Wednesday, March 08, 2006

(75) The parallel processing of the ending of two Knights and Bishop Vs a Rook

On October 24th 1991 I adjourned a London League game where I had two Knights, a Bishop and three Pawns and my opponent, David Okike, had a Rook, Bishop and Pawn.
For some time I had held an overwhelming superiority and had relaxed my attention somewhat, for I thought that at any moment he was likely to resign.

Then, to my dismay, it became apparent that I could not prevent him from taking play into a strange Pawnless ending where the only remaining units on the board would be: (Plaskett) two Knights and a Bishop Vs (Okike) a Rook.

I had seen neither a practical example nor even a theoretical reference to this ending anywhere, and so found myself having to make an assessment of it.
I thought it probably drawn.
Grandmaster Glenn Flear later told me that he had once seen it in a Russian Grandmaster’s game at a tournament in Hastings in the late 1980s.

I had arranged with Okike to resume play on October 31st 1991.

On October 28th I rang International Master Byron Jacobs and asked him what he thought of this recondite ending.

"Oh I’ve seen the game!" he exclaimed.

"What game?" I asked.

"Karpov against Kasparov."

It transpired that on October 26th 1991 a game had been played between the world’s two strongest players, Karpov and Kasparov, at the Interpolis event in Tilburg, Holland, which had come down to just this ending.
I was unaware of it.

On October 30th The Times ran a front page article —

At last - white to win in 100 billion moves
It detailed how a computer had calculated that the ending of Rook and Bishop versus two Knights (which I definitely have never seen) was a forced win, even with the optimum starting position for the defender, in two hundred and twenty three moves!
The average length of the winning process was one hundred and twenty moves.

Lewis Stiller from John Hopkins University in Baltimore had written a computer programme which had cracked the Rook and Bishop Vs Knight and Knight ending in five hours.
A diagram of that ending was given on The Times front page.

The final paragraph mentioned that a whole series of these obscure, Pawnless endings had now been solved by the application of the avant-garde "parallel processing" procedure, and that onesuch had just occurred that very week involving the top two players in the world, Karpov and Kasparov.

For an instance (one of only three known) of this ending occuring in practical play - and that in a most important match between two top class Grandmasters - see Entry 369 here -

The next day Okike and I resumed and he quickly forced the ending of two Knights and a Bishop versus a Rook.
My team-mate, David Rumens, was playing on the adjacent board and he remarked on the coincidence of this rare ending occurring twice in Grandmaster play in the same month.

"Same week," I corrected him.

He too had never seen it before the Karpov Vs Kasparov game.

Okike Vs Plaskett
King’s Head II Vs Hampstead, London League,
October 24th 1991
1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 a6 6 f4 e6 7 Bd3 Nbd7 8 Qf3 Qc7 9 g4 h6 10 h4 h5 11 gxh5 b5 12 Be3 Bb7 13 a3 Rxh5 14 0-0-0 Rc8 15 Kb1 g6 16 Nce2 Rc5 17 Rc1 Bg7 18 Rhg1 e5 19 Nb3 exf4 20 Nxc5 dxc5 21 Qxf4 c4 22 Qxc7 Rxc7 23 Nf4 cxd3 24 cxd3 Rxc1 25 Rxc1 Ng4 26 Bd2 Be5 27 h5 gxh5 28 Nxh5 Nf2 29 Nf4 Bxf4 30 Bxf4 Nxd3 31 Rc7 Bxe4 32 Bd6 f5 33 Kc2 f4 34 Kd2 f3 35 Bg3 Nxb2 36 Ke3 Nf6 37 Ra7 Nd1+ 38 Kd4 f2 39 Bxf2 Nxf2 40 Rxa6 Nd7 41 Ra5 Bc6 42 Ra6 Bf3 43 Ra5 Bc6 44 Ra6 Bb7 45 Ra7 Bg2 46 Ra5 Bf1 47 a4 Ng4 48 axb5 Ngf6 49 b6...
Black may now round up and capture the last white pawn. We agreed to a draw at move sixty-three.

Karpov Vs Kasparov
Tilburg, Interpolis,
October 26th 1991
1 d4 Nf6 2 c4 g6 3 Nc3 Bg7 4 e4 d6 5 Nf3 0-0 6 Be2 e5 7 0-0 Nc6 8 d5 Ne7 9 Nd2 a5 10 Rb1 Nd7 11 a3 f5 12 b4 Kh8 13 f3 Ng8 14 Qc2 Ngf6 15 Nb5 axb4 16 axb4 Nh5 17 g3 Ndf6 18 c5 Bd7 19 Rb3 Nxg3 20 hxg3 Nh5 21 f4 exf4 22 c6 bxc6 23 dxc6 Nxg3 24 Rxg3 fxg3 25 cxd7 g2 26 Rf3 Qxd7 27 Bb2 fxe4 28 Rxf8+ Rxf8 29 Bxg7+ Qxg7 30 Qxe4 Qf6 31 Nf3 Qf4 32 Qe7 Rf7 33 Qe6 Rf6 34 Qe8+ Rf8 35 Qe7 Rf7 36 Qe6 Rf6 37 Qb3 g5 38 Nxc7 g4 39 Nd5 Qc1+ 40 Qd1 Qxd1+ 41 Bxd1 Rf5 42 Ne3 Rf4 43 Ne1 Rxb4 44 Bxg4 h5 45 Bf3 d5 46 N3xg2 h4 47 Nd3 Ra4 48 Ngf4 Kg7 49 Kg2 Kf6 50 Bxd5 Ra5 51 Bc6 Ra6 52 Bb7 Ra3 53 Be4 Ra4 54 Bd5 Ra5 55 Bc6 Ra6 56 Bf3 Kg5 57 Bb7 Ra1 58 Bc8 Ra4 59 Kf3 Rc4 60 Bd7 Kf6 61 Kg4 Rd4 62 Bc6 Rd8 63 Kxh4 ...

and they agreed to a draw at move one hundred and fourteen -
But their pure ending of the three pieces against the one started at move sixty-three, the same point at which Okike and I terminated our struggle, although that had not been a conscious intent on my part to copy them when offering David the draw.

A computer search found just one game from international competitions in which this ending had occurred, in Finland in 1985. Matt Fletcher was to tell me that he had also seen it crop up in a minor London event of the 1990s.
On November 6th 1991 I rang Grandmaster Dr John Nunn to see if he knew of any practical examples of or theoretical references to the ending.
He said that there was almost certainly some reference to it in endgame manuals such as those of Chéron.

"As it happens I have those volumes open in front of me now."
He said that he not infrequently consulted them.
The modern computer assessment of this ending is that it should be drawn.

I note that although Stiller’s programme had cracked a whole series of these pawnless endings, the one which received a diagram in the Times article involved the same material distribution as in Karpov’s game with Kasparov and mine with Okike, i.e. two Knights, one Bishop and one Rook.
But in the article each side had a couple of those four pieces.

In the first instance, the K Vs K game, white had the three minor pieces.

Then, in the Times article, each side had two of the four pieces.

In the last instance (remembering that the actual pawnless ending did not occur in my game with Okike until after the adjournment) it would be black who had the three pieces and so was trying to win.

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