Fischer Overestimates His Position

The diagram shows the last position from Fischer - Reshevsky, Match 1961 (Game 5) that I want to examine. White played 33.Rc2, and Fischer noted,

The only way to preserve winning chances. After 33.Rxb6 Rd2+ 34.Kg1 g5 35.hxg5+ {X03} (on 35.Rcc6 gxh4 36.Rxe6+ Kg5 37.Rg6+ Kh5 {X04} 38.Rxh6+ Kg4, Black has enough play on the Kingside to hold the draw; but not 35.a5? gxh4 36.a6 h3 37.a7 h2+ 38.Kh1 Ng3#) 35...hxg5 36.Rcc6 (not 36.a5? g4 37.a6 Ng5 38.a7 Nf3+ 39.Kf1 g3 40.a8=Q g2#) 36...g4 37.Rxe6+ Kg5 {X01} 38.Rh6 f4 keeps the balance {X02}.

The moves marked X0n are points where Kasparov, building on the the analysis of Dvoretsky and Huebner, disagreed with Fischer.

1961 Match (game 5)
Fischer, Robert

Reshevsky, Samuel
(After 32...Re8-d8)
[FEN "3r4/8/Rp2pkpp/5p2/P3n2P/4P3/1P4K1/2R5 w - - 0 33"]

Without repeating all of the analysis, I count four points of disagreement.

• X01: 37...Kg5 38.Rb5 wins
  
• X02: 38...f4 39.Rhg6+ wins
  
• X03: 35.hxg5+ Nxg5 is 'more tenacious'
  
• X04: 37...Kh5 38.a5 wins

Kasparov wrote,

'I know of no other example in which Fischer commits such a serious error of judgement in a rather clarified position', concludes Dr. Huebner. In my view both this mistake, and the oversight on the 36th move, are very typical of Fischer: he was very content with the course of the game, with the flights of imagination by the two players, and when he annotated the game he did not believe that he had reached a lost position, and did not seek confirmation of this. According to his inner conviction, the logical outcome should have been a draw! Although it must be agreed, in an endgame with an exchange advantage and a passed Pawn it is possible to find a win even without the help of a computer.

It's clear from studying the analysis that Fischer overestimated his counterplay in this endgame.