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May0317
  beatgiant: <Helios727> White would trade rook for <rook and pawn> with 56...Bxf6 57. Rd1+ Kc4 <58. Rxc5+> Kxc5 59. Rxd7. 

Oct3117
  ajk68: <Howard: It appears that the 35th move was Spassky's fatal blunder, correct?> Probably not. Stockfish 9 has the following line. 1) +0.12 (41 ply) 35...Ra1+ 36.Kh2 Bd6+ 37.g3 b4 38.Rb6 Kf5 39.Rh4 Rd1 40.Kg2 h6 41.Kf3 Ke6 42.Rg4 g5 43.h4 Rd3+ 44.Ke2 Rd5 45.hxg5 Kf5 46.Rh4 hxg5 47.Rc4 Ke6 48.g4 Re5+ 49.Kd3 Rd5+ 50.Kc2 Re5 51.Kb3 Rd5 52.f3 Kd7 53.Rb7+ Kc6 54.Rbxb4 Rd3+ 55.Kc2 Rxf3 56.Rb3 Rf2+ 57.Kd1 Ra2 58.Rf3 Bf4 59.Rfc3 Bd6 60.Rb3 Be5 61.Rb1 Ra3 62.Rc2 

Oct3117
  ajk68: 40...Kf7 looks like the losing blunder. 

Nov0117   RookFile: I'd replace the word "blunder" with "error". A blunder is when you hang your queen. It's probably something other than a mistake uncovered by painstaking computer analysis 45 years after the fact. 

Nov0117
  Check It Out: 22.Bxf6 preserves the important diagonalblocking e4 pawn. 26.Bb3 drops the b5 pawn but starts a brutal campaign on black’s f7 weak point. 45…Be5 allows 46.Rb5 and black’s Q side crumbles due to a nasty pin on an overloaded R. 54.Rxg5 it’s all over. 

Dec3017
  Penguincw: Video analysis of this game: https://www.youtube.com/watch?v=qx3.... 

Sep1318   CharlesSullivan: <Analytical Breakdown #1>
29...Re7
Kasparov calls Black's 29th move "a fatal mistake." Kasparov, Timman, and Müller all agree that Spassky can keep the draw inhand with 29...Rad8 30.Bxf7+ Rxf7 31.Qxf7+ Qxf7 32.Nxf7 Rxd1 33.Rxd1 Bxe4 34.Ng5 Bf5 35.Rd5 h6 36.Rxf5 hxg5 37.Kf1 Be7 38.Ke2 g6:
click for larger view
However, here 39.Re5 (instead of 39.Rd5) will win. One example variation is 39.Re5 Kf7 40.Ke3 Kf6 41.Ke4 Kf7 42.f3 b4 43.Kd3 Kf6 44.Re4 Bd6 45.Kc4 Bf8 46.Kd5 Kf7 47.Re2 Be7 48.Ra2 Bf8 49.Ra7+ Kf6 50.Rc7 Be7 51.Rc6+ Kf7 52.Ke5 Bf8 53.Rc7+ Be7 54.g3 and Black cannot avoid the inevitable:
click for larger view
(a) 54...Ke8 55.Kd6 wins;
(b) 54...b3 55.Rb7 c4 56.Kd5 wins;
(c) 54...c4 55.Rxc4 Bf6+ 56.Ke4 b3 57.Rb4 b2 58.Kd5 Ke7 59.Rb7+ Kd8 60.Ke6 Kc8 61.Rb3 Bd4 62.g4 Bh8 63.Kf7 Kd7 64.Kxg6 Ke6 65.Kxg5 wins:
click for larger view
Despite this analytical error, the beginning of the variation (which was mostly explored by Fridrik Olafsson) was solid. The better continuation was 34...Bc2 35.Rd8 (35.Rd2 is better, but still not a win) 35...b4 36.Ne6 Kf7 37.Nxf8 b3 38.Rb8 (all of this is Olafsson's original work) when 38...Ke7 (not Olafsson's 38...c4) leads to a draw. Here is one brief but somewhat entertaining finish: 39.Nxh7 Kd6 40.Ng5 Kc7! 41.Rb5 Kc6 42.Rb8 Kc7 43.Rf8 (or 43.Rxb3 Bxb3=) 43...c4! 44.Rf4 c3! 45.Rc4+ Kd6 46.Rxc3 b2 47.Ne4+ Bxe4 48.Rb3 b1=Q+ 49.Rxb1 Bxb1:
click for larger view
So, does this prove Kasparov's point that 29...Re7 was the losing move? No, as we shall see in a later post. 

