Riddle solved: Fischer could have won!

by Karsten Müller
5/25/2020 – The 1962 Chess Olympiad took place in in Varna, Bulgaria. In round ten the 19-year-old American grandmaster Bobby Fischer faced World Champion Mikhail Botvinnik – with the black pieces. At adjournment Fischer had a clear advantage, but he had simplified too quickly and fell into a "Botvinnik trap." The game was a draw, and experts have puzzled over it ever since: could Black have won? Now we know the answer, thanks to our very diligent readers. Two of them won a prize.

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Bobby Fischer's encounter with Mikhail Botvinnik made the cover of Chess Life (October 1962). In Fischer's My 60 Memorable Games it is number 39 and gets 14 pages of notes and analysis.

The game almost did not take place, since the Soviets considered "resting" Botvinnik in the round against the US. But then he did turn up and the world was treated to a truly exciting game. In Fischer's My 60 Memorable Games, p.240, GM Larry Evans writes:

"Walking into a prepared variation, Fischer promptly refutes it. But, instead of nursing his winning advantage, he simplifies too quickly and reaches an adjournment where victory is problematical. After a sleepless night of analysis, Botvinnik finds a stunning defense. Fischer engages in a seemingly harmless transposition of moves (51 . . . P - QN4), and falls into a pit—throwing away the win he maintains was still there. – Evans, in In Fischer's , p.240.

The deep endgame has been discussed in many sources since then. But it seemed that it had not given away all its secrets yet. The most difficult question, was if 44...Kh6 wins. For this there had been no convincing winning proof. This has changed – with the help of our readers we now know the answer.

Basically all analysts had agreed early on the following points:

  1. 41...Ne4? was a mistake as this rook ending is drawn, though in the ending with the minor pieces Black must be winning and is winning
  2. 43.Ra3 was a decisive mistake as 43.Rc7 draws
  3. But if 44...Kh6!! wins was an open question. Fortunately, my assumption that it wins was confirmed.

Here are the incredibly deep analyses of all three main contenders for our prize:

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One big advantage is that you can start an engine (fan icon) that will help you to analyse. You can get multiple lines of analysis by clicking the + button to the right of the engine analysis window. The "!" key, incidentally, shows you the threat in any position, which is incredibly useful in the case of unclear moves.

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The winners

My congratulations to Charles Sullivan for winning the competition! Charles, who is 71, grew up in the San Francisco Bay Area. While at the University of California, Berkeley, he was captain of the golf team, marched with the Cal Band for one year, played trumpet in the concert band, and was tear-gassed by helicopter during the People's Park demonstrations in 1969 (it was a weird time). He taught elementary school for three years (his hardest job ever) before switching to computer programming until retirement. A favorite memory is playing chess while sitting on the steps (which was allowed in those days) of the Parthenon in Athens in 1973. Today he lives with his wife in Davis (near Sacramento).

As Alberto Oggero gave the first deeper analysis with the right conclusions, I have decided to make him co-winner. Alberto is from Turin, Italy, a chess player (Elo 1800) passionate about the chess engine world in particular. A few years ago he wrote a Montecarlo analysis tool program downloadable here (the program works only on old Win XP). He also participated in the online freestyle tournament with Rybka under the nickname Albitex. Carlos often publishes articles and reviews on the Italian forum for chess engines (Albitex nickname).

Zoran Petronijevic also supplied convincing proof. But as he has won the first competition I suggest to give him an honorary mention. Many thanks to the analysts! If you have further comments please send them to my email address.

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.


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Karsten Müller Karsten Müller 5/27/2020 07:45
The verdict of Charles Sullivan has come:
"Dear Karsten,
Overnight, my computer running Stockfish 11 (on 15 cores) shows that Black has a definite win (-5.99) after 45...h5 46.h4+ Kh6 47.Rf4 Rc5. There are so many transpositional variations that it is impossible to give a comprehensive analysis. So I just let Stockfish (as Black) & LeelaChessZero play out Leela's preferred variation. (I suspect that Leela could have made the game last quite a bit longer, but the position is hopeless for White.)
Hope this helps.
Best wishes,
albitex albitex 5/26/2020 11:36
At this link you can download an analysis PGN of 45 ... h5 46. h4+ Rh6 variant (where it is shown that 47. a5 draw while 47. Rf4 or 47. Rf6 loses.) And also a update PGN of my general analysis where I expanded the variant 44 ... Kh6:
Karsten Müller Karsten Müller 5/26/2020 05:52
Alberto Oggero has just mailed that he has reached the same result as Zoran. Only 47.a5!!= draws. 47.Rf4? loses as Van Reek, Uiterwijk and Van den Herik had claimed. But the win is really hard to prove. Are you convined Kevin or shall I give details ? By the way: Charles Sullivan also promised to take a deep look at it and his verdict is still out...
Karsten Müller Karsten Müller 5/26/2020 02:54
Zoran Petronijevic adds the following points:
"The Botvinnik-Fischer game is really fascinating! i have watched it for a many times from my youth till now, but now we are much closer to the truth.
In my opinion, four moments (although not relevant for the result of the game!) should be pointed out also:

1. Probably the best Botvinnik's move was 48.h4!! (only defence), which in fact Fischer didn't analyze.

2. Move 50.Rg7 wasn't only defence. Also possible was 50.f4 (see my analyzes).

3. 51.Kf3 isn't only move as Kasparov and Botvinnik proved. Also possible was 51.Kg2 (which was refuted by both analysts), see my analyzes.

