Saturday, May 15, 2010

Darga-Spassky, part 2 (the most beautiful bishop ending in the world)

This continues the game Darga-Spassky, Round 1 of the Amsterdam Interzonal, 1964. The first 92 moves of the game (!) are in a separate post, Darga-Spassky, part 1. This post attempts to solve the resulting bishop ending at move 92, given best play.

This ending (or at least my posting of it) has a story behind it. When I was playing through these interzonal games, I stopped and wondered why Spassky didn’t play 92...Bc2 instead of his obviously silly blunder. At first, I couldn’t find a way for White to win if Black just kept shuffling his bishop between c2 and d1. I spent some time looking at it and found a win that I thought was really beautiful. I was very enthused.

Okay, time passed. I hadn’t played or looked at chess for a while. I had a pair of chess friends visiting from out of town and I thought it would be cool to pull out this ending. To my horror, I found that I hadn’t written down the winning method. I spent some time that afternoon trying to reconstruct it, but to no avail. Well, no biggie, I thought: my friends are both strong players so we’ll just figure it out together over dinner. To my surprise, we were unable to do so. The bishops danced and danced, but zugzwang was elusive and no other winning method presented itself. A couple of weeks later, I closeted myself with the ending for the weekend and eventually figured it out. So here it is. I hope you enjoy it.

If Black plays the best defence,


Then the critical position arises after the forced exchange of d-pawn for g-pawn:

93.Bd5 Kd7

If Black tries to hold the g-pawn, he immediately gets into zugzwang: 93...Bd1? 94.Bf7 Bh5 95.Ka4 Kd7 96.Kb5 Kxd6 97.Kb6 Ke7 98.Bg8 Kd6 99.Bh7. I’m pretty sure that this was the line that so impressed me with its beauty back when; now it seems a bit callow.

94.Bf7 Kxd6

Black should just take the d-pawn and leave his bishop on c2. As in the game, if he tries to attach the bishop to the c-pawn, he just loses more quickly: 94...Bd3 95.Kb3 Kxd6 96.Bxg6 Ke7 97.Bh5! Bf1 98.Bf3 Bd3 99.Bd5 and Ka4-a5


White has "two weaknesses" to play with. One is the f-pawn, and the other is the possibility of king penetration with Ka4 (which I suppose boils down to the weakness of the c-pawn).
White's aim is to produce a position where he is attacking the f-pawn while only Black's bishop is defending it; then Kb2 will force the bishop to choose between abandoning the f-pawn or allowing Kb3-a4, so here for instance 95...Ke7? 96.Kb2 Bd3 97.Kb3 +- as above.

95...Ke6! 96.Bh5!

In a simpler world, White would be able to play 96.Bh7, which forces Black's king to move away from the f-pawn and allows White to complete his strategy. Unfortunately, after 96...Kf7 97.Kb2 Bd3 98.Kb3 Kg7 the bishop runs into a bit of trouble, and the position becomes equal. 96.Bh5 also restricts Black’s bishop.

96...Ke7 97.Bf3

so white has to attack the f-pawn from the other side, where he has a longer diagonal. If you put the white bishop on c8 here, you see that White has an immediate win on the next move with Kb2. To prevent this, Black would have to commit all his resources immediately: 97...Kd7 98.Bb7 Bd1 (to meet 99.Bc8+ Kxc8 100.g6 with 100...Bh5 101.g7 Bf7) but this loses to 99.Ba6 and now Black can’t move his bishop, or move his king away from c8; so we get 99...Kd8 100.Bb5 Ke7 101.Ba4 B moves, 102.Bc2 and Ka4.

So Black’s best defence is to bring the K around to the other side of the pawn:

97...Kf7 98.Bb7 Kg6! 99.Bc8 Bd1 100.Bd7 Bc2 101.Be8+ Kg7

and here White has three tries:

A) 102.Bh5 Kh7 and White makes no progress

B) 102.Ka2 Bd1 103.Kb2 Bf3 (or Kh7) 104.Bd7 Kg6 and again White must reset the diagram position with 105.Ka3 Bd1 106.Be8+

and the winning line:

102.Ba4! Be4
103.Bd7 Bc2

Bingo. Mednis would be proud.

Depending on how many steps Black's king took to reach g7, this position can also be reached with Black's bishop on d1. Then white wins as in the 97...Kd7 variation after 102.Ba4 B moves 103.Bc2 and Ka4.

