Historical riddle: Was Fischer’s 22.Nxd7 winning?

by Karsten Müller
11/18/2020 – One of the most amazing moves in Bobby Fischer’s rich career was 22.Nxd7+ in the seventh game of the Candidates final match against Tigran Petrosian. Endgame specialist Karsten Müller wonders whether the move was objectively the best in the position or if an alternative pawn push might have been a better try. You can help him solve the historical riddle!

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A crucial episode in chess history

Much has been written about the final match of the 1971 Candidates Tournament. Bobby Fischer came from demolishing two of the strongest grandmasters in the world, Mark Taimanov and Bent Larsen, while his rival, Tigran Petrosian, a former world champion, had the reputation of being the most resourceful defensive player of all time — he had lost only two of his 42 preceding games.

The stage was the Teatro General San Martín in Buenos Aires, located within walking distance from the venue where Capablanca and Alekhine had played the 1927 World Championship match. Grandmasters Hermann Pilnik and Miguel Najdorf were in charge of the commentary, explaining the moves to a large audience using a demonstration board. Would Fischer continue his perfect run? Or would Petrosian finally put a stop to the American’s bid to play Boris Spassky in a World Championship match?

Tigran Petrosian

Tigran Petrosian at the Martín Coronado Auditorium of the Teatro General San Martín

The streak continued in the first game of the match, despite the fact that Petrosian had surprised his opponent in the opening — the Soviet star got short of time and ended up resigning on move 40. Petrosian quickly bounced back though and levelled the score in game 2, putting an end to Fischer’s streak while showing he was in better form than his famed rival. 

Petrosian got a better position in game 3 as well, but once again he got into time trouble and allowed Fischer to find a draw by repetition. Games 4 and 5 were drawn by agreement, while Fischer obtained the first of four consecutive wins in game 6 — we already looked into the critical encounter that turned the tables in favour of the American. 

Let us now move on to game 7, one that might be even more famous and still contains several deep riddles. We will examine Fischer’s 22.Nxd7+, one of the most amazing moves he played during his rich career.

But was the move really objectively the best and winning? Or was, for example, 22.a4 even stronger? This deep question is only the start of the mysteries surrounding this famous endgame.

So your job is: How many mistakes were made and which was Petrosian’s last mistake?

 

Please share any analysis you come up with on the comments section. You may also like to use more powerful engines to assist you in your efforts. Fat Fritz, for instance, goes for some unconventional continuations and surprises. I will evaluate your submissions and discuss them with you.


Magical Chess Endgames

In over 4 hours in front of the camera, Karsten Müller presents to you sensations from the world of endgames - partly reaching far beyond standard techniques and rules of thumb - and rounds off with some cases of with own examples.


