An endgame course

The elementary checkmates

Every won game ends in one of a handful of positions, and each of them has a method a century of teachers agrees on. This course teaches the five forced mates against the bare king, from the two-rook ladder to the bishop and knight escort, the way Capablanca opens his book with them: method first, then the mate proved on the board against real resistance.

Before the moves: the big ideas

Drive to the edge

Capablanca states the shared principle in his first example: drive the opposing king to the last line on any side of the board. Every mate in this course is that one sentence executed with different tools, and the tools only change how the driving is done.

The king does the heavy lifting

Capablanca's closing remark on the elementary mates: in each of them the cooperation of the king is needed, and the least force that mates without the king's help is two rooks. Learn each mate as a king manoeuvre with escorts, not as a piece trick.

Stalemate is the only enemy

Nothing on the board can stop these mates except a careless one. Capablanca warns about drifting into stalemate in the bishops ending, and Fine and Benko catalogue the recurring stalemate traps in the queen ending. The habit that prevents all of them: before every quiet move, look at the trapped king's squares and leave it one.

Fifty moves are enough, barely

The rules grant fifty moves without a capture or a pawn move, and Capablanca notes that the bishop and knight mate requires foresight to land inside them. That is the practical reason these endings are memorised rather than improvised: the clock and the move counter both punish rediscovery.

The lessons, method then drills

Read the method first; the steps below are what the drills put to work. Learn walks a drill with the coach. Recall is free play against the engine: prove the goal within the drill's move budget, and any move that keeps it alive stands.

K+2R vs K

Two rooks: the ladder

The one elementary mate that needs no king. Capablanca's closing aside on the simple mates says why it opens this course: to force mate without the king's help, at least two rooks are required. The rooks take alternate ranks like rungs and walk the defending king off the board.

1.One rook checks; the other already holds the rank behind, so the king must step back.
2.Swap roles and repeat: check, hold, check, hold, rung by rung toward the edge.
3.When the king steps toward a rook to harass it, slide that rook to the far side of the board and carry on.
4.The mate lands on the last rank, one rook holding the seventh shut and the other checking on the eighth.

Walk the ladder

goal: checkmate within 12 moves

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K+Q vs K

Queen mate: the shrinking box

Capablanca calls this the easiest mate of all, to be accomplished in under ten moves, and it is also the easiest to spoil. The queen confines the defending king in a box and shrinks it from a knight's move away; the only losing idea available is stalemate.

1.Place the queen a knight's move from the enemy king and copy its moves; the box shrinks on its own.
2.No checks. A checked king slips through the net; a boxed king only loses ground.
3.When the box cannot shrink further, walk your own king up.
4.Before every quiet queen move, count the trapped king's squares and leave it one until your king arrives.

Shrink the box

goal: checkmate within 14 moves

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K+R vs K

Rook mate: rank by rank

Capablanca opens his book with this ending, under the principle that governs all of them: drive the opposing king to the last line on any side of the board. The rook holds a fence one rank ahead; the king does the walking, keeping it on the same file as the defending king until the two stand face to face.

1.Confine the king with the rook first: one rook move that fences it onto its back ranks.
2.March your king up the board on the defending king's file, or one file toward the centre.
3.Keep the fence; the rook only moves again to gain a tempo or to mate.
4.When the kings stand face to face, check on the last rank: that check is mate.

From the corner

goal: checkmate within 30 moves

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From the centre

goal: checkmate within 30 moves

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K+2B vs K

Two bishops: edge, then corner

Two bishops mate by walling: side by side they close a whole diagonal band of the board, and the king pushes the defender against it. Capablanca's warning is particular to this ending: the defending king must be driven not merely to the edge but into a corner, and near the corner a waiting move keeps the finish clean of stalemate.

1.Set the bishops on neighbouring diagonals; together they wall off a band of the board.
2.Walk your king up and press the defending king to the edge.
3.Herd it along the edge into a corner; against two bishops, either corner serves.
4.At the corner, mark time with a bishop so the defender must step back, then close both diagonals at once.

Wall and corner

goal: checkmate within 40 moves

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K+B+N vs K

Bishop and knight: the long march

The hardest of the elementary mates and the only one with named technique. Mate can be forced only in a corner the bishop controls, the defender runs for the other one, and the pieces must escort it all the way across. The escort goes back to Philidor, whose 1777 edition first noted it; the knight's zigzag along the rim is the W manoeuvre, the name Müller uses; Delétang published the rival triangle method in 1923.

1.Learn the map first: mate arrives only in a corner of your bishop's colour.
2.Drive the king to the edge with all three pieces moving up together.
3.When it runs for the safe corner, let it in, then evict it: the knight checks it out while the bishop seals the escape diagonal.
4.Escort it along the edge, the knight zigzagging its W beside the king, and deliver mate in your own corner.

The long march

goal: checkmate within 50 moves

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Sources

Chess Fundamentals, José Raúl Capablanca · Public domain on Project Gutenberg, read in full text with the original diagrams. Supplies four of the five demonstration lines (Examples 1, 2, 3, 4 and 39), each starting position reconstructed from the book's own diagram images and replayed to the stated mate.
Checkmate · Read as wikitext: the basic-mates sections with named attributions to Seirawan, Fine and Benko, and Pandolfini, including the ladder mechanism and the stalemate pattern list.
Bishop and knight checkmate · Read as wikitext: the W manoeuvre and Delétang histories with links to the primary scans, Seirawan's phase framing, and three complete demonstration lines by named authors.
Two knights endgame · Read as wikitext for the coverage decision: the cannot-force-mate fact cited to Mednis, Averbakh, and Speelman, Tisdall and Wade, with Keres's worked example.
Endgame Corner #50: Freeze!, Karsten Müller · ChessCafe Endgame Corner, May 2005, recovered from the Wayback Machine: names the W manoeuvre and closes by telling readers to use it.
Endgame Corner: The Damned Pawn, Part 1, Karsten Müller · ChessCafe Endgame Corner, October 2003: the direct statement that two knights against a bare king is drawn by the stalemate defense.
Piece Checkmates I (Lichess practice study), arex · Exported as PGN via the API; annotator checked and carries a coach badge but no title, so community tier. Supplies the two-rook demonstration line, with the mechanism corroborated by Pandolfini via the Checkmate article.
100 Endgames You Must Know, 6th edition (publisher sample), Jesús de la Villa · New in Chess sample of the 6th edition, 2023: table of contents as coverage evidence that the bishop and knight mate belongs to the must-know canon.

The methods come from the sources above; Stockfish checks that every drill reaches its stated goal on the board.