Solution of the endgame riddle: Was Fischer's 22.Nxd7 winning?

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Karsten Müller Karsten Müller is considered to be one of the greatest endgame experts in the world. His books on the endgame - among them "Fundamentals of Chess Endings", co-authored with Frank Lamprecht, that helped to improve Magnus Carlsen's endgame knowledge - and his endgame columns for the ChessCafe website and the ChessBase Magazine helped to establish and to confirm this reputation. Karsten's Fritztrainer DVDs on the endgame are bestsellers. The mathematician with a PhD lives in Hamburg, and for more than 25 years he has been scoring points for the Hamburger Schachklub (HSK) in the Bundesliga.

Discuss

Rules for reader comments

Karsten Müller 12/5/2020 10:43

malfa: Yes indeed interesting idea! The computer gives White only a very slight advantage at the end of your line after 33.Bxh7 and can probably defend, but over the board it would certainly not be easy...

malfa 12/5/2020 10:27

@KM: well, 26.Rh5 may well be the best move computerwise, but over the board I would be shy of playing it, since it clearly displaces the rook, and I would prefer 26.Re6 though, as I wrote, after losing control of the 5th rank White generally speaking has less grip on the position and after 26...Nc3, when the a6 pawn still remains untouchable, Black sooner or later will play a6-a5 generating active play on the very side where he was supposed to be weaker. However in this case the position preserves more complexity for White to keep some advantage than after those sterile rook endgames we usually reach. One example line I found with the help of my comp is 27.Rc2!? (in order to later go on the 'b' file) a5 28.b5 Rb8 29.Ra6 Nxb5 30.Rb2 Rdb7 31.Rxa5 Nc3 32.Rxb7 Rxb7 33.Bxh7. Maybe nothing to write home about, and furthermore Black presumably has quieter alternatives, but at least White still has a game, doesn't he?

Karsten Müller 12/4/2020 07:51

malfa: Intersting idea! Again Black's position is not comfortable, but probably defendable. The computer wants to continue after 24.a3 Nd5 25.g3 with 25...f6, e.g. 26.Rh5 g6. How to continue then?

malfa 12/4/2020 06:23

My latest try: dispense with an immediate Kf2, play at once 24.a3 Nd5 25.g3. Then Black has many reasonable defences against White's usual threats 26.Bxa6 and 26.Rc6, but again 25...a5!? might be the most challenging of all. This looks quite a theme, i.e. whenever Black has time to interfere with the knight along the 5th rank, a quick a6-a5 may well solve his problems on the queenside...

malfa 12/3/2020 04:56

Accurate Soviet reports would be typically lacking whenever one of their player lost... so we'll never know many interesting things about this game, I'm afraid.

Karsten Müller 12/3/2020 04:36

malfa: OK good. So basically we agree. Good question, why Petrosian did not play the ...d4 push. Over the board it was probably not easy to calculate that Black's activity always comes just in time before White can regroup...

malfa 12/3/2020 03:44

Well, after 27...Nd5 the upcoming ...Ne3 looks nasty to me, so instead of 28.Kd2 I would rather play 28.g3 in order to counter 28...Ne3 with 29.Bd3. As a human, for Black I liked more 27...Rad8 in order to regroup and to let the other rook free to hassle White's kingside, until I fed 27...Nd5 to the comp and found that after all there is no hurry moving the rook from a8, since the silicon monster points to the unexpected 28...a5! (according to Petrosian's supposed plan, after all...) as a very efficient retort to my 28.g3, sigh! So if White has to play your 28.Kd2 (28,Bd3 Nf4 just repeats) then my initial enthusiasm for 27.Bf1 rather boils down, unless some double rook endgame offers anything to White after he allows the minor pieces to be exchanged on f1 :-(
Apparently there is no way to achieve my ideal setup (a3, g3, Kd2) without stepping into some tactical resource by Black, since meanwhile he always gets enough time to become dynamic. Maybe no wonder, as soon as his knight starts to play in the center, so I am more and more puzzled why Petrosian did not readily push d4: after all, apart from its tactical justification on 24.Bxa6, it looks positionally quite logical (claim a stake on the dark squares, readily make a juicy square available to the knight, push passed pawn)! Maybe was he betrayed by his sometimes overcautious style (a couple of excellent diagonals dangerously open to the white bishop, Re5 free to roam along the fifth rank)?