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Karsten Müller, born 1970, has a world-wide reputation as one of the greatest endgame experts. He has, together with Frank Lamprecht, written a book on the subject: “Fundamental Chess Endgames” in addition to other contributions such as his column on the website ChessCafe as well as in ChessBase Magazine. Müller's ChessBase-DVDs about endgames in Fritztrainer-Format are bestsellers. The PhD in mathematics lives in Hamburg, where he has also been hunting down points for the HSK in the Bundesliga for many years.
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Karsten Müller Karsten Müller 11/26/2020 09:03
Malfa: I agree with your line and it is indeed quite possible that Bobby did not look deeply into 22.a4 as his choice 22.Nxd7(?) is easier and less risky. But objectively it seems that 22.a4 wins...
malfa malfa 11/25/2020 09:57
Regarding why Bobby did not choose the "obvious" (in Najdorf's opinion) 22.a4, besides the trivial reason that he loved the KB vs. N endgame imbalance, I dare to offer the following concrete one: perhaps he "read" in Black's previous play the intention to continue with 22...a5 when the obvious (and winning, as we know) 23.b5 weakens the Nc5 and allows the desperado 23...Rc7 24.Rc1 Bxb5!? 25.Bxb5 Rac8 when Black seemingly recovers the piece. Either Bobby didn't bother to delve into such complications, since he had the simple alternative of forcing is favorite endgame, or did not see that 26.g4! h6 27.h4 effectively prevents Black from regaining the piece, as after 27...Rxc5 28.Rxc5 Rxc5 29.g5 hxg5 30.hxg5 the black knight cannot move without allowing mate in one, so it is lost. Personally I am inclined to the former of the two, since Bobby notoriously loved clarity and already in the opening stage of this game he had shown his definite intention to shy away from complications: I mean exactly when he played the simple 13.Re1 instead of winning the exchange with 13.Bb5 axb5 14.Qxa8 0-0, when 15.Qa5! would have left Black with insufficient compensation. After all Fischer was already ahead in the match, so he had no intention to lose his lead again like in the first games.
Karsten Müller Karsten Müller 11/24/2020 09:24
Morfine44: Indeed we did not look very deeply at 22.a4 in the comments. Soon the analysis by Zoran Petronijevic (checked by Charles Sullivan) will be published. There are too many lines and it is too deep to be published here. But e.g. Stockfish 12 gives +3.75 at depth 59 (see CB Let's Check) for 22.a4, which is no proof of course but it indicates the potential of the move...
Morfine44 Morfine44 11/24/2020 09:11
I also agree with d4 drawing.. But still not convinced by a4 winning... And to consider Fischer move as a true mistake maybe a4 should be proven as winning also.. Otherwise I would rate it a practical choice or an imprécision...
malfa malfa 11/23/2020 05:42
So not only Tal's sacrifices fail under the cold silicon eye, but also "deep" strategical decision by the magicians of endgame technique... Very sorry for Fischer's hooligans, anyway, whatever the final verdict, an extremely interesting collective analysis, so really many thanks for proposing this riddle, GM Mueller!
Karsten Müller Karsten Müller 11/23/2020 02:34
malfa: I agree with your line and conclusion. And so I think that over the board Bobby (and also Magnus Carlsen of course) would have good chances to win after 22.Nxd7 as Black's position is very difficult to defend for humans with the clock ticking. But computer defense should hold as the complexity is reduced, Black can easier activate himself than after 22.a4 and is also closer to a rook endgame, which its large drawish tendency. So objectivly speaking it surprisingly seems that 22.Nxd7 was a mistake...
malfa malfa 11/23/2020 01:17
No, I see: 34...Rb3 is coming and it is really close to equal, similarly to the line You gave after 29.g4 Rh6.
malfa malfa 11/23/2020 01:09
KM, isn't it possibile that in the long run 29...g6 proves itself to be less profitable than 29...h6? I mean, I was less interested in capturing the pawn than in limiting Black's usability of the 6th rank, so to this purpose I was ready to waste two tempi and to reply with 30.Ra5 instead of 30.Rxh7: then if 30...Rc6 31.g4 Nb5 32.Rd1 Rc3 33.a4 Nc7 we come again to basically the same position as in previous analyses, where Black's forces look decently coordinated both for defense and for counterattack, but White has been able to keep the tension, g6 might become an attack signal, and the torture will continue for many moves on. A pleasantly carlsenesque position, isn't it?
Karsten Müller Karsten Müller 11/23/2020 11:47
malfa: 29.Rh5 can be met by 29...g6 30.Rxh7 Kg8 31.Rh4 Rc8 and Black's activity compensates for the pawn.
malfa malfa 11/23/2020 11:33
Oh, I did not notice that You commented meanwhile! Yes, I do agree: after 22.a4 Black never has such active possibilities as after the (in)famous 22.Nxd7. Regarding your suggested 29...Rh6, it is precisely the reason why I consider 29.Rh5 as a possibly necessary precaution before trying my expansion plan.
malfa malfa 11/23/2020 11:26
OK, I have Just discovered that my original reply was cached by the browser in the PC where I composer it, so bere It Is, sorry again:

"Hi everybody, sorry for my delay. I think that Z.P.'s tactical defense along the c-file is a strong one, since somewhat forces the white rook on c1 on a less comfortable square. All the given lines also convinced me that after 22.Nxd7 White has much more trouble keeping in control than after 22.a4, anyway the real question is whether any analysis at this stage is really able to demonstrate a definite, unambiguous result: after all, as the saying goes, any very long analysis contains at least one mistake ;-)
I say this, because my evaluation is that White keeps a distinct advantage, but to claim that it is enough to get a forced win would be sort of far-fetched for me at this stage, as far-fetched would be to claim that Black has a forced draw. I would rather limit myself to seek for ways to strengthen White's position so, having said that, after 28...Rcd8 what about 29. f4 or 29.g4 with the idea of improving the king and possibly gaining space on the kingside? Should this be preceded by 29.Rh5 in order to force 29...h6 and thus reduce the scope of the Rd6 along the 6th rank? And what should Black do meanwhile? Oscillate with the back rook between d7 and d8, in order to demonstrate White that he has nothing? Attack the h-pawn with 29...Rh6 so that White be committed to some less favorable pawn structure? Find some way to improve his king in his turn? One sample line, along the last one given by Z.P., could be 29.g4 Rc6 30.h4 Nb5 31.Rd1 Nc3 32.Rd2 when I think that White's rook on d2 is better than on e1, so maybe Black's play should be less cooperative. I see no forcing lines for either side, anyway."
Karsten Müller Karsten Müller 11/23/2020 10:44
malfa: Many thanks! White is indeed better, but the engines give only a slight advantage (especially compared to 22.a4). In your line 29.g4 I suggest 29...Rh6 30.Kg3 Rc6 31.h4 Nb5 32.Rd1 Nc7. In a way Black is more active here than after 22.a4...
malfa malfa 11/23/2020 09:46
Many typing errors due to the phone's dastardly autocorrect mode, hope it is understandable nonetheless, please forgive me!
malfa malfa 11/23/2020 09:43
Sorry for the delay! Actually I wrote a long answer Yesterday evening from a PC, but at presente I do not see it on my smartphone, so I am afraid I forgot to submit it :-(
The core of my answer was: 1. The latest analysis by others have convinced me that After 22.Nxd7 White has note trouble keeping in control than after 22.a4; 2. I find a bit far-fetched that an analysis may establish the exact outcome at this stage: I evaluate that after Z.P.'s latest line White still has a distinct advantage but I see neither a forced win for White nor a forced draw for Black; 3. his tactical defense along the c-file is a strong one, since it forces the Rc1 to a somewhat less useful Square; 4. my suggestioni in reply is 29.f4 or 29.g4 with the ideas of improving the king and gaining space on the kingside, mauve preceding it with 29.Rh5 in order to weaken the black strutture and reduce the scope of the Rd6 along the 6th rank. It is not clear to me how Black should react and I have not worked out any deep analysis. A sample line could run similarly to Z.P.'s one: 29.g4 Rc6 30.h4 Nb5 31.Rd1 Nc3 (31...Rc3 32.a4) 32.Rd2 when the rooks on d2 is better than on e1 so perhaps Black's play should be less cooperative, but what should he do? Just wait, moving the back rooks between d7 and di, so to prove White that he has nothing? Improve his king in his turn? Find a better way to get the counterplay along the c-file? And is my suggested plan for White a real threat? I don't know.
Karsten Müller Karsten Müller 11/22/2020 09:35
Morfine44: Many thanks! Your lines show that White has ideas. But Zoran Petronijevic thinks that Black can defend and suggests: 28...Rcd8 29.Ree5 f6 30.Re1 and now the more active 30...Rc6 31.g4 h6 32.h4 Nb5! and Black's counterplay should be sufficient for a draw. What do you think?
Morfine44 Morfine44 11/21/2020 10:42
after 28 ... Rcd8
I propose 29.Ree5 f6 30.Re1 Rb6 31.h4 h6 32.h5 Rbd6 33.Rc5 Rd5 34.Re6 Rc5 35.bc5 Rc8 36.Bg6 Rd8 37.Ke1 d3 38.Rd6 Rxd6 39.cd6 Nb5 40.Bd3 Na3 41.Ba6 Nc2 42.Kf2 Ke8 43.Bc8 Kd8 44Be6 Nd4 as possibly winning
and if 29...g6 30.Ke1 Rb6 31.Kd2 Rdd6 32.Rac5 h5 33.f4 Rd8 34.Kc2 Kg7 35.Kb3 Rd7 36.f5 Rf637.a4 g5 38.Ra5 Rdd6 39.Rac5 Nd1 40.Red5 Ne3 41.Rd6 Rd6 42.b5 ab5 43.a5 Ng4 44.Rb5 Kf6 45.Rb6 Ke5 46 Rb7 also possibly winning
yours truly
Yves Leroy
Karsten Müller Karsten Müller 11/21/2020 04:59
Zoran Petronijevic has taken a deeper look into the line 23...d4! 24.Kf2 Nd5! (Sullivan) 25.a3 Rd6 26.g3 Nc3 27.Ra5 Rc8 28.Re1 and claims that 28...Rcd8 draws and has sent me more sample lines. Can you give a sample line or winning ideas here for White, malfa? The computer engines only give White a relativly small plus, but chess of course is a very deep game...
Karsten Müller Karsten Müller 11/21/2020 09:56
malfa: Interesting idea! 25...Rd6 26.g3 indeed looks unpleasant for Black, e.g. 26...Nc3 27.Ra5 Rc8 28.Re1. The computer still does not see very big problems for Black, but unpleasant it definitely is. I underestimated this below.
So more and deeper analysis is needed. I will ask Charles Sullivan and Zoran Petronijevic.
malfa malfa 11/21/2020 09:14
These late variations show were judgement of the position makes a big difference between a professional player and an amateur: I had envisaged that the knight would easily jump to c3, but I thought that it would have nothing to do there: no targets, no defensive role. It resembles to Portisch's White knight on c6 in a famous game against Petrosjan. Besides, I did not consider as active two rooks bound to the defense of a tightly blocked d-pawn in permanent danger of being captured. Therefore I see no reason to liquidate on d5 as in the latest variation given by Morfine44. The GM (and the engines too) evaluate the dynamics of the position in a completely different way, instead.
Karsten Müller Karsten Müller 11/20/2020 11:19
Morfine: Interesting! Zoran Petronijevic then gives in your line: 25...Rd6 26.Be4 Rad8 27.Rxd5 Rxd5 28. Bxd5 Rxd5 29.a4 and now 29...Ke7 30.Rc7+ Kf8 31.a5 d3 32.Ke1 d2+ 33.Kd1 g6 and according to my computer this should draw due to the large drawish tendency of rook endings, which I have also written to the CB Let's Check. But of course over the board it is an uphill struggle. One disadvantge of Fischer's line 22.Nxd7 is that too many men are exchanged.
Or can you change that picture?
Morfine44 Morfine44 11/20/2020 10:58
after 24. ... Nd5 25.a3 Rad8 26.g3 Nc3 27.Ra5 Rd6 28.Ra6 Ra6 29.Ba6Ra8 30.b5 Ke7 31.a4 Na4 32.Rc4 Nb6 33.Rc7 Ke8 34.Ke2 Nd5 35.Rc4 Nb6 36.Rc5 Ra7 37.Kd3 Kd7 38.Kd4 Rc7 39.h4 seems difficult for black

