Back to the basics

Today I quit working on chapter 7 of SOPE.
Chapter 7 is about 4-6 pawns at one wing.
These problems are far too complicated.
So I decided to go back to chapter 2: king+pawn vs king+pawn (inspired by Montse).
In an earlier post I complained about the habit of composers to choose the most beautiful and hence the most exotic positions.
I will show you what I mean by this. You will be interested in my findings (at least I was:)
Have a look at diagram 1, part of a study by Grigoriev, used for explanation by SOPE.

diagram 1





















White to move and draw.
There is only one move for white.
The diagram is given with a lot of variants.

That is not enough to get a thorough insight of the position.
I explored the position with my Nalimov tablebase and this is what I found:

diagram 2.





















White to move and draw.
red = white is lost
blue = draw
green = white wins

From this picture it is easy to see why the study of Grigoriev is a special and not a common position.
The use of colored zones gives a much more common and a much clearer picture of what's going on in this position.
In the green area white can conquer the black pawn.
In the blue area white is in time to conquer keysquare b4 at the moment black snacks the white pawn.

Actually I hoped SOPE would do this work for me.
But it seems I have to do it myself.
Away with the beauty, come on clarity:)

Pfffew.

Learning pawn endings is very heavy.
There are so much things to learn.
I didn't know I knew so little.
And that there is so much to know.
I comfort myself with the thought that probably only a few people can go the same road, so I will definitely have an edge in the end(ing).
In the first place most people think that pawn endings are easy. And when they think it is, they will not put much effort in it.
And if in the unlikely case they do, they have to be prepared to work hard during a few months, without getting extra ratingpoints initially.
Because only when the knowledge is transformed to skill the reward will come.
And probably only after rook endings and other piece endings are mastered too.

It's so difficult that I have to take a break every now and then.
Then I relax by reading as much information about pawn structures as I can get.

I'm almost finished with chapter 6 of SOPE. Only 3 to go for the very basics.
And then: repeating, learn by heart, and doing as much pawn problems as I can get for a month or two.
And then the more complicated stuff, chapter 10-16.
But for now, one step at the time.
Pfffew.

Corresponding squares

I couldn't find a clear explanation of corresponding squares at the web, so I decided to follow the suggestion of PMD and write my own.
The theory is explained in SOPE, but I find it difficult to use it in such theoretical form in OTB play. So I try to make thinks more practical.
I develop my own terminology along the way


The simplest form of corresponding squares is the opposition.
In the next examples white is the attacker, who wants to win and black is the defender, who is happy with a draw.

diagram 1.



















White to move.
Black wants to protect his own half of the board.
Green = border area
Yellow = frontline
Not colored = hinterland

The attacker has moved his king from the hinterland to the frontline on square 6 (=f4)
To prevent white from invasion, black has put his king on the CORRESPONDING SQUARE (=f6). This square gets therefore the same id: 6
Every move of white along the frontline has to be answered by black moving to the corresponding square. Any other move will lose.
A corresponding square in the black camp has always the same id as the square in the white camp.

Square 6 on the white side is flanked by square 5 and square 7.
The same is true for square 6 of black.
So the black king will have no troubles in following the actions of the white king.
If white decides to obscure matters he can try to go to the hinterland, e.g. to square 13.
Square 13 has 3 connections with the frontline (square 4, 5 and 6)
There is a corresponding square in the black hinterland. This gets the same id: 13
From this square there are 3 connections to blacks frontline. So black can follow every move of white as long as he steps on de corresponding squares

The picture isn't distorted by pawns, so that will be no problem.
In the following diagram there are a few pawns that disrupt the pattern

diagram 2



















White to move.
Blue = keysquares
Yellow = frontline

To prevent white from invading, black as to move to the corresponding square.
The keysquares are just in the border area.
On files c, d and e you see no corresponding squares.
That is because the opposition doesn't play a role on these files since the kings can't approach each other here.
I called this the shadow area.
Black has only to make sure that he crosses the shadow area in time to step on square 2, in case white tries to pass on the queenside.
That shouldn't be a problem.
With pawns other elements come into play.
For instance black can counter attack against the white pawn, in stead of following the corresponding squares.

