Konoval and I have now started on endgames with pawns. These will be of more
practical interest than the pawnless ones, although will likely contain no new
depth records. We think that the 517 moves to conversion in QNxRBN will
remain the deepest 7-man endgame.
A note about Yakov and my collaboration: Yakov develops all the generation
programs, with very little input from me. I supply the computer hardware,
data mining programs, and verification runs. The verification run checks the
self-consistency of the tablebase by performing a one ply search for each
position (both Black and White to move) and verifying that the score of the
best move is indeed what is stored in the table. This is a necessary and
sufficient condition for tablebase accuracy. Since the verification program
was developed independently of the generation program (I don't even have
the source code for the generation program) the likelihood of errors is pretty
small. The only common code is the ZLIB compression library.
The pawnful endgames considered so far are RRPxRR, QQPxQQ, and BBPxNN. The
results are pretty interesting, and further details are given below. BBPxNN
in particular has some notable features and appears to be amenable to human
understanding.
The algorithm employed is a simple extension of the one used for the pawnless
tablebases. This results in a DTC metric, the shortest distance to capture
or promotion. The DTZ metric would be more efficient (shortest distance to
capture or pawn move), but would require more substantial code changes. But
even with the simpler algorithm BBPxNN, which has a maximum DTC of 179 moves,
took only a little under two weeks on a 3.8 GHz machine, using about 750 MB
of RAM.
Another simplification we will apply to some endings is to ignore
underpromotions. This drastically reduces the number of tables that have to
be computed and will probably give accurate results for most positions of
interest. We are currently computing PPPPxR and QPPxRR this way. Eventually
one should of course compute all tables with underpromotions. Even then, the
simplified tables then provide an efficient way to mine for underpromotion
studies. We also have not yet added en passant capability, so we are only
computing tablebases with all the pawns on one side at the moment.
At first glance RRPxRR seems to contain no big surprises. Just as in RPxR the
defender can usually draw if his king can safely control the promotion square.
If the defending king is cut off, things can get very complicated. The
addition of another pair of rooks to RPxR helps the attacker a bit, but
apparently not enough to substantially reduce Black's chances for a draw. An
obvious starting point is the well known Vancura draw (Kc4,Ra8,Pa6/Kg7,Rf6).
Adding a white rook on c3, and a black rook on d2 results the longest win for
White from these types of positions:
R7/6k1/P4r2/8/2K5/2R5/3r4/8 w - - 0 1
[Event "Vancura plus wRc3, bRd2"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "RRP"]
[Black "RR"]
[Result "1-0"]
[SetUp "1"]
[FEN "R7/6k1/P4r2/8/2K5/2R5/3r4/8 w - - 0 1"]
[PlyCount "55"]
1. Rg3+ Kh7 (1... Kf7 2. Ra7+ Ke6 3. Rb7) 2. Rh3+ Kg7 3. Ra7+ Kg6 (3... Kg8 4.
Rb3 Rc6+ 5. Kb5 Rc1 6. Rb7 Ra1 7. a7 Rda2 8. Rd3 Ra5+ 9. Kb4 R5a4+ 10. Kc3
R4a3+ 11. Kd2 R3a2+ 12. Ke3 Re1+ 13. Kd4 Rea1 14. Rc3 Rd1+ 15. Kc5 Rda1 16. Kd6
Rd1+ 17. Kc7) 4. Rah7 Rf4+ (4... Rc2+ 5. Kb3 $1 Rff2 6. R7h4 Rb2+ (6... Ra2 7.
Rg3+ $1 Kf6 8. Rf3+ $1) 7. Ka4 $1 Rb8 (7... Ra2+ 8. Ra3) 8. a7 Ra8 9. Rh6+ Kf7
10. Ra6 Rb2 11. Rh7+ Kg8 12. Rc7 Rb1 13. Ka5) 5. Kc5 $1 Rb2 6. R3h6+ Kg5 7. Rc6
Ra4 8. Kd6 (8. a7 $2 Rc2+ $11) 8... Rba2 9. Ra7 Kf5 10. Kc7 Rh4 11. Rb7 Rha4
12. Rbb6 Ra1 13. Kb7 Ke4 14. Rh6 R4a2 15. Rh4+ Kf3 16. Rb3+ Kg2 17. Rh6 Rf2 18.
Rh7 Rfa2 19. Rg7+ Kf2 20. Rf7+ Ke2 21. Rb6 Kd3 22. Re7 Kd4 23. Rd6+ Kc5 24.