25...Rd6 seems maybe the best indeed 26.Be4 Rad8 27.Rd5 Rd5 28. Bd5 Rd5 29.a4 d3 30.Ke3 Ke7 31.Rd1 Rh5 32.h3 a5 33.Rd3 ab4 34.Rb3 Rg5 35.g4 Ra5 36.Rb4 h5 37.Rd4 hg4 Ke6 39.Kd3 is my best try to reach pawn up rock ending ..if computer hold I dont know .. mine is surely not powerful enough to evaluate correctly ...
Karsten Müller Karsten Müller 11/20/2020 10:18
malfa: After 24...Nd5 (Sullivan) 25.a3 Rd6 26.g3 Nc3 Black is so active that he should be able to defend. This is one disadvantage of Fischer's 22.Nxd7. Black's pieces are not as restricted as after 22.a4. Of course over the board Black's defensive task is still quite difficult. But computer defense should hold.
malfa malfa 11/19/2020 08:45
GM Mueller, IMHO Sullivan's 24...Nd5 produces more or less the scenary I suggested in one of my previous posts, i.e. after 25.a3 Nf4 (otherwise 26.g3 follows immediately) 26.Be4 Rad8 27.g3 Black is left with a very passive position: his pawn may well advance event to d2, but then it will not have enough support by his pieces.