In the next picture you see a much bigger distortion of the smooth symmetrical set up.

diagram 3



















The border area is so distorted that the kings positions are shifted, so they must not be opposite anymore to keep the draw.
Notice that there are two squares with id = 4 on the white side.
If white heads for g2, the black king will counter attack the pawn on c2.
If the white king heads for 6 (= a1), he stands on a square next to 1 and 2.
Black is lucky he has a corresponding square at b5, next to his own 1 and 2.

This is a composition of Grigoriev, special in the sense that white has so little space to manoeuver that black can just follow.
If we shift the whole position one rank upwards, things become totally different.

diagram 4



















White has got a whole lot of hinterland for manoeuvring now.
If he plays 1.Kd1, he is next to 3, 4 and 5.
The corresponding square in the black camp is e5, which is next to 3, 4 and 5.
But since that square isn't available for the black king he can't prevent white from invading.
Notice that he can't go to e3 or f3, because he has to stay in the square of the white d-pawn, to prevent promotion.

Play can go as follows:
1.Kd1 Ke4
2.Kd2
This typical king manoeuvre is called triangulation.
The white king stands face to face with the black king, but since "der Temposchlucker ein Tempo hat geschluckt" (= the white king has lost a tempo) the black king has to give way!

2. ... Kf4
3.Kc1 and the black king is to late to protect the keysquares at queenside.

Now you know where my nickname comes from.
(From "Mein System" of Nimzowitsch)

10,000th visitor!!

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It took me 2 weeks to finish chapter 4 of SOPE.
Chapter 4 is about a small number of pawns. 2 or 3 mostly.
It was very tough, alot of problems took me 5-10 hours or more.
Some king moves look very counter intuitive, and I wanted to have the feeling that I could find such moves OTB.
I'm afraid I didn't quite succeed.
Especially triangulation and corresponding squares are difficult. I understand the principles, but I'm just not able to apply them every time in a correct manner.
But I intend to repeat the basic chapters 1-9 a few times, to learn the exercises by heart (spaced repetition and flashguards, remember?) and to do as much exercises with 2-3 pawns and kings as I can find. (Suggestions anyone? I have allready Polgars endgame brick and CET from Convekta)
There is a limited amount of fighting methods with few pawns, and I want to know them all by heart.

I did some research and found the following statistics in a database with 1,600,000 quality games.

3% pawn endings
1.5% knight vs knight
3% bishop vs bishop (48% draw)
3% bishop vs knight (35% draw)
32% rook vs rook (40% draw)

So it looks a bit silly to put so much effort in pawn endings, but it is the basis for all other endgames. Since you always have to know whether it is favourable to trade the last pieces.
It is clear that after pawn endings I'm going to study rook endgames.
I'm allready trying to steer my middlegames towards rook endings and the last 5 games I managed to get them 2 times on the board. It's a pity I don't know what to do with them, yet:)

Seeing the invisible

In books about endgames there are always a lot of positions from composers to study.
SOPE is no exception.
The problem with that is that a composer always tries to generate the most exotic position.
Allthough that's good to show the beauty of the game, it's not very helpful if you want to learn the game.
For that you have to find the most common positions and analyze them thoroughly.
I have done that for you for the following position.

diagram 1





















White to move and win.
To evoke your curiousness I coloured the winning moves for white.
All other moves result in a draw.

First you have to understand what this position is all about.
In order to win white has to conquer the black pawn.
To that end you have to know what the keysquares are (see diagram 2)

diagram 2





















The keysquares are coloured blue.
So white has two targets to head for.
The only way black can defend the keysquares is by opposition.
If white moves to b5 then black has to occupy b7.
The same with f5 - f7 and so on.
So the opposition is decisive.