Sep1318   CharlesSullivan: <Analytical Breakdown #2>
35.Rb7
"... as usual, Fischer is very accurate and squeezes everything possible out of the position (after the 17th move his play cannot be improved!) ..."  Kasparov
As we shall see, Fischer makes bigger mistakes than 35.Rb7, but it should be noted that stronger was moving the king immediately closer to the center with 35.Kf1 <+0.85> Rc8 36.Rb7 c4 37.Rb6+ Kf7 38.Ree6:
click for larger view
35...Ra1+
As the winner of the game, Fischer had most every move of his praised (see Kasparov's quote above); as the loser, Spassky saw each move minutely examined for defects. Here is one of those moves  Spassky seizes on the fact that White (with 35.Rb7) has failed to move his king towards the center; Black's 35...Ra1+ forces White to go the long way around. The fact is that Black's move is excellent and the position is equally balanced. But Spassky's move was deemed a lost opportunity: the "general opinion" (Kasparov) was that 35...b4 was the best chance for a draw.
As we shall see, 35...Ra1+ was not a mistake.
38...h5 <The first of Black's losing moves>
Robert Byrne says that Serbian GM Dragoljub Janoševic; proposed 38...Be5 as the best defense. But Byrne "persuaded him that White wins fairly smoothly after" 39.f4 Bd4 40.g4 Ra2+ 41.Kf1. Byrne says 41...Rh2 "would have been worse than useless" because of 42.Ke1. Timman agrees with Byrne and says that "it is too committal to play the bishop to a stronger square with 38...Be5." Kasparov piles on with, "Maneuvering with the bishop is also hopeless."
In fact, Black has several good replies after 42.Ke1; for example, 42...Bc3+ 43.Kf1 Rxh3 44.Kg2 Rd3 45.Rb6+ Kf7 46.g5 Bd2 47.Re5 Be3 48.f5 Bxg5 49.Rb7+ Kf6 50.Rxc5 Be3 51.Rcb5 b3 52.Rxb3 Rxb3 53.Rxb3 Bg5 54.Rb5 g6 55.fxg6 Kxg6 is a draw:
click for larger view
Another way to draw is 38...Ra6 39.Re2 c4 40.Kf3 b3 41.Ke4 Be5 42.Kd5 b2 43.Kxc4 Ra1 44.Rexb2 Bxb2 45.Rxb2 Rd1:
click for larger view 

Sep1418   WorstPlayerEver: 29... Rad8 30. Bxf7+ Rxf7 31. Qxf7+ Qxf7 32. Nxf7 Rxd1 33. Rxd1 Bxe4 34. Ng5 Bf5 35. Rd5 g6 36. g4 h6 37. gxf5 hxg5 click for larger viewLooks drawish to me. 

Sep1418   CharlesSullivan: <WorstPlayerEver> Yes, I would say that in the line you give, 35...g6 and probably 35...Bb1 in addition to 35...Bc2 hold the draw. 

