25.d4,b5
26.Bd5,Rd8
27.f4,Bh4
28.Re7,BxR
29.QxB,h5
30.Qf6+,Hh7
31.Qe7+
with perpetual check.

Here's the position, with white to play:

click for larger view

Now, I don't think that Nezh saw all the moves to the end of the game. I think he saw this sequence:

17. Nxc7 Qxc7 18. Qd5+

click for larger view

Now white threatens to pick up another pawn (and possibly the exchange) by 19. Bxd6, which forks queen and rook. Or on 18...Rf7 he gets to play 19. Re7, with all manner of threats along the seventh. Two pawns plus an attack seems a fair return for a knight, especially as black's queenside is so undeveloped.

Then when he got to 18...Kh8, my guess is that he thought again and decided to change his plan by infiltrating a rook to e8 and repositioning his black squared bishop to b2.

25.Re8+ Qxe8
26.Qxf6#

25.Re8+ Bxe8
26.Qg8#

Looks good to me.
Time to check. :D

Simple enough, but Reti also had to see a coup on e8 several moves in advance. This is the position before white's last and winning move:

click for larger view

I did not see this instantly, but after quickly examining the options (there are not many), I see

25. Re8+

Now. 25.....Bxe8 26. Qf8 mate

if 25.....Qxe8 26. Qxf6 mate

This is obviously the solution.

If 18...Kh8 19. Bxd6, 19....Nf6 is now strong. But after 19. Re8 (as in the game) Ne5, what does white do? If 20. Rxf8 Bxf8 or 20. Qxd6 Qxd6 21. Bxd6 Rxe8, black can apparently hold the position. If 20. Bxd6, then 20...Rxe8 21. Bxc7 Nf3+! 22. Qxf3/gxf3 23. Rxe1+, and black, with ♖+♖ vs. ♕+♙+♙ has a chance to survive.

<Then when he got to 18...Kh8, my guess is that he thought again and decided to change his plan by infiltrating a rook to e8 and repositioning his black squared bishop to b2.>

Carlsen is definitely talented but that's not my point. I was half-way joking in my previous post, but there is some truth in it. Even if a kid shows a lot of potential at a young age, it usually takes a lot of coaching by a strong player to help them reach their full potential. And by then, they've devoted a lot of their childhood to chess--which is kind of sad in a way. It's not that I don't like chess, obviously I do, but childhood is something you don't get back and in my opinion a lot of it should be spent playing with other kids through physical activities.

25 h4 Bxh4
26 g3 Bg5
27 f4 d5
28 Bxd5 h6
29 Re3 Qd6
30 fxg5 Rf8
31 Qe7 Qxe7
32 Rxe7 Rd8
33 Bxb7 hxg5
34 Bd5

It took awhile but then I saw it: Re8+. The past few puzzles that I've seen have been very instructive--deflection and focusing on getting pieces off of key squares to open up an attack. After seeing that leading with the queen didn't go anywhere, I thought, "Where would the ideal square be for the lady? Can she get there?" And I got it.

So I think we can discount the theory that Grandmasters routinely calculate very long lines. Unless the sequence is very forced, the possibilities are simply too great. Instead they use their intuition, honed over many games, to decide whether a position is good or bad for them.

And, as you say, history is written by the victors. So we tend to see the games where this semi-gamble pays off and the long-range sacrifice works.

I have a personal theory about sacrifices in chess. If I am playing someone graded below me, then I will allow myself a few small sacrifices - the odd pawn or two, compromised pawn positions, exchanges, that sort of thing. As long as I get a reasonably open and interesting position, I don't mind giving away some wood. Against lower graded players, this doesn't seem to matter as I reckon I will spot the tactics better than they will.

But this approach is a lot more risky - for me at least! - against higher graded opponents. They tend to grab all the material I give them, then defend stoically to an endgame where the extra material is ground down to a technical win. These are the games that don't get published, don't involve long calculation, and yet win the majority of times.

Then the rest of the attack sort of flows, with threat after threat, and not so much calculation needed.>

I seriously doubt that Nezhmetdinov was aiming to exchange a knight for two pawns. Then just happened to get 18...Kh8 which changed his plans. Even I could see that the only other legal move 18...Rf7 leads to 19. Re8+ Nf8, 20. R1e7, which is disaster for black.

So, 18 Kh8 is infact forcing, which Nezhmetdinov must have calculated.

From Wikipedia:
Grandmaster Yuri Averbakh, a strong positional and endgame player, suggested a possible reason for this in his interview by Dirk Jan ten Geuzendam in The Day Kasparov Quit:

17.Rxe5 Bxe5?! 18.Rxe5 dxe5 19.Be7 wins the queen.

Serper gives a series of tactical puzzles taken from this game: