In 'The World's Greatest Chess Games', Burgess gives the note:

"21...Ng6 22.Bxd6 Qxd6 looks like quite a reasonable alternative."

Not only does 22...Ke7! save Black's game, it gives him a clear advantage. There is no need to keep the King on f8 to defend the pawn on g7. After 22...Ke7, the pawn is untouchable as 23. Qxg7?? Rg8! 24. Qh6 Nd3+ turns the tables and Black wins (diagram below).

click for larger view

After 23.cxd3 Bxf4+!, Black wins the White Queen with a Bishop fork.

Tal lanunches nearly his entire armada of battleships in an attack targeting the desperately defended g7 square. Indeed, the position after 35...Qxc6 reminds of a game of battleship, where White has positioned his entire armada together in one corner. Now, if this were Pearl Harbor or a game of battleship, such a tactic might lose.

If you watch this video, and think it can't get any campier, just wait until 2:00 = http://www.youtube.com/watch?v=InBX...

So here are the main lines. The tree starts with tpstar’s 30 Nxe5 Qxe5 31 gxf5. A) Then 31...exf5 is one option. I came up with 32 Nxb5. I) 32...Rab7 33 c3
a) 33... Rxb5 34 Bxg7+ Rxg7 35 Rhxg7 Qe3 36 Kb1 and then 36...Qd3+ 37 Ka1 Be6 38 Rxg8+ Bxg8 39 Rxg8+ Ke7 40 Qe5+ Kd7 41 Rg7+ or 36...Be6 37 Rxg8+ Ke7 (...Bxg8 38 Rxg8+) 38 Rg1g7+ Kd6 39 Rd8+ Kc6 40 Qe8+ Kb6 41 Rb8+ b) 33...Rfe7 or Rbe7 34 Nd6 Qxd6 35 Rhxg7 Rxg7 36 Rxg7 Rxg7 37 Qxg7+ c) 33...Be6 34 Nd4 Bc8 35 Nc6 Qc7 or Qf6 36 Nd8 Qxd8 37 Bxg7+ and then 37...Ke7 38 Bf6+ Nxf6 39 Rxf7+ or 37...Ke8 38 Qxg8 Ke7 39 Bf6+ II) 32...Rad7 33 Nd6
a) 33...Rxd6 34 Bxg7+ Rxg7 35 Rhxg7 Qe3 36 Kb1 Be6 37 Rxg8+ Bxg8 38 Rxg8 b) 33...Qxd6 34 Bxg7+ Rxg7 35 Rhxg7 Rxg7 36 Qxg7+
III) 32...Rxa2 33 Bxg7+ Rxg7 34 Qxg7+ Qxg7 35 Rgxg7 Ra1+ 36 Kd2 a) 36...Rf1/Ra5/Ra8 37 Rf7+ Ke8 38 Nd6+ and 39 Rf8 mate b) 36...Nf6 37 Ra7
c) 36...Be6 37 Ra7 or 37 Rb7 Ra8 38 Nc7

B) 31...Ba6 32 fxe6
I) 32...Re7 33 Nxd5
a) 33...Qxd5 34 Rhxg7 Rxg7 35 Rxg7 Qh1+ 36 Rg1+
b) 33...Rxe6 34 Rhxg7 Rxg7 35 Bxg7+
c) 33...Rb7 34 Rf1+ Ke8 35 Qxg8 mate
II) 32...Qxe6 33 Bxg7+ Ke7 34 Bd4 or 33...Rxg7 34 Rhxg7

This is definitely a compelling and captivating game, already saved in 80+ Game Collections below, so many chess fans are attracted to this slugfest. Your analysis is very neat and orderly, and you have outlined most of the main ideas at that critical juncture. Keep this up and you will indeed become a strong and trained player. =) Note that Black avoided ... axb5 for several moves (25. Bxb5 and finally 32 ... axb5), perhaps because of an innate sense of White's attack; since the focal point was g7, it is risky to allow Nxb5 deflecting the Queen off g7 plus potentially trading off the Bd6 which defends the dark squares. Yet 29 ... axb5 was identified by Fritz 7 as "the best bet to save the position" so I think you're on the right track. Accepting the sacrifice immediately with 25 ... axb5 would also have led to a much different game. We are fortunate to live in a time where computer analysis can help amateurs and students understand unclear positions, meaning no disrespect to the players who must figure things out OTB while left to their own devices. Moreover, analysts have unlimited time to examine key variations with no ticking clock nearby; the following engine overview took several days to prepare.