So what do you think? Is it beautiful? Nice? Just another bishop ending? Is it worth falling on your sword to avoid all of this? Spassky had a slow start to the tournament, and not just because he lost this: his other early-round games didn't go so well, either. Maybe it had something to do with spending all his rest days sitting with Darga pushing the bishops around for another few hours.

Here's how the actual game went, from the starting point of this post:

93.Ka4 Bxc4
94.Ka5 Be2
95.Bb5 c4

Just a little fancy. The more natural line would be 96.Kb4 c3 97.Ba4


I wonder how long it would take a strong computer to find the win after 92...Bc2. They don’t have the concepts of “White wins if the king passes a4” or “the bishop needs to come around to the longer diagonal” so its search would be tremendously less efficient, and it might originally reject the whole concept of Bxg6/...Kxd6 as exchanging a pair of pawns while Black’s king comes out of the box. Though of course after a few billion bishop and king shuffles I’m sure it would converge on a solution.

Darga-Spassky, part 1

This game is the intersection of a couple of interests for me. First of all, I’ve found that when top-notch players lose, the game is usually something special. In this case that is very true, although sometimes it’s “special” as in “cool” and sometimes “special” as in Special Olympics. The other interest at the time was self-improvement: I had decided to play through all the games of an interzonal, to see how some top-notch players played against each other and against people who weren’t quite so good.

Darga - Spassky Amsterdam IZ, 1964

1.Nf3 Nf6 2.c4 e6 3.g3 b6
Spassky playing the QID? It soon becomes clear that this is not a good choice.
4.Bg2 Bb7 5.0-0 Be7 6.Nc3 0-0 7.d4 Bb4?!
Losing a tempo in order to give up the two bishops when your position is already really passive is not a good idea.
8.Qb3 Bxc3 9.Qxc3 d6 10.b3 Nbd7 11.Bb2 Re8 12.Rad1 Rc8 13.Rfe1?! Qe7 14.d5 e5 15.Nh4

Black's position is looking more and more like one of those textbook passive/inferior positions that will soon be wrecked by some attractive sacrifices. Put white’s rook back on f1 and use that tempo to play f4 and it becomes even clearer.

15...Nc5 16.f4 Nfd7 17.e3 a5 18.Qc2?!

Darga doesn't lose his advantage this way, but he shouldn't be pretending Black's queenside "play" amounts to anything. He has a huge space advantage and the two bishops, and he should be concentrating on a way to kill Spassky's king.

18...f6 19.a3 Ra8 20.Bc3 Qf7 21.Rf1

21...exf4 22.exf4?

I think this is where Darga starts to go really wrong. As played the rooks will just get exchanged on the e-file, instead of White being able to place them behind a pawn-storm. The crowd wants 22.Rxf4 when Black can't take the e-pawn because of 22...Rxe3 23.Nf5 Ree8 24.Rg4, threatening both Rxg7 and Nh6+


The knight is just out of play on b3

23.b4 Nb3 24.Nf5 Nf8


Just leave the Nb3 alone! White should play something like 25.Kh1 and Rg1, Be4, g4-g5. To me, this is just the quintessential Soviet game. Throughout it, Darga seems to have the philosophy of just playing solidly, doing nothing the least bit interesting, and letting Spassky hang himself. Well, it eventually works, but the whole process would have been less painful for everyone if he’d just played real chess for more than one brief phase of the game.

25...Nxd4 26.Bxd4 Qg6

Another reason to have kept a knight on f5. I'm sure that Edmar Mednis would be thrilled beyond words to exchange queens with the two bishops in hand, but 99% of all other chess players would have wanted White's huge space plus to amount to something more substantial.

27.Qxg6 hxg6 28.Rfe1 Kf7 29.Kf2 Ba6 30.Bf1 f5?!

Now Black's king is tied down to the weakness at g7, and his bishop is worse.

31.Rxe8 Rxe8 32.Re1 Rd8 33.Bd3 Nd7 34.b5 Bb7 35.Bc2 Nc5 36.h4 Nb3

The same mistake twice!

37.Bc3 Bc8 38.Re3 Bd7 39.Re1 Rg8 40.Re3

It's hard to tell whether white is in time trouble and just wants to make the time control before doing anything, or is just dicking around to make the point that he can. Judging by his play later in the game, it's the latter.