Sep1418   CharlesSullivan: <Analytical Breakdown #3>
39.Rb6
Commentators completely ignore this move, but here Fischer fails to find the correct continuation. The surprising 39.g4
click for larger view
keeps the win alive; here are 2 sample variations:
(a) 39...hxg4 40.hxg4 <+4.80, depth=55> 40...Ra2 41.Rb6 Rd2 42.Kf3 Rd5 43.Ra6 Kf7 44.Ra7+ Kf6 45.Rd7 Rd2 46.Ke3 Rd5 47.Ke2 g5 48.f3
<(There are no good moves for Black; if 48...Kg6, 49.Re6+ wins the bishop)>
49...b3 49.Rb7 <+6.46, depth=58> 49...b2 50.Rxb2 Bf4 51.Rb3 Rd2+ 52.Ke1 Rd6 53.Rc4 Rc6 54.Ke2 Kg6 55.Re4 Rd6 56.Rd3 Rc6 57.Rc4 Re6+ 58.Kd1 Rc6 59.Rd5 Bd6 60.Re4 Bg3 61.Ke2 c4 62.Rdd4 c3 63.Rc4 Rb6 64.Rxc3 Rf6 65.Rc5 Rb6 66.Kd3 Rd6+ 67.Ke3 Rb6 68.Kd2 Rf6 69.Rf5 Rxf5 70.gxf5+ Kxf5 and White mates in 38 (according to the database tables) with 71.Ra4, etc.
(b) 39...Ra6 <+4.02, depth=73, 38 hours> 40.gxh5 Be5 41.Rg4 Kf5 42.Rb5 Rc6 43.Rc4 b3 44.f4 Bxf4 45.Rxb3 Be5 46.Rd3 Ke6 47.Kf3 Rc7 48.Ke4 Bf6 49.Rd5 Be7 50.Re5+ Kf7 51.Rf5+ Kg8 52.Kd5 Rc8 53.Re4 Bf8 54.Rfe5 Kf7 55.Rg5 Rd8+ 56.Kc4 Rb8 57.Rg3 Ra8 58.Kb5 c4 59.Reg4 Rc8 60.Rxc4 Rb8+ 61.Kc6 Kg8 62.h6 Kh7 63.hxg7 Bxg7 and White mates in 45 (Lomonosov tables) with 64.Rg5, etc.
39...Rd1 <The second of Black's losing moves>
Reshevsky is simple and to the point: "If 39...Kf5; 40 Rh4 wins a pawn," period. (I suppose we are to surmise that Black's loss of a pawn would be disastrous.) None of the other grandmasters even felt it necessary to say that much  silence reigns.
But 39...Kf5!! leads to a drawn position! If 40.Rh4 (or 40.Kf3 Ra3+ 41.Re3 Rxe3+ 42.fxe3 Ke5 43.e4 c4 44.Rb5+ Kf6 45.Ke3 c3=) 40...Rd1 41.Rxh5+ Ke4!!
click for larger view
and Black's two advanced pawns and strong king ensure the draw.
40.Kf3 <White misses another win>
Kasparov: "Accuracy to the end!"
Timman: "Fischer is playing logically and perfectly."
Not surprisingly, 40.g4! <+4.80, depth=68, 16 hours> is the real winner. After 40...Rd2 41.Kf3 Rd5 [41...hxg4+ 42.hxg4 transposes to variation (a) in my comments about 39.Rb6  see above] 42.gxh5 Kf5 43.Rh4 Bc7 44.Rb5 Be5 45.Rhxb4 Rd3+ 46.Ke2 Rc3 47.Rb3
click for larger view
and White's material advantage will carry the day (although the ending will be very, very long).
40...Kf7 <The third of Black's losing moves>
Most commentators were uneasy about Black's 40th move, but none were able to actually demonstrate a better one. After a nine hour search to depth 75, Stockfish shows that 40...Rd3+ is best; for example: 41.Ke2 Rd5 42.f4 g5 43.Re8 gxf4 44.gxf4 c4 45.Re4 c3 46.Rexb4 Kf5 47.Rc4 Bxf4 48.Rxc3 Rd2+ 49.Ke1 Rd5 50.Rc4 Be5 51.Rb3 Ra5 52.Rc2 Kg5
click for larger view
and there just isn't enough on the board for White to force a win. 

Sep1518   Howard: All I can say is "Wow !!!" 

Sep2218
  diceman: <Tiggler:
<Howard: About where was the point of no return, as far as Spassky throwing away the draw for good ?> Consensus seems to be that 29... Re7 was the losing move, and that 29... Rad8 would have held.> The computer disagrees:
1) +0.47 (31 ply) 29...Re7 30.Bxf7+ Rxf7 31.Qxf7+ Qxf7 32.Nxf7 Bxe4 33.Rxe4 Kxf7 34.Rd7+ Kf6 35.Kf1 c4 36.Ke2 Rc8 37.Kd2 b4 38.Rb7 c3+ 39.Kc2 Ra8 40.Re2 h5 41.Rb6+ Kf7 42.h4 Ra1 43.Rb7+ Kf6 44.f3 g6 45.g4 Ra2+ 46.Kd3 Rxe2 47.Kxe2 Bd6 48.Kd3 Ke6 49.Kc2 2) +0.86 (30 ply) 29...Rad8 30.Bxf7+ Rxf7 31.Qxf7+ Qxf7 32.Nxf7 Rxd1 33.Rxd1 Bxe4 34.Ng5 Bf5 35.Rd5 Bb1 36.Rd8 Ba2 37.f4 g6 38.Nxh7 Kxh7 39.Rxf8 b4 40.Rb8 b3 41.Rb7+ Kg8 42.Kf2 c4 43.Ke3 c3 44.Kd3 b2 45.Kc2 Kf8 46.g4 Kg8 47.h4 Kh8 48.h5 gxh5 49.gxh5 Kg8 50.f5 b1=Q+ 51.Rxb1 Bxb1+ 52.Kxb1 

Sep2218   Howard: What about 40...Rd3+ ? Would't that move have held? 

