A pawn up in a king and pawn ending is generally a win; so is two pawns up in a rook and pawn ending. In the appendix to this mental library, however, is stored the rulebook of exceptions. Rook, a- pawn and c-pawn against rook is usually a draw; king, bishop and a- pawn (or h-pawn) against king is a draw if the bishop is of opposite colour to the pawn's queening square. A few dozen such rules, and a few hundred exceptions, special cases and anomalies, make up the database to which a player is constantly referring when calculating more complex endgames.
On the furthest limb on the tree of exceptions are those positions beloved of endgame study composers, which seem to defy the logic of the game. A lone bishop, for example, cannot conceivably draw against two rooks, yet if we put the white king on d3, bishop on f3, black king on d5 and rooks on e4 and e5, the game is drawn. If White maintains the pin, Black cannot free himself without losing a whole rook, leaving a drawn position.
Today's position is based on an equally bizarre idea, in which a rook draws against two rooks and a bishop. Composed by L Mitrofanov, the position took third prize in a 1970 competition celebrating the 100th anniversary of Lenin's birth. It is White to play and draw.
White must somehow make use of his d-pawn, and 1. Re8] is the natural way to start (1. f7?] incidentally loses to 1 . . . Re1+] 2. Kd2 Rxf7). Black's best winning chance is then 1 . . . Rc3+ 2. Kd2 Bxd7 attacking the white rook, when 3. Re1+ Kf2 4. Re2+ Kf3 5. f7 loses to 5 . . . Rc8.
The right way to play is 3. f7]] Rxf7 4. Re1+ Kf2 5. Re2+ Kf3 and now 6. Re1] White has only a rook against two rooks and bishop, but threatens both Kxc3 and Rf1+. Black's bishop and king prevent the rooks protecting each other, so Black can do no better than repeat moves with 6. Kf2 Re2+ or accept the drawn endgame of rook and bishop against rook.
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