Seeking Understanding

Five years ago, I posted "Two Endgame Compositions", giving only the solution to the second. This week I was asked to provide the solution to the first, an 1888 composition by Johann Berger that was first published in Columbia Chess Chronicle. The past two mornings, I have been studying the solution with an aim to understand every move. Although the maneuvers appear complex, they are based on some simple ideas.

White to move

J. Berger, 1888

1.Qb8

The only winning move, according to the tablebases. It forces the light-squared bishop to move because of the checkmate threat Qh2#.

1...Bc4

Threatens Be6+, followed by Bf2+ (or Bh2+).

Other moves lose more quickly.

1...Be2 2.Qf4 (see at move 4 below)
1...Bd3 2.Qf4
1...Bb5 2.Qxb5 Ba7 3.Qd5
1...Ba6 2.Qg8 Bb7 3.Qh7 Bc8+ (3...Bf2 4.Qxb7) 4.Kg3+

2.Qe5

Prevents the check while keeping the dark-squared bishop immobile.

2.Qd6 is one move slower. This move is presented as a "cook" in Harold van der Heijden's Endgame Study Database with a line leading to underpromotion of Black's pawn. It is an instructive alternative.

2...Ba6

Threatens Bc8+

2...Bd3 3.Qg5 threatens Qxg2#. 3...Be4 4.Qh4 Bf5+ (4...Bf2 5.Qxe4) 5.Kg3+
2...Be2 3.Qxe2
2...Bb5 3.Qxb5

3.Qc7

Prevents the check while keeping alive the Qh2 threat.

3.Qe1 is one move slower according to tablebases.

3...Bd3

3...Bb5 allows 4.Qg7

(4.Qc1 Is given ! in Genrikh Moiseyevich Kasparian, 888 Miniature Studies [2010]. Pins the dark-squared bishop so a check can be met by Kg3 and then Qh6+ 4...Bf1 5.Qf4 Ba6 6.Qg4; 4.Qb7)

4...Bc6 5.Qh6 Bd7+ (5...Bf2 6.Qxc6; 5...Be3 6.Qxc6) 6.Kg3+
3...Be2 is second best 4.Qg7 Bf3 5.Qa1 Be2 6.Kg3

4.Qf4

Threatening to move to g4 where checks along the c8-h3 diagonal are blocked and Qxg2 is threatened. This move forces the light-squared bishop onto the a8-h1 diagonal.

Black to move

4...Bb5 5.Qg4

Shields the king from check and threatens Qxg2#

5...Bc6

Defends g2

6.Qd1

Pins the dark-squared bishop and prepares Kg3

6...Be4

White to move

7.Kg3

Threatens Qh5+. The complex battle between White's queen and Black's light-squared bishop has concluded. Now, White threatens checks on the h-file, which Black can delay briefly.

7...Bg6

Guards h5

8.Qc1

Threatens Qh6+

8...Bh5

Prevents the check

9.Qa1

Forces the bishop off the h-file.

Black to move

The rest is easy.

9...Be2 10.Qh8+ Bh5 11.Qxh5+ Bh2+ 12.Qxh2#