Trébuchet in action

 I'm trying to find which methods are practical.

Diagram 1. White to move

8/1k6/2p5/2P5/K7/P7/8/8 w - - 1 2

What is going on?

• White must conquer the black pawn
• White cannot go via the left side
• White must go to the key squares of the black pawn via the right side
• Black cannot defend the key squares on the right side because white has a spare tempo (a4)
• Blacks only try is to conquer the white pawn on c5 via the left side
• Square d4 (red a) is mined (typical for the Trébuchet)
• White must avoid d4 until black steps on b5 (blue a)
• The two squares c4 and d5 (marked x) are rigged
• They are the cause that d4 is mined
• c4 is only rigged after the black king steps on b5

INTERMEZZO

I have the idea that I'm not yet finished with the corresponding squares and the Trébuchet. Something is missing. Let me solve that now.

Diagram 2. Pick up the white king. Where would you place it?
 White to move

Assume that the black king is on b6. Pick up the white king in a thought experiment. Where can you place the white king and still force the win? White to move.

• a = mined. This is the only true corresponding square. When both kings are on "a", they are in mutual zugzwang. What is so special about "a"? From d6, the white king does two things: It attacks the black -pawn AND defend its own pawn
• 1 = the white king attacks the black pawn
• 2 = the white king can reach 1 in one move
• 3 = the white king can reach 2 in one move

Why is there no 4?

The situation for the black king is the same. The squares around him are a point reflection of the red symbols. The black king is on a 3. Hence the white king would be losing if it was on a 4.

UPDATE

Back to the initial diagram.

Diagram 3. White to move

Thanks to the intermezzo, I can now concoct a system where the digits have a meaning.

• Blue digit = distance to attack the white pawn
• Red digit = distance to defend the white pawn
• a = mined square, distance = 1

The white king can make a smart triangulation now.

• 1.Kb3 Ka6
• 2.Kb4 Kb7

White is now on distance 1 while black is back on distance 3. This gives white some slack.

• 3.Kc4 Ka6

Diagram 4. White to move

• x = forbidden for black
• a = mined square, distance 1

White must circumvent the mined square. Actually, the square is only mined for white. Because white cannot reach the black pawn from here. It are corresponding squares, though. With mutual zugzwang.

• 4.Kd3! Ka5
• 5.Ke4! Kb5
• 6.Kd4 Ka4

White is making progress. He is heading towards d6. Black cannot defend d6, because white has the reserve tempo a4.

Blacks only "chance" is to snatch a3. This removes the taboo square b4. But it is not fast enough.

Diagram 5. White to move

• 7.Ke5 Kxa3
• 8.Kd6 Kb4
• 9.Kxc6 and white wins.

Summary

This position needs only 1 set of corresponding squares. The fact that squares are mined is irrelevant. The only thing that matters is that it introduces mutual zugzwang on these two squares.

The method to decide between moves is guided by the distance to attack and the distance to defend. The technique of triangulation was designed to get the white king closer to the pawn while keeping the black king at bay. It was more based on shouldering than on opposition of some kind.

So you are witness of the birth of the tool of relative distance (TORD).