1.
[
{B:8/6KP/6P1/8/3k4/8/p6B/b7}
{V:There is no question that this is hardest of the endgame studies. Although the position appears relatively simple, extremely subtle play is required by both players. However, all the analytical effort is worthwhile when one finds the remarkable conclusion to the study. White to play and draw.;g7g8;Correct;Incorrect.;Various endings can arise in the course of the solution, which need to be accurately evaluated. Here are some useful guidelines, firstly, an ending with a black queen against White's bishop and h7-pawn is winning for Black if his king is close enough to the h8-corner, for example if his king is on e6 or f5. Secondly, a similar ending is drawn if White still has his g6-pawn. An ending with queen against bishop and g7-pawn is lost for White.}]

2.
[
{S:g7g8}
1 Kg8
The immediate promotion is no good, because Black wins after 1 h8Q? Ke4+ 2 Kg8 Bxh8 3 Kxh8 a1Q+ 4 g7 Kf5 5 Kh7 Qa7 6 Kh8 Qd4 7 Kh7 Qh4+ 8 Kg8 Kg6, forcing a quick mate. Likewise, 1 Bg3? Ke4+ 2 Kg8 Kf5 3 g7 Bxg7 4 Kxg7 a1Q+ is an easy win for Black. Endings with a black queen against bishop and pawn(s) arise quite often in this study. The general rule is that if White still has both kingside pawns then he can draw, but if he has only one pawn left then he loses.]

3.
[
{S:d4e4}
1...Ke4
It is hard to see why this is better than moving to d5, but after 1...Kd5 2 Bf4! White draws more comfortably. The basic idea is that after a move such as 2...Bb2, White opposes bishops by 3 Bc1; then 3...a1Q 4 Bxb2 Qa8+ 5 Kg7 is a comfortable draw, while 3...Bc3, for example, is answered by 4 Bd2 with the same situation. If Black plays 2...Bh8, then 3 Kxh8 a1Q+ 4 Kg8 is the same. Finally, 2...Ke6 is met by 3 Bh6! Bc3 (3...Kf5 4 g7 and 3...Bh8 4 Kxh8 a1Q+ 5 Kg8 are also drawn) 4 h8Q! Bxh8 5 g7, forcing a draw.]

4.
[
{S:h2d6}
2 Bd6!
There is a large element of symmetry in the position, so it is not surprising that if 2...Kd5 is met by 3 Bf4!, then 2...Ke4 should be met by 3 Bd6!.]

5.
[
{S:e4f5}
2...Kf5
If Black plays 2...Bb2, then White draws much as above, for example 3 Ba3 a1Q 4 Bxb2 Qa8+ 5 Kg7 Qb7+ 6 Kg8 (but not 6 Kh6? Qxb2 7 g7 Qf6+ winning the pawns) Qb8+ 7 Kf7 Qxb2 8 g7 and the two connected passed pawns are too strong for Black to win. However, the move played explains why 1...Ke4 was better than 1...Kd5; in the note to Black's first move, 1...Kd5 2 Bf4! Ke6 3 Bh6 Bh8 4 Kxh8 a1Q 5 Kg8 was a fairly comfortable draw. However, the symmetrical line is winning for Black.]

6.
[
{S:d6f8}
3 Bf8!
Initially White plays the same way, relying on the stalemate defense 3...Kxg6 4 h8Q! Bxh8 5 Bg7 Bxg7. However, Black has a surprising finesse.]

7.
[
{S:a1h8}
3...Bh8!!
Now White appears to be in trouble, because Black's king is already attacking g6, so 4 Kxh8 loses to 4...a1Q+ 5 Kg8 Qa2+ 6 Kg7 Qa7+ 7 Kg8 (7 Kh6 Qe3+ 8 Kg7 Qe5+ wins after 9 Kh6 Qf6 or 9 Kg8 Qe6+) Kxg6 8 h8N+ Kf6 9 Bh6 Qe7 10 Bf8 Qe8 and White has no moves.]

8.
[
{S:g6g7}
4 g7!
This is the only real alternative.]

9.
[
{S:a2a1}{D:100}{X:a1}{P:BQa1}
4...a1Q
What now? After 5 gxh8Q, Black forces mate by 5...Qa2+ 6 Kg7 Qb2+ 7 Kg8 Qb3+ 8 Kg7 Qc3+ 9 Kg8 Qc4+ 10 Kg7 Qd4+ 11 Kg8 Qd5+ 12 Kg7 Qe5+ 13 Kg8 Qe6+ 14 Kg7 Qg6 mate. The other obvious possibility is 5 Kxh8?, but 5...Kg6 6 Kg8 Qd4 7 h8N+ (7 Kh8 Kf7) Kf6 8 Kh7 (8 Nf7 Qd5 9 Kh8 Qh5+) Qh4+ 9 Kg8 Qh5 is winning for Black. Only the bishop can move, but wherever it goes, Black can always pick it up with queen checks, for example 10 Ba3 Qd5+ 11 Kh7 Qd3+ 12 Kg8 Qxa3, with mate in a few more moves. Have a look at the position for a few moments to work out how White defends himself.]

10.
[
{S:g7h8}{D:100}{X:h8}{P:WNh8}
5 gxh8N!
The only move, allowing White to interpose after a check on a2. With a bishop, knight and advanced pawn for the queen White has plenty of material to draw, but his king is still in an awkward spot.]

11.
[
{S:a1a2}
5...Qa2+]

12.
[
{S:h8f7}
6 Nf7!
Not 6 Kg7? Qe6 7 Ba3 (7 Nf7 Qg6+ also wins) Qe5+ 8 Kg8 Kf6 and White cannot avoid mate.]

13.
[
{S:f5g6}
6...Kg6
Black's last throw.]

14.
[
{S:h7h8}{D:100}{X:h8}{P:WNh8}
7 h8N+!
Now the cluster of minor pieces round the king provides an adequate defense, and White draws easily. Looking at the initial position, it is hard to imagine that the only way to draw is for White to promote both his pawns to a knight.]
