The Beautiful Geometry of Corresponding Squares | Endgame Class - NM Caleb Denby

National Master Caleb Denby follows up to his class on "Corresponding Squares" with a session on the different systems to determine corresponding squares. Don't be afraid to watch this advanced class twice.

2020.08.19

[zanti]

I have my doubts that the analytic method described in this video is totally reliable. It's more like, often it works but sometimes it doesn't, or, as with many of the maxims found in chess books, the real answer is, "it depends." For example, consider the following position, which is adapted from one found in "Basic Chess Endings" (#99, study by Folbys):

White: King on b1, pawns on a2, a3, c5, d4, d3, g3. Black: King on f6, pawns on a4, b5, c6, d5, g4.

Analyzing as in the video, I suppose we start by looking for key squares where White definitely wins. The f4 square has to be one, winning the g-pawn for sure. A second key square should be a6, penetrating the queen side and winning the pawn on c6. The shortest path between f4 and a6 goes e3-d2-c3-b4-a5, while Black's shortest path to stop the invasion must be f5-e6-d7-c7(or c8)-b7. Great, we've established some corresponding squares: e3/f5, d2/e6, c3/d7, b4/c7, and a5/b7. And, there are a couple of those mini-triangles along the path:

(a) Mini-triangle e3-d2-e2 matches up with f5-e6-f6, therefore e2/f6 are corresponding squares.

(b) Mini-triangle d2-c3-c2 matches up with e6-d7-e7, therefore c2/e7 are corresponding squares.

So far, so good, except, hmm, which mini-triangle do we pick? Neither one produces an ambiguity. OK, maybe it doesn't make any difference - we've established e2/f6 are corresponding squares, and the Black king is on f6. So, let's just extend e2 to c2, and we conclude the correct first move must be Kc2. Unfortunately, that's the wrong move - the correct first move is Kc1. It turns out c1/f6 and c2/e7 are corresponding squares. So, we have a weird arrangment for the corresponding squares in this position: extending f2 to d2 to b2 works just fine, as does extending f1 to d1 to b1. However, on the c file and e file the corresponding squares get flipped: c1 and e2 match up with f6, while c2 and e1 match up with e7. All of which leads me to conclude that, as simple as king and pawn endgames may appear at first glance, a complete mastery of them is humanly impossible.

[chrisinselwyn]

I have been eagerly awaiting the next lecture on corresponding squares thanks for the brilliant content Caleb

[dmasterify]

This is good information. Reminds me of when I first learnt about triangulation and opposition. A child shall lead the way.

[kentcen]

oh my goodness, this is very advanced material! excellent work explaining it! :)

[rizka]

Lovely stuff yet again! While this is my dear endgame theme, I wasn't aware of this method either. And it seems to be the way to solve many of these studies which otherwise require memory which goes beyond my capability!

[atnorafertsera]

Beautiful lessons, have struggled with the concept for quite a while

[niravapurv]

Another brilliant video, thank you so much.
Now I do strugle with my limited brain to fully understand this. Most difficult i find to understand/identify where really the Key squares are and how squares that are restricted influence this system.
So my first question. In the last example.. at 55:15:
1. Isn't there also a Key squares at b5? Perhaps its easy for black king to Block us out there.. but they still have to calculate corresponding squares right?
2. The black king is at c6, isent he corresponding square actually d4, and then the idea is that d2 is in pair with d4??
3. So in this last position, white is winning with Kd2 because in reality the corresponding square is c8 and he cant step there? Or there are no fully corresponding square?
4. Should there not be posibilities for 1 side to step on a square that the corresponding square for the opponent is blocked or restricted... or there will in reality always be another square nerby that is also corresponding.. out of this grid system?

[ss]

Great info as always! Keep up the great work Caleb

[aminechnnoufi]

Me: spending one hour to understand this
Also me when I’ll have this position : blitzing Kb2

[dmasterify]

Ratid! I never knew they teach astro physics in Chess.