Because of the pawns there is an area where the opposition has no meaning.
I call this the shadow-area.
(coloured red in diagram 3)

diagram 3





















If both kings are in the shadow area they can't approach each other because of the pawns who are in their way. If black is on the same file as white in the shadow area, the position is a draw.
This works as follows: if white leaves the shadow, black does the same, but chooses immediate the opposition. If white wants to cross the shadow, he has to make sure the black king isn't on the same file
Further the area of black is limited because he has to stay in the square of pawn d5, to prevent a pawn sac.
So if the first move of white is e1, e2 or e3 (step into the shadow) the position is a draw.

diagram 4





















If white stays on the green line (by 1.Kf1 or 1.Kf3) black can get the opposition by 1. ...Kf7 (distant opposition, same color)
The green file is the file were the first opposition can take place.
The only way to prevent that black can seize the opposition is by going to the g-file.
1.Kg3 is the most effective, because it heads towards the keysquares, but 1.Kg1 and 1.Kg2 don't give the advantage away.

In the next diagram the paths of both kings are shown.
Black isn't allowed to get the opposition.
Hence the zigzag

diagram 5





















White to move first. Every time black threatens so seize the opposition, white escapes to the g-file. The moment black steps to the g-file it is time to change targets and to head for a5.
(see diagram 6)

diagram 6





















Since white's king can stay always 1 file to the left of the file of the black king, black can't overtake white in time. So when white moves to a5, black steps on the b7 square.
The next move white takes the opposition with Kb5 and the black pawn will be lost.

When you see these invisible patterns, the win is easy. Without them, it is near to impossible to calculate them accurate in a few minutes.

The position above is very common. When you move the same position up and down along the ranks, or to the left or right, diffirent situations appear. But it helps to know the common idea's.
I hope you like the analysis.

Unexpected side effects

If I compare my rating from a year ago with my rating now, there isn't much difference.
In spite of training tactics rigourously.
The reason I kept on training, was, besides curiousness, the feeling that I was developing a rocket launcher. (Sorry for the exaggerated style of this post, but that's they way it felt.)
If the rocket launcher went off during a game, I simply blew my opponent off the board.
If I "could come into my own" I crushed them.
It only happened seldom that I got a position I could call my own.
Playing gambits alone wasn't a garantee for that.
My opponent had to cooperate.
If he didn't, I tried to force matters.
Most of the time I came in time trouble in better position, so I had to accept a draw.
The amount of draws with under 25 moves in my games is amazing.
Solely because I tried to get the utmost from every move, thus generating time trouble.
Whithout getting the position I wanted in time.
I tried to solve this by training even more tactics, but that didn't work out.
I'm just not good enough yet to crush every opponent within 25 moves.

So I worked hard for a year, with the feeling getting better every day, puzzled by the fact that it didn't pay off.
But the last 5 games I played were different.
Since a few weeks I study pawn endings. The study itself is to premature to yield results.
But it has an unexpected side effect.

I have accepted the fact that a game can last more than 30 moves.
This means that the pressure to finish off my opponent long before the 30-move mark is reached, has disappeared.
The effect is that I'm no longer trying to get the utmost from every move, but accept every move that is tactical viable. I'm moving much faster now. (just as MDLM suggested in his article, actually)
Since I'm looking forward to the endgame I'm not afraid to trade off pieces anymore.
I actually use my tactical skills to do that in the fastest possible way.
So my games are getting longer and longer.
But I still have a rocket launcher in my backpack.
And if my game has 3x as much moves, I have 3x as much chance to launch it.
I'm much more dangerous in a long game than I expected. Even with no queens or few pieces on the board.
Ok, I've played only 5 games (3 wins, 2 draws) this way, but since they feel so different, it's time to explore this trend. Let's see if the tactical training will yield results in second wind.
Or maybe I'm just hallucinating.

Now I'm experimenting with longer games and endgames I'm starting to ask questions about my openings. A gambit is good if it gives me the position I want. If it is declined, the opponent must have a worse position, otherwise it isn't a useful gambit. If it is accepted it must get me in a position where I can fire my rocket launcher. In practice I have only succes in 30% of the cases.
That means that in the other 70% of the cases I'm left with a bad pawn structure or a pawn less. That's not a very good start for a long game.
In the Alapin I don't play a gambit but I accept an isolated queen pawn in exchange for piece play.
I belief that questioning these kind of openings is the begin of a more mature approach to chess.
Every starting chessplayer has to experiment with gambits to get the hang of active and tactical play. But at a certain moment the stage of infancy must be left behind.
Maybe this is the right moment.

