Sunday, April 20, 2008

A Knight's Tale

I lost a difficult knight ending against FM Robby Adamson in round 9 of the Foxwoods Open last month:

Adamson-Cherniack, Foxwoods Open 2008

Round 9 at the Foxwoods Open is always played after the cumulative effect of eight 6-hour games for three successive days; Round 8 began at 10:00 AM, finished at 4:00 PM, and this game began at 4:30 PM.

We were in the second part of the time control (40/2; SD/1), and this game was the last to finish in the entire tournament:

53…Ke5 54.Nb5 Nc6 55.c3 Kd5 56.Na3 Kc5 57. Kc2 Ne5 58. Nb1 Nd7 59.Nd2 Nb6 60. Kb3 Nd5 61. Ne4+ Kc6 62. Kc4 Nc7 63. Ng3 a6 64. Nf5 Kb6 65. Ne7 Nb5 66. Ng6 Kc6 67. Nf4 Kb6 68. Kb3 Nc7 69. Nd3 Nb5 70. c4 Nd4+ 71. Kc3 Nc6 72. Nc1 Kc5 73. Nb3+ Kd6 74. Nd4 Nd8 75. Kb4 Nb7 76. Nb3 Kc6 77. Kc3 Nd6 78. Nd4+ Kc5 79. Ne6+ Kc6 80. Kb4 Nb7 81. Kc3 Kd6 82. Nd4 Nc5 83. Nc2 Kc6 84. Nb4+ Kd6 85. Nd3 Nb7 86. Kb4 Kc6 87. a3 Kd6 88. Nc1 Kc6 89. Nb3 Kd6 90. Kc3 Nd8 91. Na5 Kc5 92. Kd3 Kd6 93. Nb3 Kc6 94. Kd4 Ne6+ 95. Kc3 Nd8 96. Nd2 Kc5 97. Ne4+ Kc6 98.Ng5 Kc5 99. Kd3 Nb7 100. Ne4+ Kc6 101. Kd4 Kb6 102. Kc3 Kc6 103. Kb4

At this point my opponent had 90 seconds left to finish the game, and I had 4 minutes. I claimed a draw before I made my next move, because no pieces or pawns had been exchanged for 50 moves. Dummy that I was, this claim had no validity because pawns had been moved. My opponent, an attorney, tried to counterclaim that I should be forfeited (I’m a chessplayer, not a legalist, and apparently people can be forfeited under USCF rules for making incorrect threefold repetition claims). The TD instead invoked the Continental Chess Association rules, and added two minutes to my opponent’s clock.

It was after 11:00 PM, and I was even more sick of playing on in this position, trying not to think of the subsequent 2 hour drive back to Boston and waking up to work the next day… I blundered in short order.

103…Kb6 104. Nd2 Nc5 105. Nb3 Nb7 106. a4

106… Kc6?? 107. Na5+ (this wouldn’t work with the pawn on a3) Nxa5 108. Kxa5 Kc5 109. Kxa6 Kc6 110. a5 Kc7 111. Kb5 Kb7 112. c5 Kc7 113. c6 Kc8 114. Kc5 Kc7 115. Kd5 1-0

I had promised a long-suffering Natasha Christiansen a ride back to Boston, and we eventually arrived back in Massachusetts at 1:30 AM. Her husband Larry very thoughtfully provided pizza for both of us when we returned; he had been receiving regular phone reports from Natasha throughout the evening, and recommended that Black leave the pawn on a7. After a few hours sleep I slogged through work later that day, and promised myself that I would find a way to hold this ending, if at all possible.

The question I pose to BCC members, and will try to answer, is – can Black draw this ending?


Before playing over actual games, I went to the BCC library and looked up what endgame book authors have written.

Rueben Fine, author of the granddaddy of ending books Basic Chess Endings, said that knight and pawn versus knight was usually a draw when the defending king in front of the pawn – the lone knight could usually give itself up for a pawn, or blockade it. That was promising. My king was in front of the pawns, and the extra set of pawns were rook pawns, so this drawing scenario was entirely possible:

Dvoretsky’s take on these kinds of endings (knight and 2 pawns vs. knight and 1 pawn) in Dvoretsky’s Endgame Manual is that they can be frequently be saved, although defending them requires great accuracy. He also had an interesting quote from Botvinnik, who said that “knight endings were pawn endings:” the same factors that won pawn endgames (active king, outside passed pawn, zugszwang) directly applied to knights as well.