Red7 Rb2+ 25. Kc7 Rh2 26. Rc6+ Kb5 27. Rd5+ Kb4 28. Kb6 1-0
However, most positions of this type are drawn. For example, moving Black's
rook from f6 to e6 yields a draw:
R7/6k1/P3r3/8/2K5/2R5/3r4/8 w - - 0 1
[Event "Vancura plus wRc3, bRd2, but bRe6 instead of bRf6"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "RRP"]
[Black "RR"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "R7/6k1/P3r3/8/2K5/2R5/3r4/8 w - - 0 1"]
[PlyCount "10"]
1. Rg3+ Kf7 $1 2. Ra7+ Kf6 $1 3. Rag7 Rc2+ 4. Kb3 Ree2 $1 5. R7g4 Ra2 $1 {
With the Black King on g6, and the White Rooks on h3 and h4. White could now
win with 6.Rg3+ Kf6 7.Rf3+, but here the defending king is too close.}
1/2-1/2
As usual, a number of studies are busted by the database, although the busts
appear to be mostly tactical in nature and can usually be easily found
without the database. The following study by Mitrofanov is actually
rehabilitated, although by the RRNxRR rather than the RRPxRR database:
k7/1p6/7K/5rr1/1N5R/8/8/1R6 w - - 0 1
[Event "Problem#255"]
[Site "?"]
[Date "1971.??.??"]
[Round "?"]
[White "Mitrofanov, L."]
[Black "?"]
[Result "1-0"]
[SetUp "1"]
[FEN "k7/1p6/7K/5rr1/1N5R/8/8/1R6 w - - 0 1"]
[PlyCount "15"]
1. Nc6 bxc6 (1... b6 $1 {was thought to be a cook, but after} 2. Nd4 {
Black cannot avoid losing his pawn and ends up in a lost RRNxRR ending. Most
tenacious is} Re5 (2... Ra5 3. Rxb6 Rg8 4. Kh7 {wins in 144 moves}) 3. Rxb6 Rg8
4. Rf4 $1 {and White wins in 152 moves}) 2. Ra4+ Ra5 3. Rba1 Rh5+ 4. Kg6 Rhg5+
5. Kf6 Rgf5+ 6. Ke6 Rfe5+ 7. Kd6 Red5+ 8. Kc7 1-0
The maximal line is a loss in 135 moves by Black:
8/8/4r3/1r5R/2R4P/8/k1K5/8 b - - 0 1
[Event "Maximal loss in 135"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "RRP"]
[Black "RR"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/8/4r3/1r5R/2R4P/8/k1K5/8 b - - 0 1"]
[PlyCount "270"]
1... Rb2+ 2. Kd3 $1 Reb6 {by far the most tenacious defense. Other "natural"
moves like 2...Rb3+ or 2...Rbb6 shorten the win by more than 80 moves.} 3. Rhc5
$1 Kb3 4. Rc6 Rb7 5. Rc7 $1 Rb8 6. Rc8 $1 Rb7 7. Rc3+ Kb4 8. Rc1 $1 Ka5 9. Kd4
$1 R2b4+ 10. R8c4 $1 Rb3 11. R1c3 Rb1 12. Rc5+ Kb6 13. Rc6+ $1 Ka7 14. Ke5 $1
Rh1 15. R6c4 $1 Rb6 16. Rc1 Rh2 17. Kf5 Kb7 18. Rc7+ Kb8 19. Rc8+ $1 Kb7 20.
R1c7+ Ka6 21. Kg5 $1 Rg2+ 22. Kh5 Rd2 23. Ra8+ Kb5 24. Rc3 $1 Rb7 25. Kg5 $1
Rg2+ 26. Kh6 $1 Rh2 27. Rb3+ $1 Kc6 28. Ra6+ $1 Kc7 29. Rc3+ $1 Kd7 30. Rc4 $1
Rbb2 31. Rg4 $1 Rbg2 32. Rd4+ $1 Ke8 33. Re4+ Kf7 34. Rf4+ $1 Ke7 35. Ra7+ Kd6
36. h5 Rg8 37. Kh7 $1 Re8 38. Kg7 $1 Rg2+ 39. Kf7 $1 Rh8 40. Rf6+ $1 Ke5 41.
Ra5+ Ke4 42. Re6+ Kd4 43. Rg6 Rf2+ 44. Kg7 Rff8 45. Ra4+ Kc5 46. Ra7 Rfg8+ 47.
Kf6 $1 Rf8+ 48. Kg5 Rf2 49. Ra5+ Kb4 50. Re5 $1 Rg2+ 51. Kf6 $1 Rf2+ 52. Kg7
Rff8 53. Re1 Kc5 54. Rh1 Kd4 55. Ra6 Rfg8+ 56. Kf7 $1 Rf8+ 57. Kg6 Rhg8+ 58.