4. 52. h5 also isn't only move, 52.Rxg6 leads do draw also (in contrary to Botvinnik and Kasparov) - also see my analyzes.

These notices aren't important for result of the game, but i think that radically changes the picture of the game."
Karsten Müller Karsten Müller 5/26/2020 08:26
I guess that Botvinnik was refering to the adjourned position and it is indeed a draw so there is no contradiction. Fischer's last chance to win was 44...Kh6!! before the adjournment.
Zoran Petronijevic has proved that Kevin Cotreau's suggestion 47.Rf4? is lost so here Van Reek, Uiterwijk and Van den Herik are right. But as 47.a5!! refutes their prove the adjourned position is a draw as claimed. Zoran has found 47.a5!!= earlier than me.
jyrkitheterrible jyrkitheterrible 5/26/2020 01:48
I have something to say about the game. I interviewed Botvinnik for finnish chess magazine "Suomen Shakki" in Moscow Central Chess Club.You have probably read Bobby´s "My 60 Memorable Games" and his analysis about the game. Already in 1950´s Mihail was considered as one of the best end game-players in the world.Botvinnik told that the game would have been a draw anyhow, regardless which variation Bobby wants to play. And even Bobby admitted in his book :"Botvinnik's line is best and contains a sly trap" . Bobby went to trap and lost his pawn, and Bobby claimed that Botvinnik was saved due this blunder.But Botvinnik told that the game is a draw even Bobby had not fallen to trap. I tend to believe Mihail.
Karsten Müller Karsten Müller 5/25/2020 06:30
Many thanks, Kevin! I can not answer your very deep question and again need help. It is possible that your suggestion 47.Rf4?! draws, but it also is possible that Van Reek, Uiterwijk and Van den Herik are right and after 47.Rf4? their move 47...Rc5 wins as Black has now stabilised the situation. I will mail analysts for help to decide this deep question.
PhishMaster PhishMaster 5/25/2020 05:56
@Karsten, By the way, I give you and ChessBase permission to use any of the analysis below, including the comments, in any material that you may produce (for example, should you write something for CB Magazine, or if you add some of this to the Mega Database). I do not play chess for money, so I am always happy to pass on any knowledge I can.

PhishMaster PhishMaster 5/25/2020 05:52
@Karsten, You are welcome. Your 47.a5! is more direct to drawing, but I still think that Rf4 stops black too. Even if the eventual Rf5, white plays Rd4 and if Kf6, Rd6+ forces the black king back, or if the black rook moves, then the white rook takes up the f4 square again. It looks like a positional draw to me.
Karsten Müller Karsten Müller 5/25/2020 03:35
Many thanks, Kevin! I have learnt today that a proof that 45...h5!? wins was published in 2000 in ICCA Journal by Van Reek, Uiterwijk and Van den Herik. But it is not correct as White draws with 46.h4+ Kh6 47.a5!!=. I have also written this into the ChessBase Let's Check. So 44...Kh6!! was the last move, where Fischer had a win.
PhishMaster PhishMaster 5/25/2020 03:12
I am sorry to say that I was incredibly busy this week with IT projects for two customers, so I did not have time to finish. The only part that I did not finish was still trying to really prove was a clear winning method that humans could follow without just trees of computer analysis. Of course, the computer told me that it was close at all points, but I did not consider that “proof”…yet.

I am going to add what I had completed, and hopefully, some people can appreciate the some of the understanding that I added with words, and not just variations.

(1) Botvinnik,Mikhail - Fischer,Robert James [D98]
Olympiad–15 Final A Varna (10), 07.10.1962
[Kevin Cotreau]

