Knight v. Pawns
A basic idea in an ending with a knight against pawns is that the player with the knight looks for opportunities to force the pawns to move onto squares where they are vulnerable to forks. Here is an example from a game I played last Saturday in Evanston. White can draw this position but my opponent only had about a minute left on his clock and those forky things that knights do can be very difficult to visualize when time is running low.
My opponent played 51.Ka6?? which allowed me to win by driving the e-pawn forward with 51...Nd3! 52. e6 Nc5+ 53. Ka7 Nxe6 and Black had no trouble rounding up the last two pawns. However, White could still have drawn 51.a4! Ne6 52. b4 Nc7 53. b5+ Kc5 54. Kb7 Ne6 55. Ka6 Nc7+.
Black can do nothing because his king must guard the pawn and his knight has to keep the White king off a6 lest he trade off Black's last pawn by playing a5.
Here's a tricky one from the 1956 Candidates Tournament. Black has little chance to save his own pawns, but if he can win either the White g-pawn or h-pawn and sacrifice the knight for the other one, his king can blockade the a-pawns. I stared at it for about an hour recently without coming up with the correct drawing plan for Black, but I don't feel so bad as Efim Geller didn't come up with the right move against Tigran Petrosian either and lost after 51...Nb6 52.a5 Na8.
The correct plan is 51... Nc5+! 52. Kf7 Kb7 53. Kxg7 Ne4 54. Kxh7 Nd2!.
Black is threatening to win one of the pawns with 55...Nf1 and none of White's pawn moves are satisfactory. If 55.g4 Nf3 56.h3 Ng5+. If 55.h4 Ne4 56.g4 Nf6+. If 55.h3 Ne4 56.g4 Ng5+.
Knights v. Bishops
An interesting thing about the three round Evanston tournament is that I got two positions in which I had knight, rook, and five pawns with the Black pieces against White's bishop, rook and five pawns. The results were exactly opposite, however, which may have something to do with the fact that one of my opponents was rated 2200 and the other was rated 1739.
In the first round, I had the kind of position that a knight loves. White's bishop is confined by the Black knight and his own pawns. Nevertheless it took some imagination to convert the advantage. Here I played 32...h4! 33. Rxe5 h3+ 34.Kg3 (If 34.Kg1 Nf3+ wins the rook) 34...Rxf1 and the first position in the post was eventually reached.
In the third round, I had the kind of position that the knight loathes. Here the bishop has complete freedom of movement and the Black pawns on light squares are easy targets. After 36.Rd5 b4 37.Ra5 bxa3 38.bxa3, White can pick off the a-pawn at his leisure.