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
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
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
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
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...Ra2+ was played in the line above.
60.Kh2 Ra1
White to move
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
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
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| Analysis diagram |
66...Kd3 67.Rd3+ Kf2 68.Rd4
Again, White must eye the a-pawn.
68...Ra1+ 69.Kh2 Ke3
White to move
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
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
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| After 120...Ra1 |
121.Rf3 Kb2-+
After another two dozen moves:
Black to move
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| After 145.Kh2 |
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.