The most helpful book I found on this subject was David Hooper’s Practical Chess Endgames. He wrote when the pawns were on the same side of the board, knight endings could often be won, even though they were notoriously drawish in endings with bishops, rooks, and queens. The player with the extra pawn could win this ending if the pawns were not so widely spread across the board, and if the defender was unable to attack the blocked pawn.

Hooper gave two examples.

Botvinnik-Lisitsyn, Moscow 1935 (analysis)

In this position White draws:

1.Ne1 Kd4 2.Ng2 (tying the King to the defense of the f pawn) Ke5 3.Kb3 Nf5 (3…Nb5 4.Kb4) 4.Kb4 Ne3 5.Nh4 (or 5.Nxf4=) Nd5 6.Kb5 Kd4 7.Ng2 Kd3 8.Nf4+=

Chernikov-Chehover, Leningrad 1938

However in this position White loses:

1.Nd2 Nf5+ 2.Ke2 e3 3.Nf3+ Kf4 4.Ne1 Ke4 5.Kf1 Nd4 6.Kg2 Ne2 7.Nf3 Kd3 8.Ne5+ Kd4 9.Nf3+ Kc3 10.Ne5 Nf4+ 11.Kf3e2 12.Kf2 Nd3+ -+

Perturbed, I then started playing over actual games. I was perturbed because in my game the pawns were even closer together than the above example (bishop pawn and rook pawn), and because the loser in this example was named Chernikov!


Surprisingly, I couldn’t find any games of knight, bishop pawn, and rook pawn versus knight and rook pawn in the endgame books. I could only find examples in the Informant Encyclopedia of Chess Endings that covered minor piece endgames (N B 2d), and only after mentally calculating transitions from games of knight and 3 pawns vs. knight and 2 pawns.

Haag-Kluger Pecs 1976

This game quickly made me see how foolhardy it was to let the King get out ahead of the passed pawn.

1.Kf7! Nxg4 2.Nf8+ Kh8 3.Ne6 Nf2 (3…Nf6 4. Nxg7 Nd5 5.f5 Nf4 6.f6 Kh7 7.Kf8+-) 4.Nxg7 Nd3 5.Ne6 Kh7 6.Nf8 Kh8 7.Ng6+ Kh7 8.f5 Nf2 9.f6 Ne4 10.Ke7 Ng5 11.Ne5! (11.f7? Nxf7=) 1-0

Prandstetter-Donchev Prague (zt) 1985

This game made me realize how risky it was to advance the a pawn too far up the board.

1.c4 bxc4 2.bxc4 Kc6 3.a3 Nf6 4.Ne5+ Kb6 5.a4 Ka6 6.c5 Nh5 7.Nd3 Ng3 8.Nf4 Kb7 9.Kb5 Nc3+ 10.Kxa5 +- Kc6 11.Nd3 Kd5 12.Kb4 Ne2 13.a5 Nd4 14.a6 Kc6 15.Kc4 Ne6 16.Nb4+ Kc7 17.Kd5 Nf4+ 18.Ke5 Ng6+ 19.Ke4 Kb8 20.Kd5 1-0

Fine-Naidorf New York (m/3) 1949

Although not strictly a bishop pawn and rook pawn vs. rook pawn, this knight ending showed how crucial the decision was for the defender to move the rook pawn, or to leave it in the starting position.

1.h3? Ne3+ 2.Kh2 Nc2 3.Kg2 Ne1+ 4.Kf2 Kxh3! 5.Kxe1 Kg2 6.Ke2 h5 7.Ng5 h4 8.Ne6 g5! 0-1 (9.Nxg5 h3 10.Nxh3 Kxh3 11.Kd3 Kg2-+).

Keeping the pawn on h2 held the draw: 1.Nf2 Ne3+ 2.Kg1 Nc2 3.Nd3 g5 4.Kf2 Kh3 5.Kg1 h5 (5…Nd4 6.Nf2+ Kh4 7.Kg2) 6. Nf2+ Kh4 7.Nd3 =. Even the author of Basic Chess Endings can screw this up!

And yet in the following position the rook pawn was moved up a square, and the defender held.