My first win by a pawn ending!!

Today at the club I had black and played the Icelandic gambit.
My opponent declined and I could inflict him with an isolated queen pawn.
In stead of forcing matters, I just started to press on the weak pawn.
Every tactic I used led to the trading off of more pieces.
Playing open positions and the use of tactics is the fastest way to an endgame indeed!
There is another advantage of playing endgames.
The average length of my games is about 20-25 moves or so.
Playing an endgame with 60-75 moves means that my opponent has 3 x as much opportunity to make an error. So if there is a difference in strenght, the chance that this results in a point is 3 times higher. Very interesting!
I always felt that I accepted too much draws from weaker opponents.
In defending his IQP he made an error indeed which costed him a pawn.
The pawn ending was an easy win.


From an exercise in SOPE:























White to move and win.
Calculating long lines is just a matter of knowing the compounding short lines.
A few weeks ago, I could not solve this problem by mere calculation.
Today it was easy.
In order to win, white has to get the black pawn.
First I allready knew that there isn't enough space for the white king to go thru the middle.
Second I knew that it is possible to win the pawn by going along the right side of the board.
Third I knew if I did that, that black has a forced draw because he's left with a bishop's pawn at the 2nd rank against a white queen.
So the right method is going along the left side to conquer a key square (a5 or b5) of the black pawn and to sac your e-pawn.
The only calculation I had to do is that 1. Kb3 isn't good because of 1. ... Kd4
The theory of corresponding squares told me that 1. Kb2! is the winning move.
No way that I could find this in the past.
But after only a few weeks of studying pawn endings, it was actually quite simple!

Feedback on sloppy thinking

The comments of the Knights on my blog are very important to me.
With an ICT-background I allways despise "implicit assumptions".
In the mean time I perpetrate this crime often myself.
But gladly there are allways Knights who are willing to show me the flaws in my reasoning!

I had for example the idea that a drawish opening was the fastest way to reach an endgame.
But there is no logic behind this implicit assumption, as FunkyFantom showed me with his comment:
The best way to increase your odds of reaching endgames is to play people as close to your own rating as possible.

He is right, of course.
The reason I don't reach endings is because I'm used to play on "bend or break".
This means that I take much time to force things.
The result is either a crushing win or a draw in better position because of time trouble, or a loss when I'm making a mistake.
But the reason I play so forcefully is that I have only one plan: attack the king.
There is no plan B. Especially when I can't find an immediate win I come in time trouble.
If there was a plan B (simplification to a promising -or at least equal- ending), I could play much more relaxed.
But I don't trust my endgame skills, so I never let that happen.

Actually to play open games as I do is the fastest way to reach an ending, because in an open position it is easier to trade pieces.

Episode IV A new hope

I start to see the glimpses that it might be possible to master pawn endings.
I'm getting an idea of the tools that are needed for this work.
There is of course an enormous amount of work to do, but the notification that it is not impossible is important to me.

What works very well is the method of visualisation of long lines with the eyes closed in combination with spaced repetition.

SOPE	#exercises	#repetitions
Chapter 1	19	4
Chapter 2	10	3
Chapter 3	10	2
Chapter 4	14	busy
Chapter 5	N/A	N/A

Yesterday I managed for the first time to get a rook ending.
I was a pawn up, but alas I was in time trouble so I traded it for a draw.

An overview of the remaining part of the game.

In comparison to other people of my level, I'm very good at the opening, taking the initiative and starting a king attack.
Since the Corus tournament I started to study pawn endgames.
That made me realize that the skills as stated above, cover about 30% of the game.
I can play very positional, but in my case that means that I can place my pieces well for a kingside attack and know which lines to open to keep the attack going.
Very often I hear from my opponent that he underestimated the attack.