That 28...d4 equalizes I take for granted by Your much superior knowledge and I assume that You have dug much deeper than me, since I am unable to see an automatic draw.
Karsten Müller Karsten Müller 11/19/2020 07:47
Interesting ideas and discoveries! I think that
1) Malfa: 28...f5? was indeed a losing mistake as 28...d4 draws.
2) Malfa: 27.f4? was indeed a mistake.
3) Morfine44: After 22.a4 h6 more work is indeed needed. I think that White has good winning chances.
4) Morfine44: After 23...d4 24.Kf2 Charles Sullivan suggests 24...Nd5! and Black defends.
malfa malfa 11/19/2020 07:20
Morfine44, your concrete proposal in reply to 23...d4 goes more or less along the lines of my generic evaluation, thanks!
Morfine44 Morfine44 11/19/2020 07:07
after 23 ...d4 i propose 24 Kf2 Rad8 25.Rec5 Nd5 26.a3 Rd6 27.Rc6 Nc3 28.Rd6 Rd6 29.Ke1 kE7 30.kd2 Rb6 31.Bc4 as a path for solid white advantage

as after 22.a4 I propose h6 23Kf2 Bc6 24.Re2 Bb725.Rd2 Bc8 26.Be2 g5 and it seems white if better is still far from breaking through

After all maybe Fischer was not so wrong .. I would like to think

Yours truly
Yves Leroy
malfa malfa 11/19/2020 06:51
About the lines stemming from 23...d4!? I would also like to observe that generally going straight for the a6 pawn is not a prescription by the doctor: White can simply strenghten his position by moves like a3 and g3, restricting the knight, without caring for the exchange of one rook on the c-file, since this would weaken Black's counterplay and make the defense of the a6 pawn harder. White appears to maintain a conspicous advantage, so I would not call 22.Nxd7 a mistake.
malfa malfa 11/19/2020 06:41
Sorry, I meant 27.f4.
malfa malfa 11/19/2020 06:40
On Bobby's side, 28.f4 does not gain appreciation by the engines, maybe not mistakingly, since it contributes to make Black's Rf6 an active defence. Are we sure that there was no typo here too? :-)
malfa malfa 11/19/2020 06:29
It has not been discussed yet that Marin gives 28...f5 as dubious but without providing any alternative, so that may well be Petrosian's final mistake, since here 28...d4 looks still worth a try, as well as the other thematic defense 28...Nb6. To me the advance of the h-pawn had been looking rather pointless until I noticed that certain engines consider 22.g4!? as a very pleasant alternative to the two main moves under comparison, though they may well change their idea at some deeper level of analysis, since this space-gaining move does nothing about the liberating Bb5. Anyway from some point onwards Petrosian apparently took the perspective of such an advance very seriously and applied that debatable profilaxis.
Karsten Müller Karsten Müller 11/19/2020 12:35
News from Zoran Petronijevic (2nd part):
Second invention is that i was wrong thinking that Polugaevsky was first who gave two exclamation marks to this move. After finding original source (Magazine 64, no 43 page 16) i have found that Polugaevsky didn't prize 22.Nxd7 either with one exclamation mark. My mistake is due to finding in a few sources Polugaevsky's quote and evaluating with two exclaims, i wrongly though that he had putted them as well. Marin in my favorite book "Learn from legends", had quoted the same Polugaevsky words, though putting only one exclamation mark. So, it is my mistake - Polugaevsky didn't give any evaluation to this move. I didn't find Suetin-Petrosian analyzes to our game. I doubt that Petrosian analyzed it.

In the same article, Polugaevsky had suggested on 22.a4 Be6 (not Bc6 as Marin had Quoted), which is obvious mistake due to 23.Nxe6. Maybe it was a printing mistake in fact.

Checking Marin's book, i have found that on 22.a4 his suggestion was 22....Bc8, and i have changed source - Marin is much more relevant author, than Chessbase reader (although i have mentioned him in annotations). For Marin, both moves (22.Nxd7 and 22.a4) win - it is a matter of taste what move to play. To the end of his comments he didn't give important comments.

...

Best wishes,
Zoran
Karsten Müller Karsten Müller 11/19/2020 12:34
News from Zoran Petronijevic (1st part):
Dear Karsten,

Charles have asked me to find where Polugaevsky had awarded 22.Nxd7 with two exclamation marks, I found - that i was wrong.

