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In Damanovic-Fischer, it seems like the move played, 66. bxa4+, made it easy for Fischer. Wasn't 66. Ke3 better?

       [Title "Damanovic- Fischer, 1970,"]
       [FEN ""]
       [startply "130"]

       1. d4 Nf6 2. c4 c5 3. Nf3 cxd4 4. Nxd4 Nc6 5. Nc3 g6 6. e4 d6 7. Be2 Nxd4 8. Qxd4 Bg7 9. Be3 O-O 10. Qd2 Be6 11. f3 Rc8 12. Nd5 Nd7 13. O-O Nc5 14. Rac1 a5 15. b3 Bxd5 16. cxd5 Qb6 17. Rc4 Qa7 18. Rc2 Bh6 19. f4 Rc7 20. g3 b6 21. Rfc1 Bg7 22. Bb5 Qa8 23. Qe2 e5 24. dxe6 fxe6 25. Rd1 Rd8 26. Bd4 Bxd4+ 27. Rxd4 e5 28. fxe5 dxe5 29. Rxd8+ Qxd8 30. Bc4+ Kg7 31. Bd5 Nd7 32. Qf2 Rxc2 33. Qxc2 b5 34. Kg2 b4 35. Qc6 Nf6 36. Kf3 Qd7 37. Qxd7+ Nxd7 38. Ke3 Kf6 39. Kd3 Nb6 40. Bc6 Ke7 41. h4 h6 42. Ke3 Nc8 43. Kd3 Nd6 44. Ke3 Kd8 45. Kd3 Kc7 46. Ba4 Kb6 47. Ke3 Kc5 48. Bd7 Kb6 49. Ba4 Kc7 50. Kd3 Kd8 51. Bc6 Ke7 52. Ke3 Ke6 53. Kf3 Kf6 54. g4 g5 55. h5 Ke7 56. Ke3 Kd8 57. Kd3 Kc7 58. Ba4 Kb6 59. Bd7 Kc5 60. Ba4 Nc8 61. Be8 Ne7 62. Ke3 Ng8 63. Bd7 Nf6 64. Bf5 Kb5 65. Kd3 a4 66. bxa4+ 66... Kxa4 67. Kc4 Ka3 68. Kc5 Kxa2 69. Kxb4 Kb2 70. Kc5 Kc3 71. Kd6 Kd4 72. Ke6 Nxe4 73. Kf7 Nf2 74. Kg6 e4 75. Kxh6 e3 76. Kg7 e2 77. h6 e1=Q 78. h7 Qe7+ 79. Kg8 Ne4 0-1
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    I love the last move of the game, 79...Ne4. After the forced 80.Be4 Ke4 81.a1(Q) Qd1+, he trades on a1, and then plays Kf4 winning the simple K+P ending that is left.
    – PhishMaster
    Commented Nov 20, 2019 at 20:20

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This was played almost at Fischer’s height of strength, so he almost surely would have won anyway after 66.Ke3 also. I think that white thought two things by playing 66.ba. First, that it reduced the number of pawns, which is almost always good when you are in a worse, or losing, endgame. Second, that the bishop might be able to defend a2 along the a2-g8 diagonal.

After 66.Ke3, white will fall into zugzwang due to his bad bishop, or at least, he believed he would. If that happens, the black knight can do some pretty fancy high stepping. This is what I found, but it turns out there actually is a miracle draw, but it is doubtful that any human would have put his B on a4 (to stop Nc4; bc b3 queening).

So, I guess, considering that miracle possibility, the answer is a firm "yes, it would have been better".

[FEN "8/8/5n1p/1k2pBpP/pp2P1P1/1P1K4/P7/8 w - - 0 66"]

1. Ke3 a3 2. Kd3 Kc5 3. Ke3 Ne8 4. Kd3 (4. Bd7 Nd6 5. Ba4) 4... Nd6 5. Bd7 Nc4 6. Be8 Nb2+-+

At the end of the line, the N either gets Nd1-c3-a2 or the Kc5 gets to d4. In either case, winning easily.

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    Thank you again, Brian. One of these days, I am going to figure out why that will not work for me.
    – PhishMaster
    Commented Nov 20, 2019 at 14:44
  • The position after bxa4 seems a lot harder to assess as now you also have to deal with the black king entering. Without bxa4 it seems quite easy to see that you can prevent the black knight from entering via c3, d4 or f4 by just covering the squares b5, c6 and e6 at the right moment with the bishop. So Damanovic must have seen the Nc4 idea and did not find a defense.
    – user1583209
    Commented Nov 20, 2019 at 18:24
  • @user1583209 Maybe, but you have to see that in its entirety right at that moment. If you do not see Ba4, again not a typical human idea, then at that level, he might have seen zugswang coming as you said. I have it much easier using a computer to check my work. :)
    – PhishMaster
    Commented Nov 20, 2019 at 20:11
  • Instead of heading for a4, can't the wB simply defend on the c4-g8 diagonal, e.g. 3...Ne8 4.Kd3 Nd6 5.Be6, intending to pass with Bg8-e6-g8 or Kd3-e3-d3 ?
    – Evargalo
    Commented Nov 25, 2019 at 14:06
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You are correct, 66.bxa4+ is an inaccuracy and gives Black a winning advantage. Stockfish gives 66.Ke3 a -0.64 evaluation, which remains constant as it quickly reaches higher depths of searching (+depth 60). This indicates the game was probably objectively a draw if White hadn't captured on a4 (though it wouldn't have been fun).

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