Karsten Müller 12/3/2020 10:27

malfa: Interesting idea! I suggest to defend with 27.Bf1!? Nd5 28.Kd2 Ne3. How to do continue with White?

malfa 12/2/2020 10:02

Still not fully reconciled with the outcome ;-)
While going back to my original attempts to simply strenghten the position, I again turned my attention to the line 24.Kf2 Nd5 25.a3 Rd6 26.Ke1 Nf4 and now, instead of the 27.Be4 analyzed in depth by Sullivan, what about 27.Bf1? It defends g2, keeps a6 under threat, prepares Kd2... Here the white king seems really about to enter the fray, when the passed black pawn will go under his strict surveillance, doesn't it?

Karsten Müller 12/2/2020 04:44

malfa: I agree. Objectivly computer defense should hold the draw, but over the board against human opposition Bobby (and of course also e.g. Magnus Carlsen) would have good chances to win against human opposition...

malfa 12/2/2020 04:02

@KM: Thanks, actually this is quite insipid, so from a practical point of view I would try 26.Rc5!? with much more complicated play, though by no means clearly favourable to White after both 26...Nd7 and especially 26...Re8!?
My verdict, as nearly always throughout the lines given in this article, is that then the resulting play is equal, but never a simple draw.

Karsten Müller 12/1/2020 02:16

malfa: OK good. After 32.Ke3 the computer suggests 32...d2 33.Ke2 Rh6 34.Rg8 Rxh2 35.Rxg7 Ne5 and White is only symbolically better.

malfa 12/1/2020 11:50

Sorry again: after 29.Rf2 Rd6 I meant first 30.Rc8+ Rxc8 31.Rxc8+ Ke7 and only now 32.Ke3.

malfa 12/1/2020 11:42

@KM,
I too think that White's advantage is very tiny and is given by his free a-pawn being the hardest one to stop for a knight, so generally speaking I would change at least one pair of rooks, hopefully both, according to the intuition that then Black's king and knight alone would be unable to stop the a-pawn while at the same time keeping their d-pawn defended. If instead at least one pair of rooks is left, then Black should not have trouble setting up some blockade on the dark squares. Accordingly, I like 27.Rec5 as my computer suggests, when an immediate exchange of the a8 rook should be unavoidable, since 28.Rc7 is a big threat (but certainly not the immediate 27.Rc7?? Rxb3 and it is Black who wins!), e.g. 27...Rd4 (27...d2? 28.Rd1 Rd8 29.Rc7 Rd7 30.Rxd7 Nxd7 31.Rxd2) 28.Rc7 Nd7 29.Kf2 Rd6 (so that 30.Ke3 does not come with tempo) 30.Ke3 and now I am not sure if 30...d2 is playable, or maybe Black has better.

I also like to point out that there are funny lines following 26.Rc5!? instead of 26.Bb3: then both 26...Re8 and 26...Nd7 27.Rc7 Ne5 seem to offer Black enough tactical resources, especially a very nasty knight sacrifice on g4 if White is not careful when he brings up his king to f2. For the sake of conciseness, I leave further analysis to the students, as many professors usually say ;-)

Karsten Müller 12/1/2020 10:41

malfa: Many thanks! Interesting suggestion. The computer does not see big problems for Black, but I got the point. How do you want to continue after 24.Bxa6 d3 25.Bc4 Rd4 26.Bb3 Rxb4 ? Deeper analysis might indeed be good.

malfa 12/1/2020 10:20

Sorry, I gave an incorrect move number: the line I meant is 24.Bxa6 (after 23.Rc1 d4!) 24...d3 25.Bc4 (anything better?) 25...Rd4.

Karsten Müller 12/1/2020 09:53

malfa: Can you give the full line? 22.Nxd7+(?) Rxd7 and how to continue now?

malfa 11/30/2020 10:04

One extremely late afterthought: I do not remember having discussed 23.Bxa6 in the original article, did we? Of course after 23...d3 24.Bc4 Rd4 Black gets plenty of play in exchange for the pawn and he can even regain it quickly, but has this development been explored in depth?

malfa 11/30/2020 08:18

@zoranp,

many thanks for your info. What I would particularly be interested in is the distribution of thinking time along the game, and specifically the one consumed for the most critical moments, but I am afraid that neither player had the habit of recording such data, so I doubt they will ever be available, unless some commentator closely followed the game live. The final gap of time between the two players may be a sign of many a thing, like how Bobby systematically avoided delving into complications or how Petrosian was in trouble handling his defensive problems, but in absence of further data is not particularly significant in itself.

zoranp 11/30/2020 02:49

Malfa, i cannot answer on your first question, because i do not know. Second question about time is much easier: in the book "Fiser protiv Petrosjana i Spaskog", Saraevo 1972 (book is on Serbian language), on a page 31 we can read that on 34th move Fischer had 50 mins , while Petrosian had 20 mins. So, we can conclude that Petrosian wasn't in time trouble during the game.