Gligorich-Ivkov Yugoslavia 1971

1.Nf4 Kf7 2.Kf2 Kf6 3.g4 Ne5 4.Kg3 Kf7 5.Nd5 g6 6.Kf4 Nd3+ 7.Ke3 Nc5 8.Ke4 Nd7 9.Nf4 Nf6+ 10.Ke5 gxf5 11.gxf5 Nd7+ 12. Kd6 Nb6 (12…Kf6 13.Kd7 Kxf5 14.Ne2 Ke4 15.Ke6 Kf3 16.Kf5+-) 13.Nh5 Nc4 14.Kd5 Nb6+ 15.Ke6 Nd7+ 16.Kf4 Nc5 17.Ng3 Nd3+ 18.Ke3 Ne5 19.Ne4+ Kg7 20.Nf2 Kf6 21.Kf4 Nf7 22.Ne4+ Kg7 23.h4(?) Nd8 24.h5(?) Kf7 25.Nf2 Ke7! 26.Ng4 Nf7 27.Ke4 Nd6+ 28.Ke5 Nf7+ 29.Kd5 Ng5! 30.f6+ (30.Nxh6 Kf6 31.Kd4 Nh7 and 32…Kg5) Kf7 31.Ke5 Nf3+ 32.Ke4 Nh4! 33.Kd5 Nf3 1/2-1/2 (34.Ke4 Nh4 35.Ke5 Nf3+ 36.Kf4 Nd4=). However, I suspect Ivkov drew this game only because Gligorich advanced his h pawn to the fifth rank.

So what had I learned so far?
• Great accuracy was required
• Do not allow the opposing king to get out in front of the pawn
• Moving my sole remaining pawn may or may not draw – if it moves too far up the board it can easily be captured
• Keeping my sole remaining pawn on its original square may or may not draw

I went forth to try and hold this position against Fritz.


I initially had wanted to run this ending through the Nalimov tablebases, but they only cover endings with 6 or less pieces; this ending had 7. To receive a definitive answer, I went toe to toe against Fritz 10 – the time control was 4 minutes for each side, with a 2 second increment.

Fritz repeatedly clobbered me in this position, no matter where I placed the a pawn. Its assessment in all the training games was initially +0.85, but White’s favorable evaluation dramatically increased the farther the c pawn advanced up the board. Typical games went like this:


Pawn on a5

1…Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Ne6+ Kd5 5.Nd8 Kc5 6.c4 a5 7.Ne6+ Kd6 8.Nd4 Kc5 9.Kc3 Nc8 10.Nb3+ Kb6 11.a4 Na7 12.c5+ Ka6 13.Kd4 Nc6+ 14.Kd5 Kb7 15.Kd6 +-

Pawn on a6

1…Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Ne6+ Kb6 5.c4 Nc6 6.c5+ Kb7 7.Kc4 Ne7 8.Nd4 a6 9.Nc2 Ka7 10.Nb4 Kb7 11.Kd4 Nc8 12.Kd5 Na7 13.a4 Nc8 14.a5 Na7 15.c6+ +-

Pawn on a7

1…Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Ne6+ Kb5 5.c4+ Ka5 6.c5 Kb5 7.a4+ Kc6 8.Kc4 Nc8 9. Nd4+ Kc7 10.Kb4 Kb7 11.c6+ Kb6 12.a5+ Kc7 13.Kc5 Kb8 14.Ne6 Ka8 15.a6 Kb8 16.c7+ Ka8 17.Nf4 Ne7 18.Nd5 Nc8 19.Kc6 Ne7+ 20.Kd6 Nc8+ 21.Kd7 +-

So I turned the tables, and gave Fritz Black.


Try 1
1...Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Nc2 Nc6 5.Ne3 Na5+ 6.Ka4 Nc4 =

Try 2
1...Ke5 2.Kc3 Nd5+ 3.Kc4 Nb6+ 4.Kd3 Kd5 5.Nb5 a5 6.Na3 a4 7.c4+ Kc5 8.Kc3 Nd7 9.Nc2 Nf6 10.Ne3 Ne4+ 11.Kd3 Nf2+ =

Try 3
1...Ke5 2.Nb5 Kd5 3.a4 Kc4 4.c3 Nd5 5.Na3+ Kd3 6.c4 Nb4 7.Kb3 a5 8.Nb5 Na6 =

Try 4
1...Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Ne6+ Kd5 5.Nd8 Kc5 6.c4 Ng6 7.Nb7+ Kb6 8.Nd6 Kc5 9.Ne4+ Kd4 10.Nc3 a5 11.Na4 Ne5 =

The difference between Fritz and me was that my silicon partner was using a full court press, not allowing my c pawn to advance beyond the 4th rank. In Fritz’s positions with White, I was able to win most of the time after I had switched colors on move 7.

