Evaluation of Critical squares / Key Squares

Hello my favorite Chess Community,

I am struggling right now with a specific topic and would really like to understand the evaluation process in order to determine it. I am trying to understand the concept of Key squares in Chess and I hoped you could either explain the specific thinking process (just for the evaluation of all the key squares in a specific position) or at least point me to some "really" good resources that do explain it step by step to me so even an idiot would theoretically be able to grasp it. Thank you very much for all of your help on this topic in advance. Below is a specific position that is included in one of my study resources. Here the following marked with a blue circle are "apparently" the key squares. e2, e3, and d4 are Key squares in the below diagram. I wonder why?

Example 2 is the following... where the key squares are marked in green.....

Here is example 3

If you could kindly try to explain the methods in order to evaluate these specific key squares in those diagrams and / or recommend me 1 or 2 books which explain this in a step by step approach, that would be very helpful. One more time, thanks a lot.

These questions have to do with the opposition or distant opposition in king and pawn endgames. If you can reach one of these critical squares with the other side to move, you'll place them in zugzwang.
Any endgame book should cover this topic, or Google for internet material.

Hi Lizani,

Many thanks for your reply.

Yes, this makes sense, as the other side will have to give way after reaching those squares but what I don't fully understand at the moment is what is the exact method to figure out that these are critical squares? I do know about the concept of Opposition but I struggle to determine right now why for example in example 1 e3 and e2 are critical squares? I can see that d4 is a critical square as whoever side's King reaches this square will either promote the King or be able to defend it as the Key squares are laying just in front of it being c5,d5 and e5. In example 2 I believe I have understood why these specific squares are "critical" squares... it's because if the white King can reach any of them the black pawn will fall. Either by reaching e2 or first of all f2 and the idea of Opposition comes into play and I would be able to move the d pawn to d4 and then infiltrate with my King from behind taking the black pawn and win the endgame! Example 3 I also still don't fully understand. Yes, I mean it makes sense that the white King tries to take the pawn on g4 in order to create a passed pawn. Okay, I can probably get my head around this example too come to think of it. I was just wondering why c7 for example is not also a critical square, as white's king could infiltrate and eventually try to queen his d pawn. After counting I can see it would take white a total of 12 moves to queen and it would take black a total of 11 moves to queen. Is this the reason?

Understanding the distance between the Kings is the fastest way to determine who holds the advantage. Count the squares between them: an odd number of squares means the Kings are effectively "face to face" in opposition. If one King is forced to move aside, it permits the other to advance.

By using a pawn move as a "reserve tempo," you can force your opponent to move their King. This allows your King to step forward and control the key squares necessary for the pawn’s safe journey to promotion. In the endgame, the King must open the path for the pawn, rather than following behind it.

White to play (White wins):
The King must lead by example, and the pawn provides a vital extra tempo when the King needs it.
https://lichess.org/analysis/4k3/8/8/8/8/8/4P3/4K3_w_-_-_0_1?color=white

Black to play (Draw):
The King has no tempo to spare, meaning the pawn cannot provide the necessary help to break the opposition.
https://lichess.org/analysis/4k3/8/8/8/8/8/4P3/4K3_b_-_-_0_1?color=white

Both boards are set up identically; the difference lies entirely in the tempo.

If the pawn is on edge of the board (a or h file), the defending King can hide in the corner preventing the pawn form promoting. That's another key square. What would be required is a piece that can attack the king in the corner. The bad bishop won't succeed.

I think that, to a large extent, it is a lot of trial-and-error searching and examination that locates key squares. I have my doubts about whether or not it is very often practical to do over-the-board key square analysis. In certain examples (like the one with the pawns on c2 and d3) the sort of situation may be simple enough and common enough in books that one can partially remember and partially work out what is important.