Sep2218
  diceman: <Howard:
What about 40...Rd3+ ? Would't that move have held? <CharlesSullivan:
After a nine hour search to depth 75, Stockfish shows that 40...Rd3+ is best; for example: 41.Ke2 Rd5 42.f4 g5 43.Re8 gxf4 44.gxf4 c4 45.Re4 c3 46.Rexb4 Kf5 47.Rc4 Bxf4 48.Rxc3 Rd2+ 49.Ke1 Rd5 50.Rc4 Be5 51.Rb3 Ra5 52.Rc2 Kg5 and there just isn't enough on the board for White to force a win.>> 

Sep2218   Howard: Exactly ! That's why I asked about that move. So the draw was still there after the 29th move, therefore. 

Sep2218
  Tiggler: Amazing analysis by <CharlesSullivan>. His bio credits Stockfish 9, and at one point above he mentions a 9 hour analysis up to 75ply. But that is only for one move and he has seemingly analyzed many other positions to similar depth. I would appreciate a bit more information on the total effort involved in his analysis, and about his hardware. 

Sep2718   CharlesSullivan: <Tiggler> < I would appreciate a bit more information on the total effort involved in his analysis, and about his hardware. >
Tiggler, thanks for your comment. I have an AMD 16core Threadripper 1950X with 32 GB of memory and all the important 6man Syzygy tablebases on an NVme SSD. To save electricity, I have undervolted the 1950X and it runs at its base frequency of 3.4 GHz (turboboost is turned off). I also have an Intel i77700K machine with only 16 GB of memory, but it runs with a slight overclock at 4.5 GHz (all 8 threads). My 1950X machine is about twice as fast as the i77700K.
About two months ago I started looking very closely at the FischerSpassky match games. Most of those 2 months were spent on about 12 of the games. On average, in each of those 12 games, almost all of the time was spent on 3 to 6 positions in the game. On average, about 1 to 3 days are used for each position. (I use both machines for analysis  they run moreorless 24/7 on chess.) Typically, the 1950X spends overnight (or longer) at the beginning position. I then move very slowly down the variation, letting Stockfish hit a depth of 50 (if possible) before moving to the next move in the variation. I spend a lot of time going backwards through the generated variations (usually with the i77700K), looking of improvements, etc. It is probable that a single game position requires 48 hours of computer time to create a 20move analytical variation. I'm almost embarrassed to admit that occasionally 2 or 3 weeks will be spent on one position.
As you have noticed, I usually post very long variations. I try to make sure that each move (not just the first move) in each variation is the best move. 

Sep2718
  offramp: Many thanks, <CharlesSullivan>. 

Sep2818
  Tiggler: <CS> I appreciate your detailed answer. You should not be even <almost> embarrassed to have spent so long. I would be amazed if your, seemingly comprehensive, analysis in some cases had required less. I know you could not have done it so fast with any current engine without your own skill in forward and backward sliding, as you briefly indicated. Do you play correspondence chess? I would not want to take you on in that arena! 

Sep2818
  offramp: <CharlesSullivan> I’ve been looking at all your analyses. They are bloody good. Some people simply present us with a vast computer printout of Stockfish analysis. Your posts show reasoning and literacy and they are much more readable and useful. You also have not fallen for the Flat Earth Failure, as I call it. This is when someone puts a position in Stockfish, turns it on, and subsequently prints out SF’s 20move line from that position. The final evaluation is given <as if it were SF’s evaluation of that initial position>. A Globeearther would start a new variation, then move along that variation slowly, with SF analysing each position in turn. There is a huge difference in quality. The final horizon and evaluation will be completely different. <CS> takes the Globeearth approach and his analysis is much better. 

Sep2918
  offramp: ...It's like two people who are asked to describe the Washington Memorial from 3 miles away. One uses a pair of binoculars and rapidly says it is a "very tall spike". The other guy walks all the way there, giving descriptions every few hundred yards, and eventually sees that it is a 555ft tall obelisk with memorials, an elevator, tourists etc etc. Very different results. 

Nov1618
  jonjoseph: I just think Fischer took a long time to squash the pawn on f5.Just like the film of Orca wales tipping the seal off an ice floe. You know , when he gets his tail and drags him down . As Attenborough said "Game over ". 

Nov1618   veerar: Fischer's opinion in "My 60 Memorable Games":
Defending and keeping e5 Pawn,is essential when you are Defending against the Ruy. Something to that effect. 

Nov1718   Howard: Looking forward to Sullivan's analysis of Games 17 and 19 ! 



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