Endgame Corner 2: R vs. B with 1 pawn each

Welcome to the second edition of Endgame Corner, where we will be taking a deep dive into a different fundamental theoretical endgame each week. As with last week, our goals are to:

1. Learn key positions for each endgame, and their evaluations
2. Know which fortresses can be constructed by the defending side, and how to break any apparent fortresses.

Last week, we examined the pure rook vs. bishop endgame with no pawns. Recall there that the defending side can hold a draw quite easily by keeping the king in the opposite color corner of the bishop. The endgame is lost if the king is trapped in the same color corner as the bishop, or if the stronger side can get the opposition in the right situation, leading the rook to tactically dominate the bishop.

For this week, we will extend this topic to rook vs. bishop with one pawn each.

If the stronger side's pawn is a passed pawn, then the position as a rule is always winning, except if it is an a- or h-pawn. For example, the below setup is a useful fortress to know:

Position 1 (white to move)

This is a very easy draw to hold. Black can just sit and do nothing, moving the bishop back and forth along the a2-e6 diagonal. White can never force a mating net, nor be able to force the promotion of the h-pawn. The only thing black should be mindful of is not to carelessly allow white to achieve a pawn on h7 + king on h6 (which you already have to be quite cooperative for), but even then, as long as you can meet Kh6 with moving the bishop to the b1-h7 diagonal, the h7 pawn will be lost.

If black had a dark squared bishop, it is still a draw, as long as white cannot establish the pawn on h6 -- black should use the bishop at the right moments to take that square under control. If white does get the pawn to h6, then the position is winning by forcing a trade of the h6 pawn for the f-pawn, resulting in a pure R vs B ending with the defending king in the wrong color corner.

For other situations where the pawns are on the same or adjacent files, the most important principle of defense is to keep your pawn on the opposite color square as the bishop. If the defending side's pawn stays on the same color as the bishop, then the position is almost always losing, because the stronger side's king will be able to invade and then ultimately sacrifice the rook for the bishop+pawn to reach a winning king and pawn endgame

Although it looks a little scary when you see it for the first time, the kind of position below is a fortress:

Position 2 (white to move)

All black needs to do is not to allow the white king to touch the g6 pawn. The bishop can control f6 and g5 when needed, and f5 and h5 are covered by the pawn itself. This means that black must maintain control of f7 using the king. So after 1.Rc7+ Kg8! (or 1. ... Kf8) 2.Kd5 Bf6 3.Ke4 Bg7 4.Kf4 Bf6! black can always make sure that the white king is not allowed to directly attack the g6 pawn.

Now, it is actually important in this kind of position that the bishop has enough squares on the long diagonal not to end up out of moves. If the defending side's pawn is advanced just one square further, sometimes it is possible to break the fortress with zugzwang, as in the unfortunate case below:

Position 3 (white to move)

This position is winning for white! First, you have to understand that the goal is to get the white king to attack the g5 pawn. Then, you can work out the technique required to force the bishop away from the defense of the f5 square. This is done as follows: 1.Kd4 Bc2 2.Ke5 Bd3 3.g4 (useful just to gain a little more space and control h5 from black's king) 3. ... Bc2 4.Rb5! Kg7! (trying to open the g6 square for the bishop) 5.Rb7+! (forcing black's king back to g6, since black still has to prevent white's king from reaching f6) 5. ... Kg6 now white goes after the bishop 6.Rb2! Bd3 7.Kd4! Bf1 (only square!) 8.Rb6+ Kg7 9.Ke4! and black cannot prevent Kf5, after which white picks up the g5 pawn and has a winning position.