Minor-Piece Endgames
Knights and bishops in the endgame: how a knight stops a pawn, good and bad bishops, knight against bishop, and the Centurini position, with exact results where the tablebase covers them.
Endings with a knight or a bishop are where small details decide: one tempo, one square, one colour. A knight can stop a pawn on its own if it finds the right square; a bishop can hold back several pawns from far away; and with bishops on both sides, which colour your pawns stand on can decide the game.
Each lesson gives the idea, a checklist of what it needs, each condition shown with the move that keeps the result and one that throws it away, then the method move by move and positions to solve.
Lessons
- 1Knight Against PawnA knight on its own can stop a passed pawn, even with the enemy king beside it, but only if it finds the right square in time. Guard the queening square, use checks to win a tempo, and watch for the fork against a new queen.
- 2Good Bishop, Bad BishopWith bishops of the same colour, the pawns decide. A bishop is bad when its own pawns stand on its colour: they block it, and they are targets for the enemy bishop. Attack them, and bring your king in on the other colour.
- 3Knight Against Bishop and PawnA bishop and pawn against a knight is often a draw, if the defender knows where to go. Put the king in front of the pawn, send the knight to a square that covers the pawn's path, and use checks to get there in time.
- 4The Centurini PositionAdvancedBishop and pawn against a bishop of the same colour is usually a draw, but not always. Learn Centurini's rule for the defender, and his method for the attacker: take the guarding diagonal away from the enemy bishop, then deflect it.
How these lessons were checked
Every position with up to seven pieces is checked against the Lichess endgame tablebase, which knows its exact result; larger positions are checked with Stockfish at depth 22. A move shown as working keeps the best result available, a win or a draw, or in larger positions a winning advantage of at least one and a half pawns; a move shown as failing throws it away, or is at least one and a half pawns worse. Every exercise has one answer: the only move that keeps the result (in larger positions, a move at least one and a half pawns better than any other), or, where several do, the only one that makes progress without losing time (by the tablebase's count of moves to the next pawn move or capture). The number under the board is the exact result where the tablebase covers the position.