1.c4 g6 2.d4 Nf6 3.Nc3 d5 4.Nf3 Bg7 5.Qb3 dxc4 6.Qxc4 0–0 7.e4 Bg4 8.Be3 Nfd7 9.Be2 Nc6 10.Rd1 Nb6 11.Qc5 Qd6 12.h3 Bxf3 13.gxf3 Rfd8 14.d5 Ne5 15.Nb5 Qf6 16.f4 Ned7 17.e5 Qxf4 18.Bxf4 Nxc5 19.Nxc7 Rac8 20.d6 exd6 21.exd6 Bxb2 22.0–0 Nbd7 23.Rd5 b6 24.Bf3 Ne6 25.Nxe6 fxe6 26.Rd3 Nc5 27.Re3 e5 28.Bxe5 Bxe5 29.Rxe5 Rxd6 30.Re7 Rd7 31.Rxd7 Nxd7 32.Bg4 Rc7 33.Re1 Kf7 34.Kg2 Nc5 35.Re3 Re7 36.Rf3+ Kg7 37.Rc3 Re4 38.Bd1 Rd4 39.Bc2 Kf6 40.Kf3 Kg5 41.Kg3 [I do not know if we can prove that black can win this, but it is very close.]
PhishMaster PhishMaster 5/25/2020 03:11
41...Ne4+?? [This is a practical mistake for a number of reasons, and probably an actual mistake throwing away the win. First, the N was incredibly well posted on c5, limiting the scope of the Rc3. I have only one student, and with him, I often discuss "strenght of force", meaning that if a knight worth approximately 3 points can keep a rook worth 5 at bay, that is an advantageous situation. The second reason is the drawing tendency of rook endgames. After all there is the old Russian saying that all rook endings are drawn, so unless you are 100% sure, or have nothing better, it was was not a good idea to trade down here. As a great a player as Fischer was, his judgment was flawed here.]

42.Bxe4 Rxe4 43.Ra3? [And, Botvinnik's judgment, in return, was flawed here; but it was harder to grasp why at this very moment. Normally, the natural Rc7 would be obvious, but I suspect that Botvinnik was worried about Ra4, and the possibility of black getting connected passers on the queenside...normally a death sentence. That said, it was the right way to go, but very hard to envision that he would get very strong play, and enough counterplay against g6, a7, and potentially b6 (after a5). It was a lot more difficult than it seemed to set the queenside pawns rolling. The only alternative was to let g6 drop, but in doing so, the white h-pawn would have been very fast. Of course, the only reason I can criticize these great players is experience with computer analysis, but I am striving to go beyond that, and explain the resulting positions in words.]

[43.Rc7! Ra4 44.Rxh7 Kf6 (44...Rxa2 45.h4+ Kf6 46.Rb7 Ke5 47.Kg4 Or Rg7. (47.Rg7 b5 48.Rxg6) 47...Rxf2 48.Rxa7 With enough counterplay to draw.) 45.h4 Rxa2 46.Rb7 Kf5 47.Rf7+ Ke6 48.Rg7=]
PhishMaster PhishMaster 5/25/2020 03:11
43...Re7? [43...a5!–+ And my computer almost immediately jumps to over -5. Again "Strength of force", with a5, black uses a pawn to restrict the rook. 44.Rb3 There are various moves here, but all are similar. Black eventually makes progress by advancing the queenside. 44...Rb4 45.Rd3 a4 46.Rf3 (46.h4+ The computer likes this, but if this is the only move, then white is lost...it just adds another target. 46...Kf5 47.Rd7 h5–+) 46...Rb2 47.h4+ Kh6 48.Rf6 Or else Rxa2. 48...Kg7 49.Rd6 b5–+]

44.Rf3 Rc7? [A natural move, but not best.]

[44...Kh6! Prophylactically defending h7. 45.Rd3 Re5 46.a4 Rg5+ 47.Kf4 Ra5 48.Rd4 Kg7 And the difference between this line, and the line with 45...h5 is that black cannot be stopped from bringing the king over to the queenside winning.. 49.Ke3 Kf6 50.Ke4 Ke6 51.Kf3 Rh5 52.Kg3 Rd5–+]

45.a4 [45.h4+ Kh5 (45...Kh6 To protect h7. 46.a4 Rc4 (46...Rc5 47.Rd3 Ra5 48.Rd4 Kg7 49.Rd7+ Kh6 50.Rd4= And white cannot make progress.) 47.a5 bxa5 48.Rf7 a6 49.Rd7 And it is hard to make progress.) 46.a4 Was the right move order. 46...Rc4 47.Rf7 Rg4+ 48.Kf3 h6 49.Rxa7 Kxh4 50.Ra6 Rb4 51.a5 bxa5 52.Rxa5 But white should be able to hold.]

45...Rc5? [Now it is drawn. White gets too much counterplay against either a7, b6 (after b5), and g6.]

[45...h5! Getting the pawn off h7 keeps some advantage, but it might not be enough. 46.h4+ Kh6 47.Rf4 Rc5 48.Re4 Ra5 49.f3 Kg7 50.Rf4 And although better, it is hard to see how black can make progress since the king cannot cross the f-file.]

46.Rf7 Ra5 47.Rxh7 Rxa4 48.h4+ Kf5 49.Rf7+ Ke5 50.Rg7 Ra1 51.Kf3 b5 52.h5 Ra3+ 53.Kg2 gxh5 54.Rg5+ Kd6 55.Rxb5 h4 56.f4 Kc6 57.Rb8 h3+ 58.Kh2 a5 59.f5 Kc7 60.Rb5 Kd6 61.f6 Ke6 62.Rb6+ Kf7 63.Ra6 Kg6 64.Rc6 a4 65.Ra6 Kf7 66.Rc6 Rd3 67.Ra6 a3 68.Kg1