From the other 70% of the game I have no idea how to play it.
I will try to fix that the coming years.
I decided to begin at the very end of the game.
To learn pawn endings at a reasonable level will take me about 6 month's.
In the mean time I want to get an idea about the rest of the game.
I have not really an idea what sort of endings belong to the different openings.
I guess I have to look at the pawn structure then.
Let me try to formulate possible courses for the whole game.
Idea's are welcome!

The opening.
To my knowledge the following openings are somewhat drawish, en hence maybe a good way to get some endings at the board:

• The Caro-Kan
• The Petroff
• The London system against the KID

Other idea's about drawish openings / a better way to get and endgame?

Trading off pieces.
The next phase is trading pieces to get an endgame.
The most common endgames are:

• bishop vs bishop
• bishop vs knight
• knight vs knight
  
• rook endings

Playing the piece ending.
From these the rook endings seem to have the most possibilities to give unexpected results, especially if one side knows how to play them and the other don't.
So I will try to steer my games in the direction of rook endings.

Simplification.
An ending with pieces can be simplified to a pawn ending by trading off the last pieces.

Playing the pawn ending.
Yeah.

Post pawn ending.
After the pawn ending some other endings can emerge by (minor) promotion.
Of course it is important to know how to play these.
The most common are:

• Queen vs queen
• Queen vs pawn at 7th rank
• Queen vs knight

This is only the first time I try to formulate these things.
Idea's and suggestions are welcome!

The Magic Touch

I feel a bit like King Midas with the touch of gold.
Last friday at the club I tried to get an endgame.
The games at the club aren't rated, so I use them always to experiment.
My opponent had black and played the Caro Kan.
Since the Caro Kan is played by guys who want to draw with black and play for a win with white, I thought I had a good chance to get an endgame.
But since I'm not used to take much care for my pawns during the opening, he managed to grab one and to infer a double pawn at my queenside.
Oh, that greed from those materialistic guys! Can't they leave a pawn alone?
So I crushed him in 18 moves since he had forgotten to develop and his king was still in the middle.
The same happened a few times at FICS.
How on earth can I get an endgame??

No nonsense

Yesterday (and last thursday) I showed you a problem I have trouble with.
As you probably not know I'm a little self opinionated:). So if others give me good advice my first reaction is most of the time to think that it's nonsense.
But when I continue to struggle then very often I get back to the advice asking myself "what did he actually mean?"
The same happened with the advice that Takchess gave me last thursday on my pawn endgame problem.

This was (part of) the problem:
diagram 1





















White to move and draw.
Why does 1.Ke7 draw while 1.Kf5 results in mate in 20?

The advice of Takchess was:
I suppose a way to solve this is to visualize the end position for a draw (there may be multiple options).Then determine what position is one move away from forcing that position. Then determine what position is two moves away from forcing that position. Then repeat as necessary.

After rejecting this advice as "nonsense" initially, I read it later carefully again and realized that it is actually a very good advice.
SOPE said about this position:

White has to watch out for both methods of defence (attack against the black pawn and defending his own pawn, or the key squares)

This gives a hint, but it is actually very vague.
To judge which way to go every move you need much more precision.
If you don't know exactly which squares to head for, you are actually gambling.
The method of Takchess revealed much of the subtleties of the position.
Actually there is not 1 end to this variation but there are 4 possible ends that draw.

Let's have a closer look at them.
diagram 2





















White to move.
If white wants to defend his own pawn, to which square does he have to head?
The diagram shows that reaching the key square c1 is essential for this method of defense.
This is the reason why 1.Kf5 in the first diagram doesn't work.
If the white king goes to the south along the f-file, black can shoulder him away along the d-file. So the white king will never reach c1 in time.

diagram 3





















Black to move.
This diagram show a subtlety why white has to move along the e-file while heading to c1.
There comes a moment the black king can't follow because he is blocked by c3.

