Obstacles
The following position is the same as in the previous post, but now with the black king on a different position.
The problem is that the black king has no waiting room. The two squares that he needs to wait on contain an obstacle. He cannot use b5.
White can use that to get the opposition by force. By entering the attacking square f5, he can attack two squares in the opposition zone. Black cannot put his king on the defensive square b5 because it is forbidden. Black has no choice other than to enter the patrol zone. White can immediately take the distant opposition by force.
- 1.Kf5 Kb6 2. Kf6 or
- 1.Kf5 Ka6 2.Ke6
f5 = attacking square with double attack
b5 = defensive square with double defense. But b5 is taboo.
It is essentially a triangulation. But with an explanation why you can expect it to work (the obstacle b5).
Notice how this invasion resembles a double attack.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteCORRECTED
DeleteAlready it appears that the intuition that a common terminology would be helpful in finding commonalities between disparate phases of the chess game has been proven correct. GM Averbakh's intuition regarding the commonality of the generalized concept of double attack (not limited to direct attacks, but including higher order threats as well as “attacks” against squares as well as pieces) also appears to be vindicated.
On a different subject:
Here’s a cautionary note regarding relying on AI for definitive conclusions.
I asked Claude.ai a followup question.
Followup to the last question: describe the numbering of corresponding squares in detail with examples.
Edit
The numbering system for corresponding squares is a practical method to systematically identify and map these critical squares in endgame positions. This technique was developed by endgame theorists to make corresponding square analysis more precise and teachable.
The Numbering System
In the numbering method, you assign the same number to squares that correspond to each other. The process works like this:
Identify the critical zone - the area where the key battle will take place
Start with one king's position and assign it number "1"
Find where the opposing king must go to maintain balance, and also assign it "1"
Continue mapping all possible positions for both kings
Squares with the same number correspond to each other
Detailed Example: King and Pawn vs King
FEN: 8/8/4k3/4P3/4K3/8/8/8 w - - 0 1
Let's examine a classic position where White has a king on e4 and pawn on e5, with Black's king on e6:
White King Squares:
e4 = Square 1
d4 = Square 2
f4 = Square 2
d3 = Square 3
e3 = Square 3
f3 = Square 3
Black King Squares:
e6 = Square 1 (corresponds to White's e4)
d6 = Square 2 (corresponds to White's d4 or f4)
f6 = Square 2 (corresponds to White's d4 or f4)
d7 = Square 3 (corresponds to White's d3, e3, or f3)
e7 = Square 3
f7 = Square 3
How to Use the Numbers
The rule is simple: if White's king moves to a square numbered "X", Black's king must move to any square also numbered "X" to maintain the position's balance.
For example:
If White plays Kd4 (square 2), Black must respond with either Kd6 or Kf6 (both square 2).
NOTE: THIS IS ILLEGAL!!
If White plays Ke3 (square 3), Black can respond with Kd7, Ke7, or Kf7 (all square 3).
[End answer]
There was more to Claude.ai’s answer, but this is the part that caught my attention. It illustrates that AI systems (occasionally) are so focused on one aspect of a request that they completely miss another aspect.
TANSTAAFL!
DeleteI'm too headstrong to trust the judgement of anybody else. Digital or not. No worries.
DeleteAs a control, I asked Copilot Smart similar questions. It got the answers wrong just like Claude.ai. At first, it didn't realize that kings cannot be on adjacent squares. On the second attempt, it stalemated the lone king, but "assumed" that the superior side could occupy a corresponding square and win. It only got everything right after 3 attempts.
DeleteYou're right: TANSTAAFL!
I have gone to great lengths to understand how far we are away from AGI (artificial general intelligence). ChatGPT scores 2% on the AGI 2025 test (humans do around 67%). Science doesn't know how to solve this yet. In the direction they are trying it will take about a decade. If it is possible.
DeleteThere are other tries that seem to hold some promise. But nothing is proven in that area.