An instructive King and Pawn ending

 Rapid chess isn't known for deep endgame analysis, but it can still throw up some interesting positions. In tonight's ACT Online Rapid there was a very interesting K+P ending, which both players found some very good moves, and some not so great ones. Given the time control (10m+2s) it is unfair to criticise the missed wins (and draws), but I have highlighted them anyway, to show the turning points in the game.

Of particular interest is the last variation, which shows how K+Q v K+Q isn't always an automatic draw.

RapanasCorner - chesslh [D53]
https://lichess.org/pVb9REtO

1. d4 Nf6 2. c4 e6 3. Nc3 d5 4. Bg5 Be7 5. e3 h6 6. Bh4 O-O 7. Qc2 Ne4 8. Bxe7 Qxe7 9. Nxe4 dxe4 10. a3 f5 11. Ne2 e5 12. dxe5 Nc6 13. Nf4 Nxe5 14. Be2 Be6 15. Qc3 Bf7 16. O-O c6 17. Rfd1 Rad8 18. b3 g5 19. Nh5 Bxh5 20. Bxh5 Qg7 21. Kh1 Nd3 22. Qxg7+ Kxg7 23. Kg1 Kf6 24. Be2 Nc5 25. b4 Ne6 26. c5 Rxd1+ 27. Rxd1 Rd8 28. Rxd8 Nxd8 29. Kf1 Ke5 30. Ke1 Ne6 31. Kd2 Nc7 32. Bc4 Nd5 33. Kc2 Nf6 34. h3 Nd5 35. Ba2 Nf6 36. Bf7 Nd5 37. Bxd5 Kxd5 38. Kc3 a6 39. Kb3 a5 40. g3 h5 41. h4 ( 41. Ka4 axb4 42. Kxb4 f4 43. gxf4 gxf4 44. h4 Ke6 ( 44... fxe3 45. fxe3 Ke5 46. Kc4 Kf5 47. Kd4 +- ) ( 44... Ke5 45. Kc4 +- ) 45. Ka5 ( 45. Kc4 Ke5 46. a4 Ke6 47. Kd4 Kf5 48. a5 f3 49. Kc4 Kg4 ) 45... Kd5 ( 45... fxe3 46. fxe3 Kf5 ( 46... Kd7 47. Kb6 Kc8 48. Ka7 Kc7 49. a4 Kc8 50. a5 Kc7 51. a6 bxa6 52. Kxa6 Kd7 53. Kb7 +- ) 47. Kb6 Kg4 48. Kxb7 Kf3 49. Kxc6 Kxe3 = ) ( 45... Kd7 46. exf4 +- ) 46. Kb6 fxe3 47. fxe3 Kc4 48. Kxb7 Kd3 49. Kxc6 Kxe3 50. Kd5 Kf4 51. c6 e3 52. c7 e2 53. c8=Q e1=Q = ) 41...  gxh4 42. gxh4 axb4 43. axb4 Ke6 44. Kc4 Ke5 ( 44... f4! 45. exf4 Kf5 -+ ) 45. b5 cxb5+ 46. Kxb5 Kd5 47. Kb6 ( 47. Kb4 Ke6 48. Kc4 Ke5 49. c6 bxc6 50. Kc5 Ke6 51. Kxc6 Ke5 52. Kd7 f4! 53. Ke7?? ( 53. exf4+ Kxf4 54. Ke6 Kg4 55. Ke5 Kxh4 56. Kxe4 = ) ) 47...  Kc4 48. Kxb7 Kxc5 49. Kc7 Kc4?? ( 49... Kd5 = 50. Kd7 Ke5 51. Ke7 f4 ) 50. Kd6 Kd3 51. Ke5 Ke2 52. Kxf5 Kxf2 53. Kxe4 Kg3 54. Kf5 Kxh4 55. Kf4! Kh3 56. e4 Kg2 57. Kg5? = ( 57. e5! h4 58. e6 h3 59. e7 h2 60. e8=Q h1=Q 61. Qe2+ Kg1 ( 61... Kh3 62. Qg4+ Kh2 63. Qg3# ) 62. Kg3!! ) 57...  Kg3! 58. e5 h4 59. e6 h3 60. e7 h2 61. e8=Q h1=Q 62. Qe3+ Qf3 63. Qxf3+ Kxf3 1/2-1/2