Kh6 Ke5 59. Re1+ Kd5 60. Re7 Rb8 61. Rf7 Kd4 62. Rf4+ Ke5 63. Rff6 Ke4 64. Ra5
Rg1 65. Rg6 Rc1 66. Ra4+ Ke3 67. Re6+ Kf3 68. Rf6+ $1 Ke3 69. Rh4 Rb5 70. Kh7
Rb7+ 71. Kg6 Rg1+ 72. Kh6 $1 Rb5 73. Rh3+ $1 Ke4 74. Rg6 Rf1 75. Rh4+ $1 Ke5
76. Ra4 Rf5 77. Rga6 $1 Rf8 78. Kg6 Rg8+ 79. Kh7 $1 Rgb8 80. Rg6 $1 R5b7+ 81.
Kh6 $1 Rb4 82. Ra1 Rb1 83. Ra5+ Kf4 84. Ra4+ Kf3 85. Rf6+ Ke3 86. Rh4 Rg1 87.
Rg6 Rd1 88. Re6+ Kf3 89. Rf6+ $1 Ke3 90. Rf7 Rb6+ 91. Kg5 $1 Rg1+ 92. Rg4 $1
Rh1 93. Rg3+ Ke2 94. Re7+ Kd2 95. Rd7+ Ke2 96. Rd5 Ra6 97. Rc5 Ra8 98. Kf6 $1
Rh8 99. Re5+ Kd2 100. Rg2+ Kd3 101. Rgg5 Rf1+ 102. Ref5 Rb1 103. Rb5 Rf1+ 104.
Kg6 Rc1 105. Rg3+ Ke4 106. Rb4+ $1 Ke5 107. Rg5+ $1 Ke6 108. Rb6+ Ke7 109. Rb7+
Ke6 110. h6 Rg8+ 111. Rg7 $1 Rf8 112. Rh5 Ra1 113. Rh3 Rf6+ 114. Kh7 Ra6 115.
Rh5 Rd6 116. Rh1 Ra6 117. Rd1 Ra3 118. Re1+ Kd6 119. Rh1 Ra4 120. Rg8 Ra7+ 121.
Kh8 Ke5 122. Re8+ Kd5 123. Rd1+ Kc4 124. Rc8+ $1 Kb3 125. Rh1 Re6 126. Rh4 Rf6
127. Rg8 Rf2 128. h7 Rc7 129. Rhg4 Rh2 130. R4g7 Rc6 131. Rb7+ Kc4 132. Kg7
Rg2+ 133. Kf7 Rf2+ 134. Ke7 Re2+ 135. Kd7 Ree6 136. h8=Q 1-0
QQPxQQ is usually a draw. The maximal winning line is 100 moves, and has the
interesting feature that the pawn never moves at all:
Q7/K7/8/4q3/1P4k1/8/Qq6/8 w - - 0 1"
[Event "Maximal win in 100"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "QQP"]
[Black "QQ"]
[Result "1-0"]
[SetUp "1"]
[FEN "Q7/K7/8/4q3/1P4k1/8/Qq6/8 w - - 0 1"]
[PlyCount "199"]
1. Qc8+ $1 Kh4 2. Qd8+ $1 Kh3 3. Qd3+ $1 Kg2 4. Qg6+ $1 Kf1 5. Qc4+ $1 Qbe2 6.
Qc1+ $1 Qe1 7. Qa6+ Kf2 8. Qb6+ Kf1 9. Qc4+ Q1e2 10. Qf7+ Kg2 11. Qc6+ Kh2 12.
Qh7+ Kg3 13. Qcg6+ Qg4 14. Qd3+ $1 Kg2 15. Qc2+ Qge2 16. Qhg6+ Kh3 17. Qc8+ Kh2
18. Qh7+ $1 Q2h5 19. Qcc2+ Kg3 20. Qg8+ Qhg5 21. Qd3+ $1 Kh4 22. Qgh7+ Qh5 23.
Qc4+ Kg3 24. Qhd3+ Qf3 25. Qg6+ Kh3 26. Qh7+ Qeh5 27. Qc8+ Kg3 28. Qhc7+ Kg2
29. Qc2+ Kh1 30. Qc1+ Kh2 31. Qd2+ Kg3 32. Qb8+ Kg4 33. Qd7+ Qhf5 34. Qg8+ Kh4
35. Qh8+ Kg3 36. Qc7+ Q3f4 37. Qhc3+ Kf2 38. Qb6+ Kg2 39. Qbc6+ Kh2 40. Qh8+ $1
Kg3 41. Qg8+ Q5g4 42. Qb3+ Kh2 43. Qbc2+ Kg1 44. Q6c5+ Kh1 45. Qb1+ Kh2 46.
