Can this pawn make it to the finish line?


[Event "pranshumishra2505 vs. Toureg1"] [Site "Chess.com"] [Date "2020-06-30"] [White "pranshumishra2505"] [Black "Toureg1"] [Result "0-1"] [WhiteElo "805"] [BlackElo "939"] [TimeControl "blitz"] [Termination "Toureg1 won on time"] 1. d4 e6 2. e3 d5 3. Nc3 Nf6 4. Nf3 c5 5. dxc5 Bxc5 6. Bb5+ Nbd7 7. Ne5 Qa5 8. Bd2 Qc7 9. O-O Qxe5 10. f4 Qh5 11. Qxh5 Nxh5 12. Bxd7+ Bxd7 13. a3 Nf6 14. b4 Bb6 15. Rab1 Ne4 16. Nxe4 dxe4 17. a4 Bxa4 18. c4 Bc2 19. Rbd1 Bxd1 20. Rxd1 Rc8 21. c5 Bd8 22. Bc3 f6 23. Rd6 e5 24. fxe5 fxe5 25. Re6+ Be7 26. Bxe5 Rf8 27. Bxg7 Rf7 28. Be5 b6 29. c6 a5 30. c7 axb4 31. Rxb6 Kd7 32. Rb8 Rxc7 33. Bxc7 Kxc7 34. Rb5 Kc6 35. Re5 Bc5 36. Rxe4 b3 37. Rc4 Rb7 38. Rc1 b2 39. Rb1 Bxe3+ 40. Kf1 Kc5 41. Ke2 Bf4 42. Kd3 Bxh2 43. Kc2 Kd4 44. Rxb2 Rxb2+ 45. Kxb2 Ke3 46. Kc2 Kf2 47. g4 Kg3 48. g5 Kg4 49. Kd3 Kxg5 50. Ke4 h5 51. Kf3 h4 52. Kg2 Bd6 53. Kh3 Be5 54. Kg2 Kg4 55. Kg1 Kg3 56. Kh1 Bf4 57. Kg1 Kh3 58. Kh1 Bg5 59. Kg1 Bf6 60. Kh1 Kg3 0-1
You've already figured out it was a draw there at the end. Your mistake was letting the king in with 50. ...h5. Instead, 50. ...kg4 keeping the white king out wins. For an example line, 50. ...kg4 51. ke3 kg3 52. ke2 and now h5 is safe because the king cant actually stay in 53. kf1 h4 and now the king must leave 54. ke2 kg2 and now its easy to see there is nothing left white can do to cause trouble.
The final position is a well-known "wrong rook pawn" situation where the corner pawn promotes on a square which is not protected by a friendly bishop.
The removal of the White king from the g1 and h1 squares cannot be forced once the White king reaches those two squares.
With a light-squared bishop instead (placed on e6, for example) the pawn would eventually make it to the finish line safely.
You've already figured out it was a draw there at the end. Your mistake was letting the king in with 50. ...h5. Instead, 50. ...kg4 keeping the white king out wins. For an example line, 50. ...kg4 51. ke3 kg3 52. ke2 and now h5 is safe because the king cant actually stay in 53. kf1 h4 and now the king must leave 54. ke2 kg2 and now its easy to see there is nothing left white can do to cause trouble.
41...Bc1 is likely game over for White though.
You've already figured out it was a draw there at the end. Your mistake was letting the king in with 50. ...h5. Instead, 50. ...kg4 keeping the white king out wins. For an example line, 50. ...kg4 51. ke3 kg3 52. ke2 and now h5 is safe because the king cant actually stay in 53. kf1 h4 and now the king must leave 54. ke2 kg2 and now its easy to see there is nothing left white can do to cause trouble.
41...Bc1 is likely game over for White though.
True, I didn't back up that far, started from the end and stopped once I saw a spot where the win was lost. Agree 41. ...bc1 is a highly useful simple lesson for the OP. The opportunity to restrict enemy pieces is important, and 41. ...bc1 permanently neuters the rook.
50. ...kg4 is a bit more complicated to understand why its necessary perhaps, but the concept of boxing out the enemy king can save many endgames.

Toureg, it is worth knowing that the general concept here is called "having the opposition". Once your king is separated by only one space from the opponent king, they cannot move any closer towards you, and are forced to move sideways or backwards. This theme comes up a lot in king and pawn v king and pawn endgames so worth reading up / practicing it.