Black resigned, because there is a threat of 32.Bd2#, and on 31...e4 there follows 32.Nh3#.

Black has an extra piece, but the pawn on a7 is very dangerous, and is impossible to capture with checks. For example, after 53...Qc1+ 54.Kh2! Nf1+ (54...Qb2+ 55.Qg2!) 55.Kg2 Ne3+ 56.Kf2 Qd2+ 57.Kg1 Qe1+ 58.Kh2 Nf1+ 59.Kg2 Ne3+ 60.Kh2 Qd2+ 61.Kg1 Qc1+ 62.Kf2 Qd2+ 63.Kg1, the game ends in a draw.

54.Kh1 Qe1+ 55.Kg2 Qg1#.

The white king has no protection, and Black obtains a winning queen endgame.

With a winning position.

Both kings face mating threats, but White succeeds in constructing his mating net more quickly.

Other queen retreats allow White to bring the rook into the mating attack at once:
A) 1...Qb6 2.Rd1! d4 3.h4 Bg3 4.Qd3 Be5 5.Qxh7 Qxe6 6.Qxc2+–;
B) 1...Qc5 2.b4! (a necessary move) 2...Qb6 (2...Bxb4 3.Qh5+ g6 4.Qxh7+–) 3.Rd1 d4 4.h4 Bg3 5.Qd3 Be5 6.Qxh7 Qxe6 7.Qxc2+–;
C) 1...Qc6 2.Rd1 Ba5 3.Qh5+ g6 4.Qxh7 Qxe6 5.Nxc7+ Bxc7 6.Qxc7, with a decisive attack.

2...Rf5 3.Qxe5 Rxe5 4.Nxc7+ Kf8 5.Rc1 Nd4 6.e7++–.

3...c6 4.Rd3! Qb8 5.Rf3+–.

Black has no satisfactory defence.