tale of 2 blunders involving Rook endgames

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Here Joseph made the mistake and losing the chance of forcing a draw. Below is where ginger63 turned down a draw offer to make the mistake that causes the game.
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frenckscacco's ITALIA2
grietje (1599) vs. ginger63 (1727)

1 2 3 4 5 6 7 8 h g f e d c b a -4

Result: white won 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O d6 6. Re1 Bg4 7. c3 Be7 8. d3 h6 9. Be3 O-O 10. Nbd2 b5 11. Bc2 Qd7 12. d4 d5 13. exd5 Qxd5 14. h3 exd4 15. Bxd4 Nxd4 16. cxd4 Bxf3 17. Nxf3 Bd6 18. Qd3 Rfe8 19. Ne5 Bxe5 20. dxe5 Rxe5 21. Rxe5 Qxe5 22. Qf3 Re8 23. Rb1 c5 24. b3 Qe2 25. Qxe2 Rxe2 26. Rc1 Ne4 27. Bxe4 Rxe4 28. Rxc5 Re1+ 29. Kh2 Re2 30. a4 bxa4 31. bxa4 Rxf2 32. Rc8+ Kh7 33. Rc6 Rf6 34. Rc5 g6 35. Ra5 Rc6 36. Rd5 Kg7 37. Kg3 g5 38. Ra5 Kg6 39. h4 f6 40. hxg5 hxg5 41. Kh3 Rc3+ 42. Kh2 Rc6 43. Rd5 Re6 44. Ra5 f5 45. Rc5 f4 46. Rc4 Kf5 47. Rc5+ Re5 48. Rc4 a5 49. Rc8 Kg4 50. Rc4 Rf5 51. Rd4 Rb5 52. axb5

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