Instead of 29 ... Bxc3 (which Fritz 7 harshly assigns "?") let's consider 29 ... axb5 30. Nxe5 Qxe5 31. gxf5:

click for larger view

Fritz 7 Deep Position Analysis [20MB]:

1) 31 ... exf5

a) 32. Bd2 Rfe7 33. Re1 Qd6 34. Rxe7 Rxe7 [0.44/11]

b) 32. Bd2 Be6 33. Re1 Qf6 34. Nxb5 Ra4 [1.16/12]

c) 32. Rf1 f4 33. Rxg7 Qe3+ 34. Kb1 Rxg7 = 0.12/13]

d) 32. Rf1 b4 33. Bf4 Qe6 34. Nb5 b3 [2.03/12]

2) 31 ... Rab7

a) 32. Ne2 exf5 33. Bd2 f4 34. Bb4+ Rbe7 [2.41/13]

b) 32. Ne2 Rbc7 33. f6 Qxf6 34. Nf4 Qxh6 [3.44/13]

c) 32. Kb1 exf5 33. Ne2 f4 34. Nxf4 Bf5 [1.62/13]

d) 32. f6 Qxf6 33. Kb1 Qd4 34. Rd1 Qa7 0.62/12]

3) 31 ... Rac7

a) 32. Kb1 exf5 33. Bd2 Qd4 34. Rgh1 Rfd7 [1.31/12]

b) 32. Bd2 d4 33. Ne2 Qc5 34. Bb4 Qxb4 [1.12/13]

c) 32. Nxb5 Rb7 33. a4 exf5 34. Bd2 Qe4 [2.16/12]

So Fritz 7 gives 31 ... exf5 as best play for Black (and not wasting any time with sidelines like 31 ... Rxf5? 32. Bxg7+) while White has two replies: 32. Bd2 & 32. Rf1. Since the computer didn't mention 32. Nxb5 as a candidate, that means there's a hole or refutation. After 31 ... exf5 32. Nxb5:

click for larger view

Fritz 7 Deep Position Analysis [20MB]:

1) 32 ... f4

a) 33. Kb1 Rab7 34. a4 Bf5 35. Rhxg7 Rxg7 [-2.38/12]

b) 33. Kb1 Rae7 34. a3 Bf5 35. Rhxg7 Rxg7 [-2.31/12]

So us humans are left to figure out 33. Nxa7 Qe3+ 34. Kd1 (34. Kb1? Qxg1#) Qxg1+ & 35 ... Qxa7 winning a piece while still holding g7.

A final comment on the A section: one indication of the sharp nature of this position is 31 ... Rac7 32. Nxb5 Rb7 33. a4 exf5 34. Bd2 Qe4 being while the very similar 31 ... exf5 32. Nxb5 f4 33. Kb1 Rab7 34. a4 Bf5 is instead.

click for larger view

Fritz 7 Deep Position Analysis [20MB];

1) 32. Ne2

a) 32 ... Qxg1+ 33. Nxg1 gxh6 34. Rxh6 exf5 35. Ne2 [2.69/13]

2) 32. Re1

a) 32 ... Rac7 33. Be3 Qc4 34. Rh4 Qc6 35. Bf4 [1.91/11]

b) 32 ... Qf6 33. Be3 d4 34. Ne4 Qxf5 35. Bd2 [3.13/10]

c) 32 ... Qf2 33. Bd2 Rfe7 34. Rh4 exf5 35. Rxe7 [1.81/12]

3) 32. Rh1

a) 32 ... Qe5 33. Bd2 Rfe7 34. f6 Qxf6 35. R7h4 [2.25/10]

b) 32 ... Rxf5 33. Rd1 Qg4 34. Be3 Rb7 35. Bd4 [1.56/10]

This all verifies that 31 ... exf5 is Black's best option, although note that many of these C ideas feature Bb4+ as the winning motif.

Going back earlier in the game, Fritz 7 initially thought White was right out of the opening with 20. Qh2:

click for larger view

Consider Black is already two Pawns up (and Pawns are the soul of Fritz) leading to 20 ... Nd3+ 21. Bxd3 Qxh2 22. Rxh2 throwing away a piece to get Queens off. Watching Fritz do its thing, at first it didn't like 20 ... Kf8 21. Qh8+ Ng8 22. Rh7 Bf6 23. Bc5+:

click for larger view

Fritz probably needed more time to see that 23 ... Ke8 24. Qxg8+ Kd7 and the Qg8 is trapped (25. Bf8!?). So instead Fritz 7 Deep Position Analysis gives 20. Qh2 Kf8 21. Qh8+ Ng8 22. Bd3 Bb7 23. Rdg1 Bf6 [0.50/11] with chances for both sides.

All of this analysis of course requires further analysis. :-)

click for larger view

Fritz 7 only needs a minute to give 33. Nxd5 as winning [33 ... Qxe6 34. Bxg7+ 8.63/10] but 33. Rf1+ as decisive [#11].

<hawthorne> People feel differently about computer evaluations for classic games, particularly Tal brilliancies which are often branded "murky" due to their inherently unclear nature. Some fans like the element of the unknown over these cold engine lines, and how imaginative ideas like 25. Bxb5 and 27 ... Ng4 defy conventional analysis. Hopefully using an engine to verify variations and give direction can only help us appreciate the complexity of such games.

You are certainly learning more by trying out your own lines without computer help, yet one good rule of thumb is a five ply limit where you only evaluate 5 half-moves and then stop. Sometimes a forced sequence can be 6-10 ply, but by the tenth ply the likelihood of a major improvement along the way is virtually 100%. My students and I will often play out a certain position, only to realize that we have reached 20-30 ply deep and big things must have been missed along the way. It's still good practice, but definitely more efficient to stop at five ply. =)

Future students should try <hawthorne>'s approach and evaluate these sidelines:

1) 20. Qh2
2) 21 ... Ng6
3) 25 ... axb5 26. Nxb5 (vitally important)
4) 29 ... axb5 30. Nxa7
5) 31. bxc3
6) 33 ... gxh6