was the defense I saw.

33...Ne7 ties black up even more IMO

34.Ra8,Rcc7 35.Bg6 + -

So if simply 32.Nxe4 fxe4 33.Bxe4 Rcc7 34.Bxb7 Rxb7, white gets 2 pawns and a rook (worth about 7 pawns) for two pieces (worth about 6.5 pawns). And since white was a pawn down to begin with, this leaves black with about half a pawn advantage. I would play it based on this fact alone without doing a thorough analysis which isn't always possible in a fast game (like 30 minutes). It takes about 1 pawn advantage to be "winning" and if you can reduce your opponents pawn advantage to half a pawn, it's closer to a draw.

After analyzing, I saw that I made a key mistake early on. I figured after 32.Nxe4 what if black tries to hold the pawn with 32...Rxc4? Things then got more complicated when trying to play Qb3 or Qa2 and win the exchange. But white can simply play 33.Nf6+ Nxf6 34.Bxb7. Materially, the exchange is worth about 1.75 pawns and this would leave white with a 3/4 pawn advantage.

The natural move for black (i.e. the only move I considered) was 33...Ne7, protecting the knight and guarding the c6 rook. However, this leaves white with the pleasant situation of having a free move (the rooks are still speared, so our threat of winning the exchange isn't going away).

It took me a moment to find the best move to exploit this situation, but I finally noticed that after our bishop and black's knight clear the e-file, our rook will be attacking the Ne8, and so 34.Ra8! setting up the double attack on that knight came into view.

Lombardy vs Polugaevsky, 1978 (32.?)

White to play and win.

Material: B for N+P. The Black Kg8 has 3 legal moves and is open to check on the a2-g8 diagonal. Both Black Rb7 and Rc6 are loose, as is Ng6. The White Ra1 has the open a-file; and Qb2 has the semi-open long diagonal a1-h8 terminating at Pg7. The White Kg8 is secure. The White Nd2 and Bg2 have limited scope and require activation, but they both focus on Pe4. Given the conjunction of Bg2, Pe4, Rc6, and Rb7 on the long diagonal a8-h1, the action is likely to be on the Q-side. Capture at e4 is interesting, and the piece remaining there should be Bg2, to skewer Rc6 and Rb7 while forking Ng6. The capture might also open the e-file, activating Re1 with the threat Rxe8.

Candidates (32.): Nxe4

32.Nxe4 (threatening 33.Nf6+ or 33.Nd2 then 34.Bxc6 or 34.Bxb7)

Black can accept the sacrifice:

(1) 32…fxe4

Candidates (33.): Bxe4, Rxe4

33.Bxe4 (threatening 34.Bxc6 or 34.Bxg6)

Black has only 2 responses to avoid being immediately at least a P down:

(1.1) 33…Ne5 34.Bd5+ (threatening 35.Rxe5)

White recovers at least the piece and remains a P up.

(1.2) 33…Ne7 34.Ra8 (threatening 35.Bxc6 36.Rexe8)

34...Rcc7 35.Bg6 (threatening 36.Rxe8)

35…Nxg6 36.Rexe8

White remains up Q for R+N.

Black can decline the sacrifice:

(2) 32…Rcc7

signed~~~
Mister Hyde

[ply 12/34 time 00:02 value +2.85]

32…Rcc7 33.Nc3 Ra7 [else, Bxb7] 34.<Nd5> Rxa1 35.Qxa1 Rxc4 36.Qa8 Nc7 37.Qa2 Ne5 38.f4 Nxd5 39.fxe5 Rd4 40.Bxd5+ Kh7 41.e6 Rxb4 42.e7 Qe8 43.Qd2

[ply 15/49 time 01:04 value +2.98]

Hi, <JG27Pyth>. I was not very happy with my analysis of what happens if Black declines, but my general rule of thumb is if acceptance is off-limits, the sacrifice is probably the best move.

Your line is for sure better than the game continuation, but after 35. Ra7 black is in serious trouble. Black needs to defend the knight or move it. There are very few possibilities. Certainly not 35 . . . Nd8 when 36. Re8! wins outright. 35 . . . Qf7 just pins the knight to the queen. On 35 . . . Nd6 36. c5 is strong. Best may be 35 . . . Rb8, but again 36. c5, and if, say, 36 . . . Ne7 (to prevent c6), then 37. Qe5 with powerful threats.