A New Perspective on Chess Complexity

[rblasingame]

Hello everyone!
I am a math teacher/independent researcher and I believe I have developed a new measure of chess complexity, Asset-Configuration Complexity, that I believe will sharply reduce computational loads in chess engines and database tables. I've posted the preprint of my research paper and benchmarking script to Zenodo.org here: https://doi.org/10.5281/zenodo.21288811

Since I am an outsider to the chess engine/theory industry, I'm genuinely unsure if this is a known, standard methodology or a fresh perspective. I would love your critical feedback, critiques, and general thoughts on my work. I have been unable to find any academic sources applying my methodology to chess, and I'm genuinely curious if this is a new and novel idea or something that the industry has already passed over.

Honestly looking forward to all forms of feedback and critical reviews.
Thanks for your time!!

[syzygy]

Do you really think it is a good idea to pepper a paper with self-praise? Nearly every sentence is a giant red flag...

It doesn't look like you have anything other than an index space of chess position features.
I am not going to read all the LLM slop.

This Paper Submitted in Partial Fulfillment of the Requirements for Academic Review in Game Combinatorics and Systems Complexity

What does that mean? I understand "in partial fulfillment of the requirements for [some degree]", but "for academic review"?

Advice on academic writing: start by removing all adjectives.

[rblasingame]

@syzygy, first of all, that's incredibly rude of you to make such allegations while also saying you're not gonna read the actual work, all the math, or the various analytical tools detailed in section 8.4 Second, I have no idea what you mean by "self-praise", the entire whitepaper is written in a purely clinical tone. Third, the disclaimer you're asking about is a pre-publishing tag for academic review, it is literally explained in the whitepaper's description field on the Zenodo.org host page.

[syzygy]

@syzygy, first of all, that's incredibly rude of you to make such allegations while also saying you're not gonna read the actual work, all the math, or the various analytical tools detailed in section 8.4 Second, I have no idea what you mean by "self-praise", the entire whitepaper is written in a purely clinical tone. Third, the disclaimer you're asking about is a pre-publishing tag for academic review, it is literally explained in the whitepaper's description field on the Zenodo.org host page.

Yes I am being very blunt.
But why should I not be blunt about something that has been written in such a self-indulgent grandiose style?

Purely clinical tone!? Did you read it yourself?

[rblasingame]

@syzygy, why are you being so hostile?

[syzygy]

Let k represent the number of Pawns belonging to a single player that remain unpromoted at the conclusion of a game (0 ≤ k ≤ 8). The remaining 8 – k Pawns must have undergone a substitution event.

Why would you write it like this? If k pawns remain unpromoted, the other 8-k pawns "must have undergone a substitution event".

Sure, if you start with 8 pawns and k pawns do not promote, then 8-k pawns do promote. You're not saying anything at all here, except that what you say is wrong (*).

We define the allocation of these promotions across the available asset classes using three non-negative integer variables; m, r, q ≥ 0:
• m: The number of Pawns promoted to Minor Pieces (M): m∈ℕ0
• r: The number of Pawns promoted to Rooks (R): r ∈ℕ0
• q: The number of Pawns promoted to Queens (Q): q∈ℕ0
To evaluate this configuration space using classical combinatorial theorems, the established
unpromoted Pawn count (k) formally operates as a mathematical slack variable. This explicitly
transforms the system's boundary conditions into a strict linear Diophantine equation:
m + r + q + k = 8

"Formally operates as a mathematical slack variable", "strict linear Diophantine equation", etc. Why include all this filler?

This is just way too many words to express that, in chess, each player starts with 8 pawns and that each pawn can be promoted to a knight, bishop, rook or queen. And face it, you did not write this. An LLM wrote this. I say this as a compliment to the human race.

(*) And your equation is wrong because it does not account for pawns being captured.

By introducing Asset-Configuration Complexity as a third independent pillar of game theory,

So you have founded a "third independent pillar of game theory". Very neutral, almost clinical.

this
paper successfully shifts the strategic paradigm away from pure geometry and directly into the realm
of information economics and cognitive science.

