Corresponding squares (Lasker-Reichhelm 1901)

White wins White to move · Pawn endgames · Difficulty about Elo 2100

The plan

The most famous manoeuvring position in endgame history — a position in which both sides together have ZERO pawn moves: all three pawn pairs stand blocked, only the king march decides. White threatens to break in at two widely separated spots: on the kingside against the undefended pawn, on the queenside behind the chain. The black king can cover both entry squares — but only one after the other, and so it is not WHERE he stands that decides, but WHEN. That is exactly what corresponding squares regulate: to every square the attacking king enters belongs a specific square the defender MUST occupy; miss it even once, and White gets through. The pairs are a map, not a rule of thumb — and whoever knows them sees at once that the first move does not belong in the centre, but on a single square at the edge, because only from there does the chain of correspondences work out. From there White shuttles back and forth until Black has to commit to one side, and then marches to the other. Opposition and triangulation, both separate lessons in this collection, are the same idea in miniature; here it is built out so far that mere counting no longer carries it.

Rule of thumb: don't count moves, remember the pairs of squares — the defender is lost the moment he misses his matching square.

Why this level: Lasker-Reichhelm: pairs of squares instead of counting, 46 half-moves

The solution, move by move

1. 1. Kb1 The most famous king move in the endgame — and, by everything the study has taught since 1901, the only winning move. White enters the square that corresponds to b7. One square over and the pairing no longer holds, and Black draws (sideline).
   Sideline 1. Kb2 One square over — and the win is gone. The move looks more natural than the right one, since it heads toward the centre; but it destroys the correspondence before it has even begun. 1… Ka8 Black dodges into the corner and takes over the correspondence by doing so: from here on HE has the map on his side. 2. Kb3 Ka7 3. Kc3 Kb7 4. Kb2 Kc8 Black holds off both breakthroughs and gives up neither side: a draw. The difference between a whole point and half a point was a single king square on the first move.
   Sideline 1. Ka2 The second square over — and again the win is gone. b1 is the ONE square that corresponds to b7; a1 and a2 belong to others, and those are free for Black. 1… Kb8 Black doesn't need to calculate: he simply mirrors. As long as White doesn't enter a corresponding square, Black always has a waiting square left. 2. Ka1 Kb7 3. Ka2 Kb8 White tries it on the other side — too late, the black king is back in time. 4. Kb3 Kc7 Both entry squares stay guarded: a draw. Only 1.Kb1! keeps the correspondence intact.
2. 1… Kb7
3. 2. Kc1
4. 2… Kc7
5. 3. Kd1
6. 3… Kd7
7. 4. Kc2 Black has to guard the queenside — and by doing exactly that moves away from the kingside. The shuttling forces him to choose.
8. 4… Kc8
9. 5. Kd2
10. 5… Kd8
11. 6. Kc3
12. 6… Kc7
13. 7. Kd3 Now the switch of sides: the queenside has tied down the black king, so White marches to the right. The tempi won through correspondence are exactly enough.
14. 7… Kb6
15. 8. Ke2
16. 8… Kc7
17. 9. Kf3
18. 9… Kd7
19. 10. Kg3
20. 10… Ke7
21. 11. Kh4 The march around the outside — the black king arrives one step too late. That one step was exactly the reward of the first move.
22. 11… Kf6
23. 12. Kh5
24. 12… Kf7
25. 13. Kg5
26. 13… Kg7
27. 14. Kxf5 Broken through: the first pawn falls, after pure king play and without a single pawn ever having moved.
28. 14… Kf7
29. 15. Kg5
30. 15… Kg7
31. 16. f5 Only now does the blockade dissolve — White's own passed pawn runs, escorted by the king. From here it is technique.
32. 16… Kf7
33. 17. f6
34. 17… Kf8
35. 18. Kf4
36. 18… Kg8
37. 19. Kg4
38. 19… Kf8
39. 20. Kg5
40. 20… Kf7
41. 21. Kf5
42. 21… Kf8
43. 22. Ke6
44. 22… Ke8
45. 23. Kxd6 And finally the second pawn falls too: White has harvested on BOTH wings. That was exactly the threat Black could never cover on both sides at once.
46. 23… Kf7

More in Pawn endgames

• One pawn holds two — the saving trade Draw
• Wing majority 3 against 2 — the candidate first White wins
• Eat or run — the square backwards White wins
• The active king outweighs a pawn Draw
• Rook-pawn race — the corner saves Draw
• The distant passed pawn — the decoy White wins