1.
[
{B:8/4P3/8/4br1B/2R3p1/8/6p1/2K1k3}
{V:In this study it is important to bear in mind that the ending of rook and bishop against rook is generally a draw. White to play and win.;c1b1;Correct;Incorrect.;The solution is only seven moves long, but the tactics are fairly complex. There are various lines in which both sides promote, and the big question is whether or not White can win. In most cases he cannot, but in the main line White succeeds in reaching a situation where he can indeed win, and in the most spectacular manner imaginable. White's tricky first move introduces all the tactics, and is based on the idea of preventing ...g1Q by threatening a rook check on the first rank. 1 Re4+? Kf2 2 Rxg4 Bg3 is better for Black. 1 Rxg4? Bf4+ 2 Rxf4 Re5 3 Rg4 Kf2 is a draw.}]

2.
[
{S:c1b1}
1 Kb1!
Already quite a tough move to find. The immediate 1 e8Q? g1Q is bad for White because the only check, 2 Re4+, is itself met by a check, 2...Kf2+, and Black gains the initiative. A more reasonable try is 1 Rxg4?, but after 1...Bf4+ 2 Rxf4 (or else ...Re5 in any case) Re5 3 Rg4 Kf2 Black secures an easy draw. Finally, 1 Re4+? Kf2 2 Rxg4 is met by 2...Bg3 and Black threatens to promote with check.]

3.
[
{S:f5f1}
1...Rf1!
Black cannot promote, because first of all he must deal with the possibility of Rc1+. After 1...Kf2 White plays 2 Rc2+ and 3 Rxg2, after which he can safely promote the e-pawn.]

4.
[
{S:c4g4}
2 Rxg4
Curiously, although the two pawns stand ready to promote, both players have more important matters to attend to first. The immediate 2 e8Q? (2 Rc1+? Kd2 even loses for White) is bad because of 2...Kd2+ 3 Ka2 Ra1+ 4 Kb3 Rb1+ 5 Ka4 g1Q, and although White has the first check, he cannot force mate because Black's pieces are too active, for example 6 Qd7+ Ke3 7 Qa7+ Kf3 and Black is safe.]

5.
[
{S:e5g3}
2...Bg3!
The best defense. It is tempting to play 2...Kf2+ 3 Kc2 Bg3, but after 4 Re4! Black cannot promote because of mate on e2, while otherwise Re2+ will eliminate the g-pawn, and then White's own pawn will decide the game.]

6.
[
{S:e7e8}{D:100}{X:e8}{P:WQe8}
3 e8Q+
At last the moment comes for White to promote his pawn. 3 Rxg3? is bad because of 3...Kf2+ and 4...Kxg3, while after 3 Kc2? Rf2+ 4 Kd3 Re2 Black stops the White pawn, leading to the drawn ending of rook and bishop against rook after 5 Rxg3 Rxe7 6 Rxg2.]

7.
[
{S:e1f2}
3...Kf2+
The best square for the king, since 3...Kd2+ 4 Kb2 g1Q allows mate in five by 5 Qd8+ Ke3 6 Qd4+ Kf3 7 Qd5+ Ke2 8 Re4+ Kf2 9 Qd2 mate.]

8.
[
{S:b1c2}
4 Kc2
We shall see in a moment why this move wins, and no other.]

9.
[
{S:g2g1}{D:100}{X:g1}{P:BQg1}
4...g1Q
Another position with two queens. A move such as 5 Qf7+ leads to nothing after 5...Kg2, because Black's pieces are well placed to defend the king.]

10.
[
{S:e8e2}
5 Qe2+!!
This queen sacrifice is the only winning move. Suddenly, the clustering of Black's pieces, normally so helpful in defense, turns out to be a fatal handicap.]

11.
[
{S:f2e2}
5...Kxe2]

12.
[
{S:g4e4}
6 Re4+
Now we can see why White's king had to move to c2.]

13.
[
{S:e2f2}
6...Kf2]

14.
[
{S:e4e2}
7 Re2 mate.]