If you decide to sacrifice your pawn, you have to know where your king has to head for to defend the key squares of the black pawn in time.
The next diagram gives you a clue.

diagram 4





















Black to move.
To block the black king after sacrificing your pawn, you have to be in time on b2.
That means that in this position you have to be allready on one of the blue squares.
So here again you find c1 to be the square to head for from the initial position.

What about the other method of defense?
This can be a possible end of the line when you decide to head for the black pawn.

diagram 5





















Black to move.
If you keep the distance between your king and the opponents' at 1 square, he never can fetch your pawn. If you decide to give your pawn away in this position, you have to be sure that you catch his one in time.
The following diagram gives you a clue where your king has to be.

diagram 6





















White to move.
When you reach the blue squares in time you can prevent the connection of the black pawn and the black king. The blue squares can be derived from the red one, the last square before the black pawn reaches its refuge.

So Takchess is right.
Before you can do such lines OTB you have to have a database of such positions. Otherwise you have no clue what you are doing.
The keyword is precision.
What is incomprehendsible is that I wasn't prepared for these difficulties. If you look on the web nobody talks about these difficulties. The same is true for the booklet of Nunn and the big book on endgames of Euwe. Relatively spoken SOPE is an exception. That's why I bought it in the first place. But even they are somewhat vague about this position, as you can see above.

What's the matter?
Am I so stupid that I'm the only one who has this problem?
Do other people have the same problem but don't they realize they do?
As I said before, even grandmasters fail sometimes at these positions in official games.
Is there a psychological buffer at work which makes us to deny such difficulties?
Or is it a conspiracy?

I still don't get it.

If logic is your guide, life can be a burden sometimes.
I want to play better chess. Recent analysis of my games at Corus revealed that endgame study would benefit 44% of my games. So I started endgame study.
That's logical.
Since I don't want to do a half job, I started with the mother of all endgames: pawn endgames.
Because any endgame can only be well-evaluated by the underlying pawn endgame, when all pieces are traded off.
That's logical.
At this moment I can say I master endgames with only one pawn.
So I moved on to endgames with two pawns on the same file.
And now I'm lost. I use SOPE, which has a lot of exercises with explanations.
Much to my surprise I read in about 25% of the cases that a grandmaster didn't play that specific exercise well in an official game and lost unnecessary. Mind you, we are talking about only two pawns!

Take for instance the diagram below.






















White to move and draw.

It is part of the same problem I showed you thursday. Only two moves later in the line.
If white plays 1. Ke7 here he can hold the draw.
If he plays 1. Kf5 the Nalimov tablebase says: lost by mate in 20.
Actually any other move loses too.
Why?
If I would get such a position in a game and would play it by intuition, I would give it 70% to 30% in favour of 1. Kf5. Inspired by some sort of reasoning as "this has nothing to do with opposition, it is a kind of a Reti manoeuvre with two targets: both pawns. If I stay in the middle between them that must be good enough."
If I toss a coin my chances are better than playing by intuition.
But this line is about 11 moves long! Tossing a coin 11 times results in a chance of 0.00048828125 to bring the line to a good end.
I looked at this position for hours and hours. I did a lot of similar problems that revealed much mysteries about such endgames. I know for instance a lot more now about the impact of pawn moves in such positions.
But I still don't quite get it.
I want to find the rationale for the choice between 1. Ke7 and Kf5.
If I have to analyse such lines in time trouble OTB there must be a reasoning which I can trust.
If I would be wise I probably would move on and accept that you can't understand everything. At this pace I'm at Lucena's position in 2078.
But that's wise and not logical.
So I'm going to use my time to reveal the mystery of this diagram.
How can I ever understand more complex endgames if I don't understand this?
That's logical.
After all I've seen people busy with much more silly occupations like solving Sudoku's or throwing darts:)

More thoughts about tactics

King of the spill tried to develop a theory about tactics. If such theory will help to improve your chess is another matter, but I see developing theories as a means to clear up the mess that usually resides in the head. A sort of defragmentation of the hard disk so to speak.
I have a lot of fragments which are not put together into a consistent theory, but maybe King or others will derive some idea's from it.