My impression from these practice games is that White wins if the c pawn reaches the 5th rank (no matter where Black places the a pawn), while keeping back the other pawn no farther than a3. Then White has less distance to defend the squares around the advanced c pawn and attack Black’s a pawn simultaneously, and can use the threat of knight forks to ram the extra pawn down to the last rank.

If, however, Black can keep the c pawn on the 4th rank (which is MUCH easier said than done), then White will eventually be forced to advance his a pawn farther and farther up the board to avoid three-fold repetition claims. Then you’ll reach an ending like Gligorich-Ivkov, where White’s pawns were so close together that both could be attacked at once (see the note to move 30). As confirmation, I turned Mr. Smarty-Pants on itself:


1...Ke5 2.c3 Kd5 3.Kb3 Kc5 4.Ne6+ Kd5 5.Nd8 Kd6 6.c4 Ng6 7.Nb7+ Kc6 8.Na5+ Kc5 9.Kc3 Nf4 10.Nb3+ Kc6 11.Nc1 Ne6 12.Nd3 Kb6 13.Kb4 Kc6 14.a4 Kd6 15.Kb5 Nc7+ 16.Ka5 Kc6 17.Kb4 Ne6 18.Ne5+ Kd6 19.Nf3 Kc6 20.a5 a6 21.Nd2 Nd4 22.Kc3 Ne6 23.Nf3 Nd8 24.Nd4+ Kc5 25.Nb3+ Kd6 26.Kc2 Nc6 27.Kb2 Ne5 28.Kc3 Nc6 29.Kd3 Ne5+ 30.Kd4 Nc6+ 31.Ke4 Nb4 32.c5+ Kc6 33.Ke5 Kb5 34.Kd4 Nc6+ 35.Kd5 Nb4+ 36.Kd6 Nc6 37.Kd7 Nxa5 38.Nxa5 Kxc5 =

To conclude, I will attempt to annotate the moves of this endgame, along with position evaluations from Fritz, and will not attach any question marks until my stinkers at the end. I can’t speak for my opponent, but I was exhausted!

Adamson-Cherniack, Foxwoods Open 2008

53…Ke5 (.88) 54.Nb5 (.73)

More promising is 53.c3 and 54.Kb3, as the computer invariably played.

53…Nc6 (.74) 55.c3 (.64) Kd5 (.65 ) 56.Na3 (.56) Kc5 (.64) 57. Kc2 (.59) Ne5 (.65) 58. Nb1 (.46) Nd7 (.66 ) 59.Nd2 (.66 ) Nb6 (.90)

59…Ne5 60.Kb3 a6 makes it harder for White to advance the c pawn.

60. Kb3 (.87) Nd5 (.95) 61. Ne4+ (.91) Kc6 (.92) 62. Kc4 (.92) Nc7 (.94) 63. Ng3 (.92) a6 (.95) 64. Nf5 (.96) Kb6 (.99) 65. Ne7 (.93) Nb5 (.93) 66. Ng6 (.72)

After 66.Nd5+ Kc6 67.Ne3 Nd6+ 68.Kb4 Ne4 69.Nf5 Nc5 70.Kc4 White’s king is securely in front of the passed pawn, has plenty of a pawn tempi moves in reserve, and has excellent chances to advance farther.

66…Kc6 (1.02)

66…Nd6+ 67.Kb4 a5+ 68.Kb3 leaves White back at “square 1” – see Cherniack-Fritz, try 2.

67. Nf4 (.93) Kb6 (.99) 68. Kb3 (.72) Nc7 (1.14)

Better was 68…Nd6. Now 69. c4 is possible, since Black can’t play 69…Kc5 and attack the pawn twice.

69. Nd3 (.94) Nb5 (.94) 70. c4 (.94) Nd4+ (.94) 71. Kc3 (.94) Nc6 (1.14)

71…Ne2+ 72.Kd2 Ng3 forces White’s King back.

72. Nc1 (1.03) Kc5 (1.00) 73. Nb3+ (.97)

73. a3 forces zugwang, as 73...a5 74.Nb3+ Kd6 75.Kd3 Kd6 (75…Kb6 76.c4 Ka6 77.c5 wins) 76.Kd3 a4 77.Nc1 Kc5 78.Kc3 Kb6 79.Nb3 forces more zugwangs.

