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A single knight or bishop usually isn't enough to force checkmate. However, I know there are certain positions where the defending side has his king in front of a rook pawn where a win can be forced.

So I have two questions related to this:

  • What is the longest forced win where the winning side has only a knight or bishop?
  • Are there any nontrivial (i.e., not mate in 1) forced wins that don't involve the losing side having his king trapped in front of a rook pawn?
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According to this website, the longest checkmate for K+B vs. K+P is a simple mate in one, e.g.

[FEN "8/8/8/8/8/8/p7/k1K1B3 w - - 0 1"]

The K+N vs. K+P case is slightly more interesting, the following position is mate in seven:

[FEN "8/8/8/8/p7/8/N7/k1K5 w - - 0 1"]

1. Nb4 a3 2. Nc2+ Ka2 3. Nd4 Ka1 4. Kc2 Ka2 5. Ne2 Ka1 6. Nc1 a2 7. Nb3#

You can play these endgames with online tablebases, e.g. this one from Shredder.

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  • 2
    Oh, now that's a helpful website. Looking at the 5-man ones, there appears to be one that isn't just a forced simplification to the above two positions: KB vs KNP. Neat.
    – eyeballfrog
    Commented Jan 24, 2018 at 22:23
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The longest, trivial (trivial in terms of this question that is) known forced wins where White has just a knight or a bishop are 48 moves and 38 moves, respectively. These records can be seen in Grigory Popov’s Russain "Chess Book Of Records" on superproblem.ru.

[Title "Patrick O’Shea, The Problemist 1989, 1st Prize, Mate In 48"]
[FEN "8/p2N4/p7/p7/p7/K5pp/1p3npk/6bn w - - 0 1"]

1. Ne5 b1=N+ 2. Ka2 Nd2 3. Ka1 Nb3+ 4. Kb1 Nd2+ 5. Ka2 a3 6. Ka1 Nb3+ 7. Kb1 a2+ 8. Kxa2 Nd2 9. Ka1 Nb3+ 10. Kb1 Nd2+ 11. Ka2 a4 12. Ka1 Nb3+ 13. Kb1 Nd2+ 14. Ka2 a3 15. Ka1 Nb3+ 16. Kb1 a2+ 17. Kxa2 Nd2 18. Ka1 Nb3+ 19. Kb1 Nd2+ 20. Ka2 a5 21. Ka1 Nb3+ 22. Kb1 Nd2+ 23. Ka2 a4 24. Ka1 Nb3+ 25. Kb1 Nd2+ 26. Ka2 a3 27. Ka1 Nb3+ 28. Kb1 a2+ 29. Kxa2 Nd2 30. Ka1 Nb3+ 31. Kb1 Nd2+ 32. Ka2 a6 33. Ka1 Nb3+ 34. Kb1 Nd2+ 35. Ka2 a5 36. Ka1 Nb3+ 37. Kb1 Nd2+ 38. Ka2 a4 39. Ka1 Nb3+ 40. Kb1 Nd2+ 41. Ka2 a3 42. Ka1 Nb3+ 43. Kb1 a2+ 44. Kxa2 Nd2 45. Ka1 Nb3+ 46. Kb1 Nd2+ 47. Ka2 Nb1 48. Nf3#

[Title "ChristopherJeremy Morse, The Problemist 1978, Mate In 38"]
[FEN "8/2p2p2/5p2/1B3p2/5p2/p2n4/kp1K1p2/b4r2 w - - 0 1"]

1. Bc4+ Kb1 2. Bxd3+ Ka2 3. Bc4+ Kb1 4. Bxf1 Ka2 5. Bc4+ Kb1 6. Kd1 f3 7. Kd2 f4 8. Kd1 f5 9. Kd2 f6 10. Kd1 c6 11. Kd2 c5 12. Kd1 f1=Q+ 13. Bxf1 Ka2 14. Bc4+ Kb1 15. Kd2 f2 16. Kd1 f3 17. Kd2 f4 18. Kd1 f5 19. Kd2 f1=Q 20. Bxf1 Ka2 21. Bc4+ Kb1 22. Kd1 f2 23. Kd2 f3 24. Kd1 f4 25. Kd2 f1=Q 26. Bxf1 Ka2 27. Bc4+ Kb1 28. Kd1 f2 29. Kd2 f3 30. Kd1 f1=Q+ 31. Bxf1 Ka2 32. Bc4+ Kb1 33. Kd2 f2 34. Kd1 f1=Q+ 35. Bxf1 Ka2 36. Bc4+ Kb1 37. Kd2 a2 38. Bd3#
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