I divide tactics in two main area's.
To win a piece (be it a king or otherwise) from the enemy there are two possibilities.

Trap.
The first one is the TRAP.
Here is only ONE target involved.
If you are after a target, it usually escapes after every move you do to attack it. Ad infinitum (=move 50:).
Only if the target has a lack of SPACE you have chances to catch it.
I consider checkmate as a special case of a TRAP.

Duplo attack.
The second possibility is the DUPLO ATTACK.
I posted about this earlier. I use this name to distinguish it from the term "double attack", which is a part of all possible duplo attacks.
A duplo attack means that there are TWO TARGETS involved.

I use the following distinctions:

• There are ONE or TWO attackers.
• There is an attacking square. This is the square from where the attacker attacks. An attacker can be allready on its attacking square or not
• There is a target square. A target can allready be on it's target square or not.
• The two targets are IN LINE with the attacker or not.

So there are 8 elements to describe a whole lot of combinations.
1-2 attackers
1-2 attack squares
2 target squares
2 targets

A few examples:
diagram 1





















White to move
Blue= attacking square
Green= target square
The attacker is allready on its attacking square and the targets are allready on their target square.

This is the common picture of a double attack.
A similar picture can be made for a double attack of a knight (phork), a queen, king, bishop, pawn.

diagram 2





















White to move
Blue= attacking square
Green= target square
The same sitiation as above, but the rook isn't on its attacking square yet.

Diagram 3





















White to move
Blue= attacking square
Green= target square
The targets are in line with the attacker.
Depending on the values of the hostile pieces this is called a pin or a skewer.

diagram 4





















White to move
Blue= attacking square
Green= target square
A coloured square can be subject for some actions.
Here one of the target squares is empty yet. There are all sorts of preparational moves that forces the target to the target square. Here you can drive the bishop with Ng6 to its target square.

diagram 5





















White to move
Blue= attacking square
Green= target square
Here you use another preparational move to force the king to its target square.
A simple exchange Bxg7 will do the job.
If the value of the piece you exchange is higher than the one you get for it, the exchange is called a sacrifice.

It works about the same with the attacking squares.
It can be necessary to clear the attacking square by chase away the defender, by exchanging or sacrificing on the square etc..

diagram 6





















White to move
Blue= attacking square
Green= target square
Here you have the most basic form of an attack with two attackers.
The attackers are allready placed on the attacking squares and the targets are allready placed on the target squares. You will probably never find this basic form in practice.

diagram 7





















White to move
Blue= attacking square
Green= target square
By placing the knight on its attacking square both attacks come into action.

diagram 8





















White to move
Blue= attacking square
Green= target square
Clearance. By moving the knight away, both attacks come into action.

Summary.
There are two methods to win a piece:

• A trap
• A duplo attack.

A duplo attack can be descibed with:

• 8 elements (2 attackers, 2 attacking squares, 2 target squares, 2 targets)
• Preparational moves to get the attackers on the attacking squares and the targets on the target squares.
• Are the targets in line with the attacker.
• Are there one or two attackers.
  

I just don't get it.

White to move and draw.

I spend hours to this problem, but I just don't get it.
I can find the line by trial and error but not by reasoning.
White has two means to defend: he can try to hunt for the black pawn or he can defend the key squares of the black pawn.
But the two pawns are not sitting ducks, they can move whenever suitable. That makes it very confusing.
I'm just not able to find a reasoning that can guide the white moves.

The plus side on this is: even the simplest situations with only two pawns sometimes are too difficult for grandmasters. So if I master this I can score with it.

The downside is that I don't have a clue how to find a reasoning.

This is the only line to a draw:
1. Kg5 Ke4 2. Kf6 Kd5 3. Ke7 Kc6 4. Ke6! b6 5. Ke5 Kc5 6. Ke4 Kc4 7. Ke3 b5 8. Kd2 Kb3 9. Kc1 Ka2 10. b4! Kb3 11. Kb1 =

Can you find a reasoning to guide white's moves?
Only two pawns, how difficult can it be?