Horizon effect

In a recent tournament game I had played into the ending of rook and bishop vs rook and opposite-coloured bishop, arriving at the position shown in the diagram. For an aggregate of small reasons White is clearly better here. His pieces are more active and he has fewer pawn islands. He can make progress by attacking Black's kingside and either weakening his pawns or hemming in his king. But one of the biggest elements in White's favour is a psychological pitfall that many players would fall into as Black.

White's next move was 37.h5!, fastening onto Black's kingside and forcing him to make a very difficult choice. Can he keep White's advantage within manageable limits and if so how?

My opponent, who was well behind on the clock, thought for only a few seconds before playing 37...Rd6?! 38.Rxd6 Bxd6 39.hxg6 hxg6 40.Bxg6 Kg7, simplifying into an ending a pawn down but with bishops of opposite colour. Now as everyone knows, endings with bishops of opposite colour are often difficult if not impossible to win for the stronger side, an extra pawn or two making no difference at all. The big problem for Black is that this abstract idea does not apply to the present case. White is in fact winning easily. The game concluded 41.Bd3 Kf6 42.f4 Bb4 43.Kf2 Bd2 44.Kf3 Be1 45.g4 Bb4 46.g5+ Kg7 47.f5 Kf7 48.Kg4 Kg7 49.f6+ Kf7 50.Kf5 and Black resigned (1-0).

Instead of 37...Rd6 Black can try several other ideas:
A) 37...gxh5!? 38.Rxh7+ Kg8 39.Rxh5 Kf8. This keeps the rooks on the board, which may help with counterplay later on. White should probably play 40.Rf5+ Kg7 41.g4 in order to make progress on the kingside.
B) 37...g5!? 38.Rxh7+ Kg8 39.Rb7. Yet another way of keeping rooks on the board, with the additional idea of making it difficult for White to get connected passed pawns. However, White can still make progress with Kg2-f3-g4.
C) 37...Rc6. Black passes and waits to see what White will do. How about this: 38.h6 Bf6 39.f4!? and Black is well on the road to zugzwang; for example 39...Re6 40.Kf2 Re3 41.Bc4 Re8 42.Rf7 Bd8 43.Bb5 Rg8 44.Kd2!
D) 37...Bd6 38.h6 Be7 39.f4! Re3 (or 39...Bf8 40.Rd8 Rf6 41.Kg2, playing for zugzwang as before) 40.Kf3 Rxe3 41.Rxe7 Kg8 42.Rg7+ Kh8 43.Rb7 and the rook ending is hopeless for Black.

The conclusion is that Black's position is very difficult to defend no matter what he does. From White's side of the board the paradoxical 37...g5!? looks to be the defensive idea needing the most effort to overcome.

For a dash of perspective I gave the position after 37.h5 to Toga II, one of the strongest chess playing programs on the market. After some time it too played 37...Rd6?!, which I would attribute to the horizon effect. The program cannot “see” that Black will lose his bishop to the advancing White pawns because it is too far over the event horizon.