73…Kd6 (.97) 74. Nd4 (.97) Nd8 (1.01) 75. Kb4 (1.01) Nb7 (1.05) 76. Nb3 (1.05) Kc6 (1.55) 77. Kc3 (1.00) Nd6 (1.04) 78. Nd4+ (1.04) Kc5 (1.04) 79. Ne6+ (1.04) Kc6 (1.04) 80. Kb4 (.97) Nb7 (2.47)

During the game I thought the pawn on a6 and the knight on b7 made a good barrier to stop White’s king from penetrating the 5th rank. However Fritz REALLY hates the knight on this square (see the notes to moves 99 and 105). Is there such a thing as a long side and a short side in knight endings? 80...Ne4 81.Ka5 Nc5 holds the fort.

81. Kc3 (0.00)

White’s caution is understandable in a sudden death time control, but with the knight on b7 he could have pulled the trigger much sooner. 81.c5+ and 82.Kc4 wins easily (81…Kd5 82.Nc7+ Kc6 83.Nxa6).

81…Kd6 (1.02)

Fritz for some reason considers the position dead equal (0.00) after 81…Nd6. I don’t know why – I don’t see any threefold repetition, and after 82.Kd3 the evaluation reverts to 1.10.

82. Nd4 (0.00) Nc5 (.97)

Same weird 0.00 evaluation here after 82…Nd8. 83.Nf3, and it’s back to .83.

83. Nc2 (.90) Kc6 (1.13) 84. Nb4+ (1.13) Kd6 (1.13) 85. Nd3 (1.13) Nb7 (1.47) 86. Kb4 (.97) Kc6 (.96) 87. a3 (.93) Kd6 (1.04) 88. Nc1 (.96) Kc6 (1.18)

88…Nd8 89.a4 Nc6+ 90.Ka3 Ne7 is more stubborn.

89. Nb3 (1.16) Kd6 (1.64) 90. Kc3 (.97) Nd8 (1.04) 91. Na5 (.94) Kc5 (.94) 92. Kd3 (.94) Kd6 (.94) 93. Nb3 (.94) Kc6 (.97) 94. Kd4 (.94) Ne6+ (.94) 95. Kc3 (.94) Nd8 (.97) 96. Nd2 (.93) Kc5 (.96) 97. Ne4+ (.94) Kc6 (.94) 98.Ng5 (.92) Kc5 (.92) 99. Kd3 (.93) Nb7 (1.41)

99…Kb6 100.Kd4 Nc6+ forces the king back to c3 (101.Kd5 Ne7+ 102.Ke4 Kc5).

100. Ne4+ (1.28) Kc6 (1.18) 101. Kd4 (1.18) Kb6 (1.30) 102. Kc3 (.94)

102.Kd5 Na5 103.c5+ (or 103.Nc5 Nc6 104.Ne6 Ne7 105.Kd5 Nc8 106.Kd7 Na7 107.c5+ +-) Kc7 104.Ng5 Nc6 105.Ne6+ Kd7 106.Nd4 was more conclusive.

102…Kc6 (.97) 103. Kb4 (.97) Kb6 (.97) 104. Nd2 (.97) Nc5 (.97) 105. Nb3 (1.04) Nb7? (2.29)

The same mined square, and this time it’s the fatal, losing move. 105...Nd3+ 106.Kc3 Nf4 107.Kd4 Ne2+ 108.Kd3 Ng3 holds the king back, as in the note to move 71.

106. a4 (2.27 ) Kc6?? (7.46)

The game can no longer be held, even with best moves. Both 106…Kc7 107.c5 Kc6 108.Kc4 Kd7 109.Nd4 and 106…a5+ 107.Kc3 Kc6 108.Kd4 Kd6 109.c5+ Kc6 110.Kc4 lead to zugzwang.

107. Na5+ (White is winning ) Nxa5 108. Kxa5 Kc5 109. Kxa6 Kc6 110. a5 Kc7 111. Kb5 Kb7 112. c5 Kc7 113. c6 Kc8 114. Kc5 Kc7 115. Kd5 1-0

I could speculate further on this ending, but I’m afraid that I’d be talking out of my butt. Knights are slippery, unpredictable buggers that hit you sideways. With perfect moves I had good chances to hold, but with perfect moves from my opponent, the game could have dragged out to to move 200 and beyond.

No comments: