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,

92...Bc2

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

95.Bxg6


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
104.Kb2

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:



92...Be2?
93.Ka4 Bxc4
94.Ka5 Be2
95.Bb5 c4
96.Ba4

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

1-0

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.