I ended up struggling quite a bit to finish off this position against a better player (I had the knight) and I'm pretty sure he did not play optimally. I've not found much info of this end game. Is a King, Rook and Knight vs King and Knight end game generally a win for the player with the rook?
I think the way to approach the problem of winning this type of position is to look at what the textbooks have to say about KRvKN and try and apply that with the benefit of having an extra knight.
Nunn identifies two wins, one where the knight and king are widely separated and one where the king gets trapped near a corner. The drawing plan for the K+N is to keep the two pieces together near the center of the board.
Fine (still a useful reference more 70 years after being published!) identifies 3 winning strategies:
1) Mating threats
2) Pinning the knight against the king when the king has to abandon the knight
3) Stalemating the knight and capturing it.
With an additional knight these threats can be more generalized because if the knights are exchanged the win is easy and the stronger side can even sacrifice his knight to lure the opposing knight far enough away from the king to make it winnable.
King + Rook + Knight versus King + Knight. Win? Yes!
My spontaneous thought is to win in two stages.
- Catch and win the enemy knight or exchange knights.
- Checkmate the enemy king
The first stage should be achieved by hunting down the enemy knight. The second stage is a K+R vs K checkmate.
The Win for the player with the Rook would be very hard to achieve. There is no real way to explain it without an in depth book reading im sorry to say.