Karsten Müller 11/28/2020 06:09

malfa: Good questions. I can not answer them. More sources are needed here. Can the readers help?

malfa 11/28/2020 05:32

@KM: I do agree that 22.a4 is definitely stronger than 22.Nxd7, and you know from the discussion in your previous article my opinion about the players not evaluating accurately the tactical outcome of 22...a5, which presumably was what Petrosian had planned to reply to 22.a4 in view of all his previous play starting with 20...Rea7 (BTW this I rate as already dubious, 20...Nd7 looking to me the natural way to counter that dominating Nc5). I am not sure that the analysis after Black's presumably best defence, i.e. 22...Bc8, is totally convincing, since Black's play looks rather poor, but indeed this may well be because hopelessly poor is his position with two extra pieces on the board, since with respect to the developments of 22.Nxd7 he clearly lacks manoeuvring space. Apart from this, I have a couple of further questions: 1. Do you know on what grounds did Kasparov comment that 22.a4 was the move Petrosian was hoping for? Was this statement based on some historical witness? 2. Do we have any information on the time handling by both players?

Karsten Müller 11/28/2020 05:00

Nordlandia: I will add it to the list of possible candidates for endgame riddles.

Nordlandia 11/28/2020 03:26

Yes. 22. Nxd7 seem to be weaker but still nevetheless strong enough to keep strong initiative. By the way, i would appreciate if a similar article could be written about a particular endgame. Not exactly as well known players but interesting enough in my opinion. Goldin vs Korzubov, Dushanbe 1980. FEN:

Maybe top GMs in combination with computer aid can give some definite conclusion about the outcome. Currently the consensus is that it is believed to end in a draw.

Karsten Müller 11/28/2020 01:04

malfa: You have a point. As the claim that Fischer's 22.Nxd7+(?) is a mistake is new and matters are very deep I have mailed more analysts. Several have promised to try to find a win. So stay tuned! But one point already seems to be very clear: 22.a4! is better. Even if 22.Nxd7+(?) also wins, it would be much, much deeper. But I think that White can not win at all after 22.Nxd7+(?) against computer defense and I can not refute Zoran's analysis...

malfa 11/28/2020 11:38

Still not entirely convinced by such a drastic verdict: after all, no analysis has yet demonstrated an automatic draw, so to me it would be fair to conclude that 22.Nxd7 only offers Black excellent chances to equalize, doesn't it?

Karsten Müller 11/28/2020 11:29

Zoran Petronijevic has just pointed out:
"Sarhan Guliev was sure that it is a matter of taste what move to choice. Marin is a bit different: he was sure that 22.a4 Bc6 loses..., but as a better he gave 22...Bc8 with explanation "even though White's advantage would be indisputable anyway." Strictly talking, he didn't tell that White for sure wins."

Karsten Müller 11/28/2020 09:48

Zoran Petronijevic points out that
Sarhan Guliev in "Ideja v sahmatnoj partii", Moscow 2012, page 15
and Mihail Marin in "Learn from the Legends", 3rd edition Quality Chess 2015,
already give that 22.a4 wins. So the really new point is that Fischer's 22.Nxd7+(?) only draws.

malfa 11/27/2020 02:17

@Davidx1

For what it is worth, Fischer also wrote that 1.e4 is best by test, among other maximalist nonsense. And maximalism often cost him precious points. Regarding your 2500 rating, I suppose you mean at playing darts or something like that, but I do not know if they have a rating system there.

Karsten Müller 11/27/2020 02:16

GM Alex Fishbein had already noted in ACM 12:
"However, in this case I am not sure this is the right plan. I found (with a lot of help, of course!)
an interesting tactical idea: 22.a4!? Bc6 Black is threatening 22...Nd7, trading the knight and
easing the tension, and Fischer didn't see a good way to play. But there is one: 23.Re2! Nd7
(23...d4 is also unlikely to save Black: 24.Rb2 Nd7 25.Rc2 Ne5 26.Bf1 and he will lose one or
both of his weak pawns) 24.Nxa6!! Rxa6 25.Bxa6 Rxa6 26.Rc1! and the back-rank mate threat
will cost Black a piece."

