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Recently, I came across a game Vishwanathan Anand vs Veselin Topalov from Norway Chess 2022. In the second round, Anand who was playing with the black pieces won on time against Topalov as his clock ran out. The position was equal according to the engine.

Is this the highest-rated classical game that was lost on time? Or is there any other game much higher rated?

The ratings were: Topalov (2730) vs Anand (2751)

NOTE: By highest rated, I mean according to FIDE classical ratings and the sum of the ratings of the players. In this example, it is 2730 + 2751 = 5481

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    In the 2013 Candidates, Ivanchuk was rated 2757 and lost on time four times. It'll be one of those, I think. Jun 3, 2022 at 12:13

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Not sure if this is the all-time highest-rated classical game ever lost on time but Magnus Carlsen's game against Veselin Topalov from Round 1 of Norway Chess 2015 was lost on time.

Yes, one more loss on time from Norway Chess itself! This time Veselin Topalov got the win :).

Carlsen was rated 2876 and Topalov was 2798 making it 2876+2798 = 5674. Here's that game:

[Title "Carlsen vs Topalov Norway Chess 2015"]

[FEN "1b6/1P3k2/8/6Q1/5p2/6PK/4Bq2/8 w - - 2 61"]
1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. Nc3 e6 5. Bg5 h6 6. Bxf6 Qxf6 7. e3 Nd7 8. Rc1 g6 9. Be2 Bg7 10. cxd5 exd5 11. b4 a6 12. a4 O-O 13. b5 axb5 14. axb5 Qd6 15. O-O Nb6 16. Qb3 Rb8 17. Nd1 Bf5 18. Nb2 Rfc8 19. Nd3 Bxd3 20. Qxd3 c5 21. dxc5 Rxc5 22. h4 Na4 23. h5 Rbc8 24. Rxc5 Nxc5 25. Qc2 gxh5 26. Nd4 Qg6 27. Nf5 Bf8 28. Rd1 Qe6 29. Rc1 Nb3 30. Qxc8 Nxc1 31. Qxc1 Qxf5 32. Qc7 Qb1+ 33. Bf1 d4 34. exd4 Qd1 35. Qe5 Bg7 36. Qe8+ Bf8 37. Qd8 Kg7 38. Qd5 b6 39. Qe5+ Kg8 40. Qf6 Bg7 41. Qxb6 Bxd4 42. Qxh6 Qg4 43. Qd6 Qd1 44. Qd8+ Kh7 45. Qc7 Kg7 46. b6 Qg4 47. b7 Qh4 48. g3 Qf6 49. Qc2 Qe5 50. Qd3 Ba7 51. Qf3 Qf6 52. Qe2 Qc3 53. Kh2 Qd4 54. Qf3 Bb8 55. Kh3 Bc7 56. Be2 Bb8 57. Bd1 f5 58. Be2 f4 59. Qxh5 Qxf2 60.Qg5+ Kf7 0-1

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