Rook vs Bishop Endings

A Rook versus Bishop endgame occurs where one player has a Rook, and the opponent has only a Bishop. Both players have pawns and a King.

In theory, a Rook is worth 5 pawns, and the Bishop is worth only 3 pawns. That gives the Rook a two pawn advantage, which sounds like an easy win, and it usually is. In a Rook-vs-Bishop ending with equal pawns, the Rook will usually win except in special cases (e.g. the Bishop is supporting a very advanced passed pawn).

Endgames where the Bishop has an extra pawn or two are more interesting, and also more common in practice. The Rook should still win with one extra pawn (R vs B+P with extra pawns), but again with exceptions for advanced passed pawns.

With two extra pawns, and a material balance of R vs B+2P, the position is more equally balanced. The odds still favour the Rook, but there are more positions where the Bishop can draw or even win.

If there are three (or more) extra pawns with the Bishop, then the Bishop actually has theoretically more material, and also in practice has good chances for a win.