Definition of Key Squares vs. Critical Squares

Technical questions regarding Openings, Middlegames, Endings etc.
Paul McKeown
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Definition of Key Squares vs. Critical Squares

Post by Paul McKeown » Fri May 28, 2021 7:57 pm

Wikipedia equates the two terms:
https://en.wikipedia.org/wiki/Key_square wrote: a key square (also known as a critical square) is a square such that if a player's king can occupy it, he can force some gain such as the promotion of a pawn or the capture of an opponent's pawn
Here there is no reference to establish this definition, but there is an appended bibliography, which includes, inter alia, Müller and Lamprecht, 2007.

But elsewhere Wikipedia, whilst also equating the two terms, defines them differently:
https://en.wikipedia.org/wiki/King_and_pawn_versus_king_endgame#Key_squares wrote:The first concept that needs to be introduced is that of the key square, also known as a critical square. A key square is a square such that if White's king occupies it, White can force the pawn to promotion, regardless of where the black king is and regardless of which side is to move, and against any defense.
In this instance, they reference Müller and Lamprecht, 2007, which is Secrets of Pawn Endgames, published by Gambit.

I don't have Müller and Lamprecht, 2007. I do have their earlier, more general work, Müller and Lamprecht, 2001, Fundamental Chess Endgames.

This work defines key squares as follows:
Definition: when the king occupies a key square, this secures the win, no matter where Black's king is.
However it does not seem to have a definition of corresponding square. However the term corresponding square does seem to arrive undefined a few pages later:
The game shows that Black can't defend his pawn if the white king reaches d6. This means that the squares d6, e6 and f6 are critical squares of the g6-pawn (if the white king occupies one of them the pawn is lost). If the pawns are blocked, the three squares directly adjacent to the pawn are critical. For White, the critical squares of the g6-pawn are also key squares, because taking the pawn reaches a winning position.

With Black to move it is different. He can reach the critical squares (d6, e5 and f5) of the g5 pawn using the opposition (fight for three adjacent squares) but this is not sufficient because White's king can defend the key squares of the g6-pawn
.

So FCE it would appear that occupying a key squares wins, but occupying a critical square might gain a pawn but only wins if it also happens to be a key square.

Reading Müller, Chess Endgame for Kids, there are specific and different definitions for key square and critical square:
If the attacking king can reach a key square of the pawn then the attacker always wins
We define a critical square as one that, if reached by the attacking king, it can force the capture of the enemy pawn.
It then goes on to elucidate that critical squares may or may not also be key squares leading to a win.

Checking other endgame books doesn't make things much clearer.

Grivas, Practical Endgame Play - mastering the basics gives definition of critical squares but does not seem to mention key squares. It's definition of critical squares seems to cover the case, however, that Müller uses for key squares.

Dvoretsky's Endgame Manual defines key squares:
Key Squares are what we call those squares whose occupation by the king assures victory
.

There does not seem to be mention of critical squares.

van Riemsdijk & Hajenius, Veldjes Tellen, 1994 (Dutch language) defines Kritieke velden:
Kritieke velden zijn alle velden die, als ze door de koning van de aanvallende partij bezet worden, in een gewonnen stelling resulteren en waarbij het niet uitmaakt wie er aan zet is, noch waar de verdedigende koning zich bevindt
Thus here "critical square" seems to be the term that Müller uses for key square. Moreover, there does not seem to be a definition of "sleutel velden" or anything else which would seem to correspond with "key squares".

Kere's Practical Chess Endings appears to omit both terms.

Averbakh and Maizelis, Pawn Endings seems to muddy the waters further:
We are forced to conclude that the game is decided by the white king's occupation of QN7 (or Q7). We shall call squares such as these critical, because when White controls them Black is placed in a critical position. Even more correct is to refer to them as key positions, for White must set up that situation in order to queen his pawn.
(I have to say that I find that woffle particularly unhelpful!)

Fine's Basic Chess Endings does not appear to mention either term.

Anyone able to clarify matters for me?

Nick Ivell
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Re: Definition of Key Squares vs. Critical Squares

Post by Nick Ivell » Sat May 29, 2021 12:46 pm

I wouldn't want this excellent question to disappear without trace, even though I only have a personal opinion to offer.

I would like 'key' to mean 'important'; 'critical', I would like to mean 'the difference between winning, losing or drawing'. In other words, I'm giving to 'critical' something of its medical meaning: hovering between life and death.

Remember learning about the opposition in K & P v K & P? How disappointed I was when I found out that winning the pawn did not necessarily mean a winning position! By my definition, the square which allows the attacking K to penetrate and win a pawn and the game, is critical.

Right, I'll run away and hide now, aware as I am that I've only offered a linguistic preference.

Still, at least I've offered something, after all the work Paul did in framing the question.

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Matt Mackenzie
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Re: Definition of Key Squares vs. Critical Squares

Post by Matt Mackenzie » Sat May 29, 2021 7:12 pm

And in contrast, a "key square" might be d5 in a Najdorf Sicilian. Vital in many lines, but not normally going to win the game by itself.
"Set up your attacks so that when the fire is out, it isn't out!" (H N Pillsbury)

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IM Jack Rudd
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Re: Definition of Key Squares vs. Critical Squares

Post by IM Jack Rudd » Sat May 29, 2021 7:57 pm

In the world of chess problems, "critical square" has a different definition; it's a square on which you can play interference tactics.