Quest for Understanding

I have been trying to hold a draw against Stockfish from a position that Jan Timman failed to hold against Anatoly Karpov (Belfort 1988). The position was brought to my attention when I began rereading Jacob Aagaard, Excelling at Technical Chess (2004). Nearly twenty years ago, I read this book quickly and superficially, spending very little time with the instructive positions. I did read all the text and it had a profound impact on my game, particularly in my attitude towards offering or accepting draws when there is even a faint chance of battling for a win. In "Excelling at Technical Chess" (2011), I presented an annotated game where I prevailed in a minor piece battle, somewhat inspired by Aagaard's work.

Aagaard's annotations of the game elaborate the importance of activating your strongest piece. Timman does this well early in the endgame, but then seems to lose the thread and "play without a plan" (Aagaard 13).

White to move

Here, Aagaard writes, "everything has gone wrong for White", noting the passivity of White's rook compared to Black's active rook. However, according to Stockfish and tablebases, White's position remain a technical, however difficult, draw. A comment on chessgames.com credits Karsten Müller and Yakov Konoval, Understanding Rook Endgames (2016) with pointing out that the position is drawn.

Drawn according the computer is one thing, however, and holding such a position as a human is quite another. Aagaard points out in the next chapter of the book, "an advantage does not have to be decisive in order to win" (24). The defender must continue to find the best moves, while the side that is pressing for a win can try different things.

When Timman played his next move, 53.Ra3, the position was then technically lost. However, Karpov's technique was not without error. Five moves later, Timman again had chances to draw and missed the correct moves.

Likewise, playing 53.Ke3, 53.Rc4, or 53.Rd4 does not immediately secure the draw. Many subsequent positions offer a single move that must be found. Others offer two options, but no more. I played the position against Stockfish 18, needing help and takebacks at least half a dozen times to hold this position. Then I studied my efforts with the engine running, and practiced the ending again. After several efforts, I was able to hold the position against a weaker version of Stockfish on my iPad.

Alas, errors were made both by the weaker Stockfish and by me. So, more time was spent playing the latest Stockfish on a computer with the determination to reach such an understanding of the position that I can draw the machine with no errors.

One such exercise continued:

53.Rd4 h5 54.Ke3 h4 55.a4 Rf1 56.Rd8 Ra1

White's rook has become active, while Black's rook's mobility has been reduced.

White to move

I am beginning to understand that in this position (and likely similar ones) Black's rook must balance continuous checks with threats to capture the a-pawn should it be undefended. The king must get in front of the h-pawn.

57.Rd5+ Kg4 58.Kf2 Rxa4 59.Kg2

Each of White's last three moves were the only move to maintain a draw.

59...Ra2+ 60.Kh1 Kg3 61.Rd3+

The side check is the only chance.

61...Kf2

White to move

62.Rd5

This move both restrains the mobility of Black's rook with a threat on the pawn and prepares checks from the rear.

62...Ke3 63.Rc5

63.Re5+ Kd4 64.Rf5 also holds.

63...Kd4 64.Rf5 h3 65.Rb5 h2

White to move

66.Rb5+

The next 50 moves were efforts to get the engine to capture my rook for stalemate.

A Longer Battle

Starting from the initial position at the top of the post with a different move still led to a position in the line above.

53.Ke3 h5 54.Rd4 h4 55.a4 Rf1 56.Rd8

56.Rd7 also holds

56...Ra1 57.Rd5+ Kg4 58.Kf2 Rxa4 59.Kg2

Black to move

59...h3+

59...Ra2+ was played in the line above.

60.Kh2 Ra1

White to move

In this position, White has two viable moves, but for most of the next thirty or so, only one move holds.

61.Rd4+

61.Rc5 was the other option. Would it make subsequent moves simpler?

61...Kf3 62.Rd5

A check allows the king to attack the rook, so cannot be played. After 62.Rd3+ Ke4, White's rook can neither check the king nor attack the a-pawn. Hence, Black's rook becomes more active and the a-pawn becomes a credible queening threat.

At least, that has been my understanding. However, if Black attacks the rook with 62...Ke2, White is lost nonetheless. 63.Rd5 attacks the pawn 63...a4 is now the only winning move. 64.Rd4 a3. Again, Black had to push the pawn to maintain the win. After 65.Ra4 Kd2 66.Rf4, White appears close to setting up Vancura's defense, but 66...Rc1 refutes White's plan (Black also might slide the king back to the e-file temporarily). 67.Ra4 Rc3 Both of Black's pawns are secure and the king is free to move to b2 where all possible checks can be blocked.

62...a4 63.Rd4

Why does 63.Rc5 fail? 63...Re1 64.Ra5 Re4 65.Kxh3 Ke2 and Black's king will reach b2 while his rook is also more active.

63...Ra2+ 64.Kh1

64.Kxh3 was possible here, but not in many other positions that I reached during my training exercises.

64...Kg3 65.Rd3+

Of course, the mate threat must be stopped.

65...Kh4 66.Rd4+

66.Rc3?? The loss of a single tempo allows Black to reposition the rook with a winning advantage. 66...Rb2 (or Rd2 etc.) 67.Ra3 Rb4. An instructive line continues 68.Kh2 Kg4 69.Rg3+ Kf4 70.Rxh3 Rb2+ 71.Kg1

Black to move

Analysis diagram

71...Rb3 is the only winning move, but it is not difficult to find.

66...Kd3 67.Rd3+ Kf2 68.Rd4

Again, White must eye the a-pawn.

68...Ra1+ 69.Kh2 Ke3

White to move

70.Rc4

A rare instance when White has four viable options, all along the fourth rank.

After dodging many checks, Black advanced the pawn to a3 on move 78. White continued the checks from the side without difficulty as the position is essentially the same as found in the Vancura defense.

Then, 90...Ke4 offered White some choices.

White to move

Again, any move along the third rank that does not hang the rook holds the draw.

91.Rc3 Kd4 92.Rf3 Kc5 93.Rf5+

This check was unnecessary with Black's king temporarily on holiday.

93...Kb4 94.Rf4+

This check, however, was the only move.

94...Kc5 95.Rf5+ Kd6 96.Rf3

Either check from f6 or return to the third rank.

Both players shuffled their pieces for many moves until Black set a tactical trap: a discovery that wins a critical tempo.

White to move

After 120...Ra1

121.Kh2

121.Rf3 Kb2-+

After another two dozen moves:

Black to move

After 145.Kh2

145...a2

This move was what White had been anticipating, for now the ending has become a simple one that I have played many times.

146.Ra3 with an easy draw, but the engine took it out to move 195 when the game was drawn by the 50-move rule.

Has this exercise increased my knowledge in a way that might be applicable to new positions? The central theme of this ending, as analyzed by Aagaard, and as played out against the computer in the effort to improve on Timman's play, is the mobility of the strongest piece--the rook.