40...Nc5 41.Bd4 Ra8 42.Ke1

42...Ne4 43.Bd1

Spassky is willing to give up a pawn immediately just to get opposite colored bishops, and indeed 43.Bxe4 fxe4 44.Rxe4 Re8 45.Rxe8 Bxe8 46.Kd2 Bd7 47.Kc3 Bg4 48.Kb4 Be2 is a clear draw

43...Re8 44.Bxa4

Darga, for his part, is willing to trade a good pawn for a lousy one in order to get the rooks off

44...Nxg3 45.Rxe8 Bxe8 46.Bc2 Nh5 47.Be3 Ke7


Now Darga plays very energetically, precisely and resolutely for the only time in the entire game, and acquires a winning advantage. Edmar Mednis would faint for joy over his play over the next 17 moves.

48...Kd7 49.a5 bxa5 50.Kd2 Ng3 51.Kc3 g5! 52.hxg5 Bh5 53.Kb3 Be2 54.Bd2 a4+ 55.Kb4 a3 56.Bb3 Ne4 57.Be3 g6 58.Kxa3 Nc5 59.Bxc5! dxc5 60.Ka4 Bd3 61.Ka5

White will spend the rest of the game trying to achieve this sort of breakthrough again.

61...Be2 62.b6! cxb6+ 63.Kxb6 Kd6 64.Kb7 Bd3 65.Kc8 Be2

White now has a fairly standard win by walking his king over to f6, forcing Bh5. Then Black has to move his king, and (after Ba4-b5) White will be able to play Ke5, d5-d6, Kd5 and take the c-pawn (or just queen the d-pawn if Black puts his king on b6).

I'm wrong here -- as Todd Rowland points out in his comment below, Black has a stalemate cheapo: 66.Kd8? Bxc4! 67.Bxc4 stalemate. So Black has an unusual sort of "blockade" along the back rank, and the position must be drawn because the White king has no route into the Black position.

66.Kb7?? And all these question marks are undeserved... :-)

However, Darga, under some sort of hallucination, now painstakingly negates all his previous progress. This is the sort of continuation that gives rise to those stories of Soviet collaboration...

66...Bd3 67.Ka6?? Bf1 68.Ka5?? Bd3 69.Ka4?? Bf1 70.Ka3?? Be2 71.Kb2?? Ke7 72.Kc3 Kd6 73.Bc2 Ke7 74.Bd3 Yeah, that's going to work 74...Bd1 75.Kd2 Bb3 76.Be2 Kd6 77.Kc3 Ba4 78.Bd3 Bd1

At this point, both players seem to feel that all black needs to draw is to keep his bishop on this diagonal to keep the White king out -- counterattacking the c4 pawn if necessary.

79.Kd2 Bb3 80.Kc1 Ke7 81.Kb2 Bd1 82.Bc2 Be2 83.Kc3 Kd6 84.Ba4 Ke7 85.Bb5

85...Kd8 ?!? ?? And this is just a losing move.

At first, I thought that this gives White some chances he doesn't deserve, after Black has clearly demonstrated that he knows how to draw. But perhaps White can just place his bishop on b3 and walk his king up the board anyway, decoying the Black king if necessary by pushing the d-pawn.

This shows a big difference between chess then and modern chess with sudden death time controls. Both players (being much stronger than me and seeing the stalemate defence) must have realized that the position was a dead draw, for the reasons mentioned above. However, Darga was able to exercise his privilege of playing on and on and on, and eventually Spassky either lost concentration, had a mad impulse, or committed a fingerfehler... we'll never know. In a modern situation, Black could have pointed out that White isn't really trying to make progress and had the game called a draw that way -- and White wouldn't have been able to continue without risk, since he would also been in danger of losing on time.

Perhaps one day we'll consider the adjournment era as backwards as the pre-clock 1800s, where the slower players used to consider for hours over one move.


This rules out the win just mentioned, because of the vulnerability of White's d-pawn. So now the win is very complicated. On the other hand, if the win in the last note doesn’t work, then this is White's only winning try and Black blew it on the previous move.

86.d6 Bf3 87.Kb3 Bd1+ 88.Ka3 Bc2 89.Bc6 Bd1 90.Ba4 Be2 91.Bb5 Bd1 92.Bc6

At this point, Spassky played 92...Be2? and resigned four moves later. However, he can continue his previous policy of king-containment with 92...Bc2, reaching the critical position for this ending. That position is the starting point for the second post in this series, Darga-Spassky, part 2 (the most beautiful bishop ending in the world)