Where is the "success" exactly?

The Asset-Configuration Model completely abandons
the micro-state noise of where pieces are located and when they moved. Instead, it focuses entirely
on the macroscopic physical reality of what assets remain in play versus what assets reside in the
graveyard at a game's conclusion.

Very poetic.
But material balance tables have existed since forever.

Through a rigorous multi-variable combinatorial summation bound
by strict weak integer composition constraints, this framework establishes a definitive, self-
documenting mathematical envelope around the human experience.

Maybe not so rigorous if you forgot about captures?

[syzygy]

@syzygy, why are you being so hostile?

Why should I have sympathy for a wall of unadmitted LLM slop?
You're not the first here to present a "revolutionary new framework" that claims to relegate 80 years of accumulated knowledge to the dustbin of history.

[OttoLau]

From the text:

2.4 Prior Work: The Geometric Limitations of Traditional Tablebases
The concept of pre-calculating and mapping endgame states to achieve constant-time lookup
velocities is not entirely unprecedented in computer chess architecture. The most notable
implementations are the Nalimov Tablebases and the subsequent Lomonosov Tablebases, which
successfully solved all endgame configurations containing up to seven and eight active pieces,
respectively (Nalimov et al., 2000).

Arent we still working on 8 piece tables?

And also why so many fancy words in the text, i cant understand a thing!

[syzygy]

And also why so many fancy words in the text, i cant understand a thing!

I think the paper can be summarized as follows:
- there are at most 300,586 possible material configurations for each side.
- so there are at most 300,586 x 300,586 = 90,351,943,396 possible material configurations for both sides.
- this is a manageable number. One could make a database with a few bytes per 2-sided configuration.
- the author needs 37 pages to say this.

Section 7.3 proposes 8 bytes per entry:

This 8-byte block provides a generous hardware envelope to store critical game-ending metadata, such as deep strategic evaluation metrics, reinforcement learning heuristic weights, and global human player win/loss/draw ratios.

Sure why not.

Page 33 contains Python code which seems to calculate these numbers without distinguishing between knights and bishops.
Page 34 contains Python code which does distinguish beween knights and bishops.

I don't know if the number is correct. I guess I could ask ChatGPT for the answer.

[syzygy]

I don't know if the number is correct. I guess I could ask ChatGPT for the answer.

in chess, what is the total number of possible combinations of white material that could appear in a legal position ? Do not distinguish between light-squared and dark-squared bishops.

Treat a white material combination as a vector

(P,N,B,R,Q),

with the white king always present and with all bishops counted together.

For a given number P of surviving pawns, at most 8−P promotions can have occurred. The original allocation is:

Q≤1,R≤2,B≤2,N≤2.

Therefore, the minimum number of promotions required for a material vector is

max(Q−1,0)+max(R−2,0)+max(B−2,0)+max(N−2,0).

The vector is possible precisely when

max(Q−1,0)+max(R−2,0)+max(B−2,0)+max(N−2,0)≤8−P.

Counting the solutions gives:

Code: Select all

White pawns P	Material combinations
8	               54
7	              135
6	              261
5	              443
4	              693
3	            1,024
2	            1,450
1	            1,986
0	            2,648
Total	            8,694

Thus, the total number of possible white material combinations is

8,694.

This includes combinations consisting only of the king, and does not distinguish light-squared from dark-squared bishops.

Hmm...
54 = 2 * 3 * 3 * 3 is correct. 0/1 queens, 0/1/2 of each of N,B,R, so 2 * 3 * 3 * 3.
The other entries are probably correct as well.

It seems the 37-page paper distinguishes between captures pawns and captured pawns that were promoted to knight, bishops, rook, queen. Of course that makes little sense and just wastes space in the database.

With 8 bytes per entry, 577 MB of storage would apparently be enough "to capture the human experience".