Pawn Structure Classification Codes

What is the practical value of the height metric? The same number can be arrived at in so many different ways.

For example, how is the contribution of losing a single pawn (6) similar to advancing three pawns three ranks (5-2+5-2+5-2=6)?

I guess my question boils down to what does the height metric actually measure?

Good question. It measures the advance of a game toward its end, the pawnless game corresponding to the height 16x6=96. In this context, the loss of a pawn is equivalent to its promotion, so the height = 6 = 2+2+2. So, it's equivalent to advancing 3 pawns on 2 ranks.

Btw, U made an error, the advance of 3 pawns on 3 ranks gives the height 3+3+3 = 9.

Good Job!!

Thanks.

All your recent posts are right up my alley, but I'm having great trouble reading them because of their extreme mathematical focus. Your text reads like a typical mathematical textbook that throws out a definition without any kind of motivation, and no illustration or example, either. I just don't have time to plow through the formal definitions to try to visualize what you're trying to do. And unless somebody can determine what you're *trying* to do, they can't tell how well you've succeeded, which means they can't give you useful feedback. With an overly technical presentation like that I always get the impression that the author is trying to hide behind a veil of complexity, and that maybe the approach is flawed.

Not at all, The author is a professor of Mathmatics, and for him, he breaks it down into numbers that are even over my head. i think he is working his way through the numbers and moves and its a work in progress...My Rhyming Openings will be for the undermathgraduates...lol...

Hey, it's just my normal style, natural for a mathematician, to write like that. Even my book on religions and metaphysics is written in the same style, Billy knows it. As usual, in order to understand formal things, we should look at examples. Here is the sequence of PSCC leading to Najdorf:

1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6

2E -> 2Ec -> 2Ec1d -> 2DEc1d -> 6Dc3d2E1d -> 6Dc2E1d -> 6Dc2E1ad.

The number 6 stands for files without pawns. The height of Najdorf:

h(6Dc2E1ad)=6x2+2+2x1=16

Just ask questions and I'll explain my notations.

Even as I start to understand what you're doing, I'm reacting negatively to it for several reasons:

(1) A "classification" is exactly that: a (hopefully intuitive) category to which one can conveniently refer with a single, simple reference. For example, ECO codes are classifications and are short, like "B22" (for Alapin's Variation of the Sicilian), and like "Dutch Stonewall" is short for a certain well-known pawn formation. In contrast "2Ec1C" is neither short nor intuitive.

(2) Instead of using a string like "6*5*4*3*2*1*0*" where evidently the number of symbols present varies, why not use the computer science notation of brackets for optional symbols, as in EBNF (https://en.wikipedia.org/wiki/Extended_Backus%E2%80%93Naur_form)?

(3) Pawn "structure" refers to *shape*, which is an extremely complex concept that will require at *least* several parameters (infinitely many is more likely!) to describe accurately, but you're trying to use a single number (pawn height) to do this. The result will neither be intuitive or useful. For example, the film rating system (https://en.wikipedia.org/wiki/Motion_Picture_Association_of_America_film_rating_system) *began* to move in the right direction by using four parameters to classify the potential offensiveness of a film (language, substance abuse, nudity, and sexual content), but even this was not enough, and then to make things worse they  mixed these values according to their own perceived priorities into five categories (G, PG, PG-13, R, NC-17) that mean nothing to a person who doesn't have average taste. No single number or letter is going to work well to describe complex entities.

(4) Pawn height is not very related to shape, so is probably the wrong measure to use. 

For example, consider the following (admittedly rare and weak for Black) pawn structure:

The attributes that would especially interest chess players about this position are things like: (1) the pawn structure is locked; (2) the pawn structure from White's perspective points toward the kingside (which in turn suggests the kingside is where White should attack), (3) the locked part of the pawn structure consists of 3 pawns (which is fairly large amount), (4) the space advantage is equal but unbalanced; (5) there exist pawns that can be used as levers to create pawn breaks; etc.

None of these concepts are going to be captured by using pawn height. You *might* reasonably use those 5 concepts I mentioned as parameters and create a 5-parameter description that *might* be useful, but there exist so many other considerations I didn't list that even that approach won't work well. Again, this is a case where math should be helping humans by filling in the gaps of what they haven't quantified in detail, but measures like pawn height are a new concept that doesn't help to do that, and just creates new complications where people have to try to understand what an inventor is trying to do, then try to relate that to what is useful to them, and ultimately probably ignore it because the classification system is too lengthy, unnatural, and doesn't address the issues of interest to them.

Sqod: LoL U are good in criticizing others, U could search for a job in this domain.  The pawn height is a natural concept but U are right, it explains nothing. It just divides the set of all chess positions into 96 strata (+ the initial position).  [Splitting it on white/black parts makes additional subdivisions]. The notation used for pawn structures could be probably improved but it's a secondary thing. The true job is to categorize all chess positions in databases by pawn structures. It would require a good database programming but I'm kinda old and lazy to undertake this task.

As for my own background, I have a very heavy academic background in computer science, some background but less so in math, and my specialty is artificial intelligence, therefore I tend to see things from a computers/A.I. standpoint. For example, I've studied the problem of shape in depth, and recently I've completed (but am still expanding) a book on chess/life principles that incorporate formulas very similar to what you're creating, but I rely heavily on the "intuition" reality check, and in fact I state that heuristic explicitly in one appendix (that I'm still writing) on how to apply heuristics to solve deep problems.

As for databases, all this relates to what little I've done there. For example, in my own chess repertoire text file, because of the extreme problems there of detecting transpositions (which is also a problem for conventional databases) I've taken a semi-A.I. approach in that I created well-defined terms for certain features, such as the position of the four knights on the board, or whether the position is symmetrical, or whether the queens are on the board, then I put all such names together at the start of each section so that I can see at a glance which attributes the position has. That aids in search for transpositions, suggested plans, and associative memory type search when I want to post examples that relate to something somebody mentions in a forum thread. This approach partly relates to feature detectors in A.I., especially in the visual system of animals. A really good system would combine the features to which I gave names into composite features, but I haven't done that yet. That's partly what I meant by a multi-parameter classification system.

Sqod: It sounds interesting. I encountered A.I. only in computer role-playing games when it leads the actions of NPC during battles. Some games allowed to create your own A.I. for your companions, like healing someone when HP is below certain level etc. It was quite interesting.

Thanks.

interesting endeavours