Chess Mania

Numerical Chess: Revealing the Numerical Structure of the Game
NUMERICAL CHESS – CURRENT STATE 2026
Episode 25 – Structural Analysis [9] – What Can We Know Without Seeing the Position?
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Numerical Chess — Credo
Chess positions are numerical structures.
Pieces create connections that generate measurable influence.
The game unfolds through the transformation of these numbers.
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Take a look at the attached simplified NC algorithm table.
This table contains only data about the number and zonal distribution of
• IC (Invasive Connections)
• AC (Advancing Connections)
• BC (Base Connections)
extracted from a particular game position.
Now imagine the following challenge:
You are asked to describe this position, evaluate it, and suggest what both sides should do — without seeing the board.
Is that even possible?
First of all, it must be said:
There are certainly millions of positions that could display similar data regarding the number and zonal distribution of IC, AC, and BC. Visually, many of these positions would look very different from one another.
However, it is still possible to describe the numerical structure and to provide a structural evaluation of the entire group of positions.
Everything beyond that becomes partly speculative — for example, which pieces are actually on the board.
Since the author of these lines had to see the position in order to enter the data into the table, his faithful AI collaborator AI-Sha was asked about the matter.
At first, she was shown only the table — not the position itself.
Most notably, her structural analysis — the most important part of the evaluation — proved to be astonishingly accurate and, among the millions of possible positions with similar connection data, almost perfectly applicable to the actual position.
Here are some excerpts from her observations:
“This is a very interesting exercise, because the table actually contains far more positional information than one might expect without seeing the board. Structural connections alone already reveal a surprising amount about the phase, balance of forces, and strategic tendencies of the position.”
Game Phase
“Late middlegame or endgame.”
In fact, it was an endgame.
But what kind of endgame?
AI-Sha proposed several possibilities, one of which turned out to be remarkably precise:
“Rook + 3–4 pawns each.”
Indeed, in the actual position White has a rook and four pawns, while Black has a rook and three pawns.
No other pieces are present except the kings — whose approximate placement AI-Sha could also infer from the connection structure.
General Evaluation of the Position Group
AI-Sha’s answer:
“Approximately balanced, with a slight advantage for White.”
This was fundamentally correct. In the actual position, White has only one concrete winning motif; otherwise the game should end in a draw.
Naturally, AI-Sha also pointed out structural asymmetries in AC and BC, which generally give White better long-term prospects. This is because AC and BC can, in principle, be transformed into IC, and White has significantly better chances in this respect.
White needs this advantage, of course, because his current IC values are still well below the tactically critical thresholds that AI-Sha knows and has partly calculated herself.
She wrote much more, and from a purely structural perspective, almost everything was correct.
Afterwards, the actual position was finally shown to her, and she was asked whether anything about it surprised her.
She replied:
“Yes — to some extent it is a surprise, but interestingly most structural conclusions remain remarkably consistent with the real position.”
And further:
“The real surprise is not the board. The real surprise is how much was already correct without seeing it.
From the connection numbers alone we correctly inferred:
✔ structural imbalance
✔ initiative vs. structural depth
✔ moderate pressure level
✔ absence of decisive tactical overload
✔ stable but asymmetric structure
That is remarkably strong information for a purely numerical reading.”
She added:
“This position is actually an excellent teaching example. It shows that structural connections alone already encode the strategic DNA of a position.”
And also:
“Even without the board, we could already see:
• who has the initiative
• who has the deeper structure
• which side benefits from time
• which side must act sooner
And the real board confirms most of these structural signals.”
A Final Question
Finally, one more question — somewhat rhetorical from the perspective of Numerical Chess:
How could AI-Sha say so many correct things based solely on structural connections?
The answer is already contained in the Credo:
“Pieces create connections that generate measurable influence.”
Yes — pieces create connections.
Some of these connections can be used for subtractions (“capturing”) of opposing units.
Checkmate itself is the terminal connection.
The pieces themselves, numerically speaking, are variables.
Once a piece is subtracted, it can no longer create connections.
Connections are the true core of the game of chess.
That is precisely why a purely structural analysis of connections is already so informative.
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Numerical Chess
Exploring the hidden numerical structure of chess.

Numerical Chess: Revealing the Numerical Structure of the Game
NUMERICAL CHESS – CURRENT STATE 2026
Episode 23 – Structural Analysis [7] – Recognizing and Counting Connections [6] – Exercise 5
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Numerical Chess — Credo
Chess positions are numerical structures.
Pieces create connections that generate measurable influence.
The game unfolds through the transformation of these numbers.
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Exercise 5 – Recognizing Base Connections (BC)

In this exercise, the task is to count all Base Connections (BC) for White and Black.
Base Connections represent the structural foundation from which AC and IC can develop.
The zonal BC values (shown in the blue rows of the table) are, as always, already entered in the Numerical Chess Algorithm Table.
Below you can find the individual Base Connections generated by White and Black in both strategic zones (20-zones) and their respective sub-zones.
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White
Zone 1
Ra1 → {b1,c1,d1,e1(x-ray),a2,a3}
Qc2 → {b1,c1,d1,a2,b2,d2,e2,c3}
Nc3 → {b1,d1,a2,e2}
Rd1 → {a1,b1,c1,e1,d2}
e2 → {d3,e3}
f2 → {e3}

BC = 26
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Zone 2
Ra1 → {d1,e1,f1,g1}
Qc2 → {d1,d2,e2}
Nc3 → {d1,e2}
Rd1 → {e1,f1,g1,d2}
e2 → {d3,e3,f3}
f2 → {e3,f3,g3}
Kg1 → {f1,h1,f2,g2,h2}
Bg2 → {f1,h1}
h2 → {g3,h3}

BC = 28

Black
Zone 1
Bb7 → {a8,c8,c6}
Qb6 → {d8,a7,b7,c7,c6}
Rc8 → {a8,b8,d8,e8,c7,c6}
Nd7 → {b8,b6}
Re7 → {e8,d7,e6}
f7 → {e6}

BC = 20
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Zone 2
Qb6 → {d8}
Rc8 → {d8,e8,f8,g8}
Nd7 → {f8}
Re7 → {e8,d7,f7,e6}
f7 → {e6,f6,g6}
Kg8 → {e8,h8,f7,g7,h7}
g7 → {f6,g6,h6}
h7 → {g6,h6}

BC =23
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Numerical Chess
Exploring the hidden numerical structure of chess.