Digging through old chess magazines, I have found something unexpecting - which isn't connected with our game, but it is connected with Petrosian-Fischer game no 6 which was our riddle as well. Searching for various sources, I have found WHO is the inventor of move 42.f4 in that game. In the magazine Sakhmaty Riga, 1971/23 page 14, Hort and Jansa in their article about our game, had noticed that the inventor of this interesting move was Czech master Thelen Bedrich. So, Matanovic only had seen this article and had used it in Chess Informant no 12. I remember that you wanted to ask even Averbakh who is inventor. We know now :).
Karsten Müller Karsten Müller 11/19/2020 10:26
malfa: Marin claims that both moves 22.a4 and 22.Nxd7 win. But at the moment it seems thet 22.Nxd7? was a mistake from an objective point of view. As Charles Sullivan put it below: "In retrospect, Najdorf's gut reaction was pretty good!"
malfa malfa 11/18/2020 09:56
GM Mueller, did You have a look at Mihail Marin's comments in his "Learning from the Chess Legends", too? I translated it into my language, but it was long time ago and I should open both editions to check if there is something significant for your points, but I remember that the Rumanian GM dedicated some of his usually deep analysis to this endgame. If You didn't, then I hope to find something useful as soon as I approach my library ;-)
CharlesSullivan CharlesSullivan 11/18/2020 08:47
I am not aware of any direct quotes from either Fischer or Petrosian regarding 22.Nxd7.
From "Both Sides of the Chessboard" (by Robert Byrne and Ivo Nei) comes this regarding 22.Nxd7: "This exchange, which wins the game, was completely overlooked by the press room group of grandmaster analysts. Najdorf, in fact, criticized it(!), suggesting instead the incomparably weaker 22 P-QR4. Now, in addition to his potential outside passed pawn, Bobby has a bishop vastly superior to the knight and his rooks will possess the only open files."
In retrospect, Najdorf's gut reaction was pretty good!
Karsten Müller Karsten Müller 11/18/2020 07:45
Many thanks! I think that 27...Nb6! indeed draws and 29...Nf6 loses but Black is already lost in any case. What do the readers think? And more sources are also very welcome of course.
Zanoni Zanoni 11/18/2020 05:47
Euwe in his book "Von Steinitz bis Fischer" quoted some comments from Petrosian and Suetin. They gave two exclamation marks to 22.Nxd7 and as better defensive tries later in the game 27...Nb6 28.Ree7 Rf6 +/- and 29...Nf6 30.Kd4 Ne4 31. Rec2 +/-.

For Fischer 22.Nxd7 was probably a normal move and nothing special. I do think so because of his comment to move 16...Nxe2+ of his 11th match game vs. Reshevsky 1961. He exchanged his splendidly looking Nd4 against the Be2 in a rather closed Kingsindian structure and annoted laconically "Otherwise the Bishop retreats to KB1" (My 60 Memorable Games by Bobby Fischer, Game 28.).
Karsten Müller Karsten Müller 11/18/2020 04:29
Very good question! A first reaction from Zoran Petronijevic:
Dear Karsten,

unfortunately I do not have such data. I completely agree that such data would be extremely interesting. I have two indirect data: 1. Fischer thought that the best game in the match was 7th game, which indirectly means that he had played it excellently. 2. In Soviet magazine "Shahmaty v SSSR", Averbakh who was close to Petrosian, did not prize 22.Nxd7 move with any evaluation, which probably means that Petrosian did not estimate this move so high. First, as far as I know, who gave two exclamation marks to 22.Nxd7 was Polugaevsky, and after that this the move is prized as ingenious in every book I know.

Data which I have isn't enough, but that is all I have.

Best wishes,

Zoran
treetown treetown 11/18/2020 03:29
I understand and appreciate the desire to find the "best" move. In today's game, computers and their relentless analysis has shown many moves that look horrible to the aesthetics of the past are in fact playable and often very strong.
Yet, it is important to understand that these moves (i.e. Morphy Anderssen, Steinitz Lasker, Capablanca Alekhine, Tal Botvinnik, etc.) were played in a sporting circumstance with time pressure and human emotion. It would be wonderful to have heard Petrosians' immediate comments after the game when his emotions were more raw and fresh and what his thoughts were when 22. Nxd7 was played. Was he surprised? Did he think it was a mistake? And what were Fischer's thoughts?
Karsten Müller Karsten Müller 11/17/2020 10:03
marcguy: Several points:
1) 22.a4 indeed should win.
2) After 23...d4 24.Ra5 Nd5 25.Be4 Rad8 26.Bxd5 Rxd5 27.Rxa6 d3 Black is so active that the double rook endgame should be drawn.
3) Charles Sullivan's sources have convinced me that 33...Nxf4 was indeed played. Many sources give 33...Nxb4 as game move but this is most likely due to a misreading of 33...NxBP
4) There are more mistakes to find later in this fascinating endgame...