malfa 11/27/2020 12:12

@Davidx1,

I know the game you quoted very well, like many other Fischer's games: his "60 memorable games" is the 3rd chess book I have read in my life, just shortly after th2 "Match of the Century", which prompted me to play and study the game for many years until today and, I hope, many tomorrows, so I suppose I am rather accustomed to analyze and evaluate chess positions without resorting to a computer. That said, you continue to make statements proving that you are far from being the most accountable person to suggest anybody what to study: every decent player knows that your supposingly absolute strategic superiority of bishop over knight in reality is just one positional element among many others, so for example the relative value of the two pieces in the endgame depends at least on pawn structure and on the activity of the kings. If you talk of these as "tactical and occasional aspects" you only prove your rather poor understanding of chess. At least recollect that, just to give a well-known example, there are opening systems, like the Nimzoindian defence and the French Winawer, which aim specifically at obtaining a better pawn structure, as a long-term, *strategic* advantage, at the cost of conceding the bishop pair.

malfa 11/27/2020 10:11

@Davidx1,

that "the value of the Bishop over the Knight has been clarified and definitively affirmed", as every absolute generalization, is totally false, since there are way many positions where exactly the opposite is true. But even if always true it were, the discovery of such a truism would not be Fischer's merit at all: chess literature abounds of examples showing that Fischer's predecessors perfectly knew how to exploit the superiority of B over N in certain positions, as well as the reverse, as I said.

Karsten Müller 11/26/2020 06:09

ICCF Grandmaster: Many thanks! Really a Python- or maybe even Petrosian-like white win.

Mr Toad 11/26/2020 05:56

@Davidx1 - Yes, you got it absolutely right. It's instructive and fun to second guess the old masters - but the truth is elsewhere. At the time of the match, the conditions include too many variables to claim that heavy analysis will clarify the situation that the two players faced. You want to allow computers and logic to dominate when they know nothing of the heights to which humanity is capable of reaching? Computers, at the present time, are mere tools in the service of humanity's grander vision.

ICCF Grandmaster 11/26/2020 05:49

My own analysis in depth confirm that White is winning after 22.a4. Yet, I like to add two points.
1) Ironically, White wins here in the style of a Python - a method that was actually typical of Petrosian and is set out in his book "Python Strategy" (Quality Chess 2015).
It is instructive and not too difficult to explicate the computer analysis in terms of human play.
Black is permanently tied to the weakness of the a6-pawn and deprived of any counterplay. This is the purpose of the a-pawn's advance to a5 and the king's march to d4. Two key moments that define the pattern. An important tactical motif is the threat Nc5-a4-b6, which limits Black‘s space and possibilities even more. Attempts by Black to relieve himself by exchanging pieces backfires.
It is only a matter of time when an overload occurs at one of the critical points a6 and d5 and White‘s rooks will penetrate into Black‘s position.
In this regard, the winning line given below (>2)seems to me slightly more conclusive than the one already presented in the above article.
2) 22... Bc6
23.Ree1 Bb7
24.a5! Bc8
25.Re5 h5
26.h4 Rb8
27.Rb1 Rba8
28.Kf2 Re7
The same position as in the article. But here I prefer 29.Re3 instead of 29.Ree1. We will see, there is no need for White to play Kg3 etc. The king will go directly to d4.
29.Re3! g6
If 29...Nd7, so 30.Rc1, and 30...Nxc5 31.Rxc5 doesn‘t improve Black‘s position, on the contrary.
30.Rbe1 Rc7
31.Re5 Rca7
Black‘s rooks shuffle around like in prison, just waiting for the sentence.
32.Ke3! Rb8
33.Rb1 Rba8
34.Kd4! Rb8
35.Rb2 Kg7
What else?!
36.Kc3 Rc7
37.Rc2 d4+
Stockfish NNUE gives this as best with 5.60 for White in dephts 52 dspite the material balance. - Despair...
38.Kb3 Rc6
39.Rc4 Rd6
40.Re7 Bd7
41.Nxd7!
Now is the time ...
41...Nxd7
42.Rc7 Rd8
43.b5! axb5
44.Bxb5 Rb8
45.Ka4 Nf8
46.Rxf7+ White is clearly winning.
Note: Strong engines are like pythons, if they have time enough to go into depth.

JoshuaVGreen 11/26/2020 05:32

Had anyone else played 22. Nxd7+ and failed to win -- or if these lines were noticed at the time -- the annotator would have certainly written something like "Of course it was a mistake to trade the good Knight for the bad Bishop" and either a win would have been demonstrated after 22. a4 or that would have been the end of the analysis. Will this game be annotated that way going forward?