You can better understand a position if you try out the same position but reverse who's turn it is to play first.
OP Example 1:
White to play and mates in 28 moves.
https://lichess.org/analysis/8/8/8/1p6/1P6/3P1k2/3K4/8_w_--0_1?color=white
Black to play, but white still mates, but this time in 22 moves
https://lichess.org/analysis/8/8/8/1p6/1P6/3P1k2/3K4/8_b--_0_1?color=white

OP example 2:
White to play and mates in 22 moves.
https://lichess.org/analysis/8/8/8/8/5k2/2pP4/2P5/4K3_w_--0_1?color=white
Black to play and because of the tempo advantage draws the game.
https://lichess.org/analysis/8/8/8/8/5k2/2pP4/2P5/4K3_b--_0_1?color=white

Op example 3:
White to play and mates in 34 moves.
https://lichess.org/analysis/6k1/3p4/3p4/3P4/4P1p1/6P1/8/K7_w_--0_1?color=white
Black to play and draws because of the tempo advantage.
https://lichess.org/analysis/6k1/3p4/3p4/3P4/4P1p1/6P1/8/K7_b--_0_1?color=white

You're starting with too complex positions.

Here's a much easier example. Imagine a K + P vs K endgame. Now let's place a white pawn on e2. In this position the key squares are d4, e4 and f4. So in this position if a white king occupies the e4 square then it's a forced win for white. On the other hand if the black king occupies e4 then it's a forced draw.

Why is this the case? For white as pawn is on e2 and king is on e4 white has a reserve tempi so can always win the opposition. On the other hand if black king is on e4 then white king can't get in front of the pawn with a reserve tempi so black can maintain the opposition and white can't make progress as black maintain access to key squares from e4 and e5.

When white pawn advances key squares advance with it so it remains 3 squares 2 tiles in front.

https://lichess.org/analysis/8/8/8/8/4k3/8/4P3/4K3_w_--0_1?color=white is always drawn regardless of whose move it is
https://lichess.org/analysis/8/8/4k3/8/4K3/8/4P3/8_w--_0_1?color=white is always winning regardless of whose move it is

Once you understand that position you can then move on to more complex ones

It's so funny. I took the time to post the same thing in a prior post 4.

@Toscani said in #8:

It's so funny. I took the time to post the same thing in a prior post 4.

It's what happens when I don't check diagrams closely enough. Although what I posted was mainly what I remembered from Dvoretsky's Endgame Manual. However I'll add that if you check my post in 7 it helps explain your positions in 4.

I mentioned that the key squares are d4, e4 and f4. When it's white to play white can play Ke4 after black plays Ke6 so reaches key square and wins. When it's black to play first black is a bit more advanced and can counter Kd3/e3/f3 with Kd5/e5/f5 with opposition and thus controls key squares so white can't reach them.

I'll add that the opposition approach you mentioned is usual teaching method but since he asked about key squares I figured that was simplest example.

The other rule you can use for the endgame is if you have 2 out of 3 of the following endgame is won:

1. King is in front of the pawn
2. You have the opposition
3. Pawn is on 6th Rank

So you can use opposition, key squares or the rule I gave above to quickly evaluate K+p vs K endgame.

Long answer incoming - I hope it helps.

A critical square indicates a position on which if your king sat, you would win no matter which side was to play. You can derive them (in the black and white diagram) by working backwards from c5 - since if the white king sat on c5 there would be no defense of the b5 pawn no matter where the black king sat. You can then put your king on d5 and find you still win the b pawn no matter which color is to play, and also e5.

The 3 critical squares you have circled indicate places where if your king sat, there would be no defense to stop you from reaching one of the c5-d5-e5 trio, no matter which color is to play, and therefore from those squares you will always win the b pawn.

The most difficult position in the diagram would be with the white king on the critical e3 square and the black king on d5 with white to move since the position must be won with a pawn race instead of brute force to the c5-d5-e5 squares.

If the white king can not reach any of the 3 circled squares, he can be also kept from c5-d5-e5 and will not win the black b pawn.

Example 2 has the exact same situation - derived from the same trio of squares directly beside the black pawn, this time d3-e3-f3, and the three to the other side b3-a3 and if there were another file to the left of a, there would be a third critical square. Reaching the indicated critical squares will allow white to force his way to the pawn to win it no matter which side is to play.

Example 3 is more complicated to play out, since the critical square theory is compounded by the need for corresponding square theory to decide if the white king can force his way to the critical squares. The square d3 for example corresponds to g6 where if the white king sits on d3, the black king must move onto g6 or white will force his way to one of the critical squares.

Happy to elaborate if that isn't clear enough. If you have any other positions to show without giving the answer we can derive the critical squares on the thread.