Knight
vs
Rook
Without pawns to defend, a knight can draw against a rook provided that the knight and king stay together. If separated, then the rook's greater mobility will overpower them. Karsten Mueller, in his wonderful 4-DVD set on the endgame, covers this lesson. He even challenges the reader, " If you don't believe me, try it yourself. " The saving grace for the defending side is that the knight can give a check whenever the opposing king comes in for a mate, but for the stronger side to effect a mate his king has to come closer. So, a quandary exists and the knight draws with correct play.
Here is an example from the Endgame Training feature of Fritz9: you can see that the knight prevents the black king from approaching via e3 or g3. The f3 square is protected indirectly by a check on h2, and the king has to back off. If the rook temporizes along the second rank, then you can also temporize with Nh2-Nf1. White can move out of the corner where he has more chances at losing. Just remember to keep the knight and king in close proximity of each other.
Let's look at some lines: 1. Nh2 Rd2 2. Nf1 Ra2 3. Nh2 Kg3 4. Nf1+ Kf3 5. Nh2+ and black cannot make progress. Another: 1. Nh2 Kg3 2. Nf1+ Kh3 3. Kh1 Re1 4. Kg1 Rd1 5. Kf2 Rb1 6. Nd2 Rb2 7. Ke3 Kg3 8. Nc4 Rb3+ 9. Ke4 and black cannot make any progress.
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