Which pieces do I have to keep on the board, to win my endgame?

Question

How do I win this endgame?

2R5/pr6/3kp2p/4n1p1/5B2/P4P2/2P1K1PP/8 w - - 0 1

More specifically, I want to know whether I should trade off pieces, and in case of a trade, which pieces I should keep on the board.

I considered three options here:

A Keep all the pieces on the board.
This could be done by 1.Bg3 Kd5 2.Rh8 etc.

B Trade off the rooks.
This could be achieved by 1. Rd8+ Rd7 2. Rxd7 Nxd7 etc.
1...Nd7 is bad because of 2.Kd3 Kc6 3. Rh8!?

C Trade off the light pieces.
This can be done by 1.Bxe5 Kxe5 2.Rh8 etc.

My further questions are:

1. Is the rook ending in C a draw? If it is possible to win it, how would it be done?
2. Which endgame is better/easier to play A or B?
3. I guess that A and B are both winning for White. How are the winning strategies in both cases, i.e. how to win them?
4. In general, in Rook + Bish vs Rook + Knight endings, who wants to trade of the rooks?

Answer 1

Endgame D, after exchanging rooks AND minor pieces, is a trivial win.

Endgame C, with rooks, looks winning as well but might require more tactful play.

Endgame B, without rooks, is quite an easy win.

Endgame A, with R+B, is winning. The best strategy will probably involve a rook exchange...

Question 4: generally, the side with the bishop wants to keep rooks and the side with the knight wants to keep queens. There are a lot of exceptions though, including cases like this one with material imbalance (an extra pawn).

From the diagram, the logical continuation should be 1.Bg3 Kd5 2.Rd8 Nd7!, keeping rooks. White should win nonetheless. The plan (loosely explained) will be: centralisation, threats against h6/g5, helping the c-pawn forward. A bit of concrete thinking is needed too, because you don't want to allow too much counterplay against your somewhat loose queenside pawns.

Answer 2

As is evident from the comments, tactics often trump strategy. For example, although I agree with Evergalo's general comments,in his variation 3.Kd3! wins immediately because of the mate threat. In fact, after 2.Bg3, The threat of Rd8 is enormously strong (..Rd7 3.Rh8) The move that loses most slowly seems to be 2..Kd7, but then 3.Rh8 (forcing the Knight to a poor square) Nf7 4.Ra8 and the a-pawn is about to fall (Bf2!) This very nicely illustrates the power of the Bishop in open positions, a pin, a mate threat, switching from one wing to the other. But Bishops blocked by their own Pawns are easily outshone by a Knight.

Reaching this position in a game I would realise that I am a Pawn ahead, and that if I could exchange all the pieces it would be an easy win. But I would not like the ending after Bxe5 because I would not see a way to exchange the Rooks and I also have some vulnerable Pawns. I would see that Black has more weak Pawns than I do, and they are easier to attack than mine, and they are all on the color of my Bishop, so I would probably retreat to g3 quite quickly. Even so I would be a bit surprised by how nicely the tactics work out. A stronger player would already see the tactics and base his decision on them.

One little-noted advantage that the Bishop has over a Knight, is that if, perhaps after a change in the Pawn structure, exchanges become desirable, then exchanges are often more easily forced by the Bishop. In other words the player with the Bishop has more chance to dictate WHEN exchanges occur.

Answer 3

Capturing the knight enables you to play Rh8. So I'll trade minor pieces and keep rooks on board. I don't think there is any need for any deep calculation here.