The Cochrane Defense is a method for drawing in the chess endgame with a rook versus a rook and bishop, shown here. It was discovered by John Cochrane. This combination of material is one of the most common pawnless chess endgames. Accurate play is required for the defense. The defense is most effective near the center of the board, and doesn't work on the edge (Nunn 2007:161ff). The Cochrane Defense works when:

the defending rook pins the bishop to the king on one of the four central files (c through f) or ranks (3 through 6), and
there are two or more ranks or files (respectively) between the kings (de la Villa 2008:213-16).
Contents [hide]
1 Details
2 See also
3 References
4 Further reading

[edit] Details
Budnikov-Novik, 1991

Cochrane defense. Black to move, draw with either side to move.The defense is most effective near the center of the board. In this position, if the pieces on the e-file were moved to the f-file, then if 1. Ke5 the response 1... Kg8, puts the black king dangerously close to the corner (Nunn 2007:161ff). The defense does not work on the edge of the board.

In this position from a 1991 game between Alexandar Budnikov and Maxim Novik, White would like to get his king to d6 and bishop to d5, to win by a method of Philidor (see Philidor position#Rook and bishop versus rook) – however the pin of the bishop to the king prevents it. If White plays 1. Kd5 or 1. Kf5 then Black moves his king in the opposite direction, so if the bishop then moves, the black rook cuts off the white king. There is another drawing method in positions with this set of material, called the "second rank" defense (with the king and rook both on a rank or file next to the edge of the board). However, the Cochrane Defense is more popular among grandmasters (Nunn 1999:174ff).

There are some key ideas for the defender to observe:

wait by moving the rook between e1 and e2
answer Kd5 with ... Kf8 and Kf5 by ... Kd8
drive the rook away from the seventh rank at the first opportunity
move the king away from the eighth rank, as near the center of the board as possible
once the king has left the back rank, hold off the king for a few moves
when the white king gets back to the fifth rank (or equivalent in other directions), switch the rook around and head for the Cochrane position again (perhaps rotated 90 or 180 degrees). This phase is important because the opposing king must not be allowed to reach the sixth rank (or equivalent).
The game continued:

1... Re1
2. Kd5 Kf8!
3. Bf5 Re7!
4. Ra8+ Kf7
5. Ra1 Kf6
6. Bc8 Re5+
7. Kd6 Re2
8. Rf1+ Kg5
9. Bb7 Re3
10. Kd5 Re2
11. Kd4 Re7
12. Bd5 Re8
13. Rf7 Rb8
14. Ke5 Rb5
and the position is back to the basic Cochrane position, rotated 90 degrees, and the fifty move rule is closer to coming into effect. The Budnikov-Novik game continued, with the Cochrane position being reached again. Eventually a draw was claimed by the fifty move rule (Howell 1997:145-47).

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