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Being a five-piece endgame, the rook and bishop versus rook endgame has been fully analysed using computers. Endgame tablebases show that 40.1% of the legal positions with this material are theoretical wins, but that includes many unnatural positions that are unlikely to occur in games.
In a king and pawn versus king endgame with a rook pawn, the defending king only has to get in front of the pawn to draw the game. In contrast, in the endgame with a bishop and the wrong rook pawn, getting the defending king in front of the pawn will not necessarily draw. In this position from Edmar Mednis, White wins if it is their move. 1 ...
The modern consensus is that the side with the two bishops need at least a pawn when facing rook and knight, even then the side with the two bishops is underdog. William Steinitz reckoned that often two bishops and two pawns are superior against rook and knight. A rook and bishop usually work better together than a rook and knight in the endgame.
Positions with two rook pawns are often a draw. A position with a rook pawn and bishop pawn on the same side of the board is usually a draw if they are not far advanced, but the defense is difficult. Overall, the rook pawn and bishop pawn win in 61% of games. [85] The rook pawn and bishop pawn almost always win if they both reach their sixth rank.
A rook and a rook pawn always win against the wrong bishop, as in this position. The defender has the wrong bishop if it is the one on the same color as the pawn's promotion square. The winning procedure is to give up the pawn at the right time to get to a winning rook versus bishop endgame. If the bishop was on the other color, the defender ...
The example here is a study by Henri Rinck first published in La Stratégie in 1920. It is White to play and win. Normally, Black would be able to sacrifice his rook for the white bishop, leaving a drawn position (sacrificing it for a knight would be no good, since it is possible to force mate with bishop and knight), but in this case it turns out that the rook is dominated, and its capture ...
The knight on d7 often hops to c5, where it attacks a white pawn on e4; or to e5, where it attacks a pawn on c4. The knight on f6 can go to e8 (when Black placed their rook on d8) to defend the d6 pawn, or to d7 or even to h5, if unoccupied. The black queen can be moved to b8 (unmasking the rook on c8 and perhaps supporting ...b5) or a8 (eyeing ...
If the pawns are on the opposite color as the defender's bishop, the defender may be able to blockade the pawns and draw. If both pawns can safely reach the sixth rank, they win unless one is the wrong rook pawn, i.e. the rook pawn that promotes on the square of the same color as the defending bishop. [23]
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