns in x-vertical and black have no pawns in y-vertical but doubled pawns in x-column.

http://www.chess.com/forum/view/chess-openings/qga-and-other-cd2c-gambits

http://www.chess.com/forum/view/chess-openings/danish-and-other-de2d-gambits

http://www.chess.com/forum/view/chess-openings/blackmar-diemer-and-other-ed2e-gambits

There are also natural notions of heights, distances and coverings between openings.

http://www.chess.com/forum/view/chess-openings/height-of-an-opening

http://www.chess.com/forum/view/chess-openings/distance-between-openings

I'll give more details later.

You are welcome to put your classification system into practice at the Open Encyclopedia of Chess Openings (OECO). There are currently two formats used to categorize openings. The first is the standard ECO listing and the second (see: Table of Contents) is based around the first move of the opening (1.a3, 1.a4, 2.b3, etc.).

http://oeco.dyndns-wiki.com/mediawiki/index.php/Main_Page

Regards,

-Gary

All right Gary, thanx for the invitation! I can add my classification codes, based on pawn structures, to all openings in the encyclopedia. I just need some indications how to do it.

As plans may often be based on the pawn structure, your system not only classifies openings, but also indirectly classifies strategic plans. There could be potential here for the writing of a chess book which formally classifies pawn structure, openings and common plans for each opening. An excellent book which may be of interest (If you don't already have it) is 'Pawn Structure Chess' by: Andrew Soltis, which also examines all the different pawn structures.

Thanx Malcolm, interesting! Nope, I don't have this book at the moment.

Okay, I started to add Pawn Structure Classification Codes (PSCC) to all Book Openings here starting from A00. For example,

http://www.chess.com/opening/eco/A00_Amar_Opening_Gent_Gambit

http://www.chess.com/opening/eco/A00_Creepy_Crawly_Formation_Classical_Defense

http://www.chess.com/opening/eco/A00_Grob_Opening_Grob_Gambit_Basman_Gambit

Please feel free to ask if U need precisions about the format that I use.

I will also make cross-references for all openings having the same pawn structure. Finally, I'm planning to indicate all possible transitions as well.

In parallel, I'll do it for Gary's Open Encyclopedia of Chess Openings.

I agree with MalReid that your system appears to have quite a bit of potential. Getting a good idea to catch on (i.e. marketing the idea) is often a battle in and of itself. So, if you find it adventageous to implement your idea in the Open Encyclopedia of Chess Openings (OECO) then I am in full support. Feel free to make any necessary additions needed to show the full potential of your system.

Please feel free to contact me for any reason and I will try to get back with you within one day. Good Luck!

your willingness to work hard really impresses me. But i have a doubt: isn't this classification system a bit inconsistent? i mean, let's look at a random game.

1.d4 d5 2.c4 e6 3.Nc3 c5 (QGD tarrasch variation)

now we have a 4c4d/5c5d6e structure. Everything is ok so far.

4.dxc5 exd5 

Now we have a different structure. but it's not over. From now just some random moves 

5.Nf3 Nf6 6.g3

New structure

6...Be7 7.Bg2 0-0 8.dxc4

New structure

8...d4

New structure...and so on. We can suppose that the structure changes 14 times in the next 40 moves, until a drawn endgame(with his own pawn configuration of course) is reached.

Now my question is: how do you classify this game? at a certain point you must stop and say "this is the pawn structure of the game". But in fact it will change again and again, making the classification incorrect. How do you solve this?

Bresando: this is a pertinent question. Now, it's not important how U formally call your game: QGD Tarrasch or maybe Arctic Defense: Drunken Knights. The whole string of changes in pawn structures should be encoded till the end! In this way, when U are in the middlegame and at each move, U can find many games with similar pawn structures. U could always find closest games and probably best moves. I'm sure that it will be the next generation of chess databases. Technically, it's not difficult to do it.

But what is the point exactly?
What will it improve?

Hmmm... so the amar opening in your example above is better classifyed not under  fh3g|e5d but under 

"|5d - 3g|5d - 3g|5d5e - 4f3g|5d5e - fg3|5de2.7,4f - fg|5de2.7,3g - f3gh|5de"  

(there is probably some mistake since i'm not practical with your notation).....no offence but you can see that this contains less information and is longer than giving all the moves!

"1.Nh3 d5 2.g3 e5 3.f4 Bxh3 4.Bxh3 exf4 5.O-O fxg36.hxg3"

Maybe i'm missing the point but why a classification sistem that put toghether very different positions (i mean, the same structure might be +/- with the queens on and -/+ with the queens off, just to make a very obvious example) and is very long (Not much shorter than a full game!) and impractical is better than the current one? 

Please don't take my criticism as a personal attack, i'm just trying to understand how your classification works!

Bresando: yes, the dynamical string of pawn structures is:

|5d - 3g|5d - 3g|5de - 3g4f|5de - f3g|e4ff5d - fg|e3gg5d - fh3g|e5d

And yes, U miss a point: each entry in the string codifies the whole pawn structure of the current position at each move!

When U are in the middlegame and current opening databases don't work any more. If U play seriously, would U like to look at similar games? Not exactly the same positions, but quite close with the same pawn structures. That's the point.

Of course it does. But you missed my point: this is not relevant to the classification problem. The game is only classifyed with the whole string. And this is less practical and invormative that just giving the whole game.

What i mean is:

-as a way to classify games and openings as stated in the title, this system looks very bad to me for the reasons stated above. Your answer is not relevant to the classification problem. This is my main remark.

-Now a completely different topic underlined by your answer: it's true that every entry gives some information on the position.

However:

-The "whole pawn structure" string you are using is definitely not best for this purpose. The strategic feathures of the positions usually depends on 4-5 pawns( usually the central ones) and not on the whole pawn formation. In a lot of positions (not always!) it's rather irrelevant to strategic planning where (a2 or a3?) the a pawn is. Using the W|B string you are going to classify several identical(strategically speaking) positions under different strings.

-To really define the position you need some information about the pieces on the board. Without this you can't really say what's going on.

So a refined proposal is: an "advanced search" function can be added to databases. The player can fill a pawn structure query with something like "find positions with a W pawn on e5, black on e6, open d file,no other open files" and a piece position query "W 0-0,B 0-0, W and B LSB on,B DSB off". this (if used correctly, and it doesn't looks easy) can find strategacally similar positions, improving the classical "position search" feathure. And could indeed be very useful.

Thanks for your answer.

Scid has a search function for games with the same pawn structures. So basically you want to simplify the search by adding a code instead of having a search engine go trough all the games.
Correct me I'm wrong, I'm always interesting such projects.

Bresando: yes and no. This is definitely relevant to the classification problem, though I don't pretend at all to give the ultimate answer. The stratification by pawn structures is only the first step. Btw, U can always extract the info about "central pawns" from the string.

I totally agree with your idea about "advanced search" function within databases.

Yes, indeed, U are right. I didn't know about this Scid feature. I work by my hands at the moment.

Sure. I hope that with your competing skills, U'll become the first 3000+ player at chess.com Though David Pruess and cheat hunters observe attentively your outstanding performances.

Yigor, your work is very impressive.  Given the number of possible positions each game of chess offers, it is essential for us to be able to further organize and classify our understanding of it, and pawn structures seems like a great place to do this.  

Thanx Jacques, I just started to work but hope to finish during this summer.