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H. G. Muller wrote on Tue, Jul 8, 2008 03:15 PM EDT:
Betza's HFD (= (1,1)+(2,0)+(3,0) leaper) can mate a bare King (with the
aid of its own King) even on a 14x14 board. With white to move the K + HFD
vs K end-game is 100% won. There really isn't a single position that is
not won. (Some KXK end-games have a few draws when the X is trapped in a
corner by the bare King, or when they cannot lift a stalemate condition of
a cornered King that attacks the X. But not when X = Half Duck) The number
of moves it takes is:

14x14: 94
12x12: 66 
10x10: 42
 8x8:  27

On 16x16 it is usually draw: only 7.78% of the positions with white to
move is won. The longest win on 16x16 still takes 65 moves, though, from
the following position:

 k . . . . . . . . . . . . . . . 16
 . . . . . . . . . . . . . . . . 15
 . . . . . . . . . . . . . . . . 14
 . . . . . . . . . . . . . . . . 13
 . . . . . K . . . . . . . . . . 12
 . . . . . . . . . . . . . . . . 11
 . . . . . . . . . . . . . . . . 10
 . . . . . . . . . . . . . . . . 9
 . . . . . . . . . . . . . . . . 8
 . . . . . . . . . . . . . . . . 7
 . . . . . . . . . . . . . . . . 6
 . . . . . . . . . . . . . . . . 5
 . . . . . . . . . . . . . . . . 4
 . . . . . . . . . . . . . . . . 3
 . . H . . . . . . . . . . . . . 2
 . . . . . . . . . . . . . . . . 1
 a b c d e f g h i j k l m n o p
White to move, mate in 65.

Solution:
1. Hc5, Kb15 2. Hc8, Kc14 3. Hc11+, Kd14 4. Kf13, Ke15 5. Kg14, Ke14 6. He11+, Ke15 7. Kg15, Kd14 8. Kf14, Kd13 9. Kf13, Kc13 10. Ke13, Kc12 11. Ke12, Kc13 12. Hd10, Kd14 13. Hd13, Ke15 14. Kf13, Kf15 15. Hg13, Ke15 16. Hh12, Kf15 17. Hh14, Kf16 18. Kf14, Kg16 19. Kg14, Kf16 20. He14, Kg16 21. He16+, Kf16 22. Hf15, Ke15 23. Hf13, Kd14 24. Kf14, Kc14 25. Ke13, Kb13 26. He12, Kc13 27. Hd11, Kc14 28. Hd14, Kb13 29. Kd12, Kb12 30. Hd11, Kb13 31. He10, Kb12 32. Hc10, Ka12 33. Hb9, Kb13 34. Kd13, Ka12 35. Kc12, Ka11 36. Kc11, Ka12 37. Hb12, Kb13 38. Hd12, Kc14 39. Kc12, Kc15 40. Kd13, Kd16 41. He13, Kc15 42. Hf14, Kd15 43. Hg15+, Kc15 44. Kc13, Kd16 45. Kd14, Ke16 46. Ke14, Kd16 47. Hd15, Kc15 48. Hd13, Kb14 49. Kd14, Kb15 50. Hb13+, Kb14 51. Hb11+, Kb15 52. Kd15, Ka14 53. Kc14, Ka13 54. Kc13, Ka14 55. Hb14, Kb15 56. Hd14, Kb16 57. Kc14, Ka14 58. He15, Kb16 59. Hb15, Ka15 60. Hb13, Ka16 61. Kc15, Ka15 62. Ha12+, Ka16 63. Ha14+, Ka15 64. Ha11, Ka16 65. Ha13#