Qcc2+ $1 Qg2 47. Qh7+ $1 Qh3 48. Qbc2+ Kg1 49. Qg8+ Kh1 50. Qd5+ Kg1 51. Qdd1+
Qff1 52. Qd4+ Kh1 53. Qc6+ Kh2 54. Qd2+ Kg1 55. Kb6 Qh4 56. Qg6+ Kh1 57. Qd5+
Kh2 58. Qgd6+ Kg1 59. Q6c5+ Kh2 60. Qc7+ Kg1 61. Qg7+ Kh2 62. Qge5+ Qg3 63.
Qh5+ Qgh3 64. Qde5+ Kh1 65. Qe4+ Kh2 66. Qhe5+ Kg1 67. Qg6+ Kh1 68. Qc6+ Kg1
69. Qg7+ Kh2 70. Qb2+ Kg1 71. Ka5 Qd1 72. Qg7+ Kh2 73. Qgc7+ Qg3 74. Qh7+ $1
Qh3 75. Qcc7+ Kg2 76. Qcg7+ $1 Kh2 77. Qe5+ Kg2 78. Qg6+ Kh1 79. Qee4+ Qdf3 80.
Qb1+ $1 Qff1 81. Qc6+ Kh2 82. Qbc2+ Kg1 83. Q2c5+ Kh2 84. Qe5+ Qg3 85. Qc2+ Kh1
86. Qce4+ Qgg2 87. Qh8+ Kg1 88. Qe3+ Qff2 89. Qc1+ Qff1 90. Qc5+ Qff2 91. Qa1+
Kh2 92. Qh5+ Qh3 93. Qae5+ Kg2 94. Qe4+ Kh2 95. Qhe5+ Kg1 96. Qc5 Qa3+ 97. Kb5
$1 Qa1 98. Qh4 Qaf1+ 99. Kb6 Q1g2 100. Qhxf2+ 1-0
There are 14 full point mutual Zugzwangs in this ending. Below is a simple
one (at least if the QPxQ database is handy) as it immediately reduces to a
5-man ending:
8/q4q2/8/3Q4/4P3/Q7/K1k5/8 w - - 0 1
[Event "Full-Point Mutual Zugzwang"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "QQP"]
[Black "QQ"]
[Result "*"]
[SetUp "1"]
[FEN "8/q4q2/8/3Q4/4P3/Q7/K1k5/8 w - - 0 1"]
[PlyCount "0"]
*
Below is more complicated example:
4Q3/8/2P5/Q1K5/8/1q6/1k5q/8 w - - 0 1
[Event "Full-Point Mutual Zugzwang"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "QQP"]
[Black "QQ"]
[Result "*"]
[SetUp "1"]
[FEN "4Q3/8/2P5/Q1K5/8/1q6/1k5q/8 w - - 0 1"]
[PlyCount "34"]
1. Qae1 (1. -- Qhc2+ 2. Kd6 Qcd3+ 3. Kc7 Qh7+ 4. Kc8 $1 Qhh3+ 5. Qd7 Qh8+ 6.
Qad8 Qh1 7. Qd2+ Kb1 8. Q8d3+ $18) 1... Qhc2+ $1 2. Kd6 Qa3+ $1 3. Kc7 Qh7+ 4.
Qd7 Qa7+ $1 5. Kc8 Qg8+ 6. Qde8 Qa8+ 7. Kd7 Qg7+ 8. Q8e7 Qd4+ $1 9. Kc7 Qda7+
10. Kd6 Q7b8+ 11. c7 Qa3+ 12. Ke6 Qh3+ 13. Kf7 Qh5+ 14. Kf6 Qbh8+ 15. Ke6 Qg8+
16. Kd7 Qb5+ 17. Kd6 Qbd5# *
BBPxNN has some interesting features. It appears as if it is usually a win
if White has a knight pawn, but a draw for other pawns. For example, the
position (Kb1,Bb2,Bc2,Pa2/Ka7,Nb7,Nc7) is drawn. If this position is shifted
one file to the right, White wins, while if it is shifted 2 or 3 columns to
the right it is a draw. Understanding the following position may shed some
light on this:
8/2k5/1n6/1n6/1P6/1K2BB2/8/8 w - - 0 1
[Event "Knight Pawn"]
[Site "?"]
[Date "2006.08.26"]
[Round "?"]
[White "BBP"]
[Black "NN"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/2k5/1n6/1n6/1P6/1K2BB2/8/8 w - - 0 1"]
[PlyCount "49"]
1. Bg1 {Strangely, this seems to be the only way to make progress. This also
wins if the Black knights are on b5 and d6. It looks like after other moves
White eventually has to play Bg1 anyway. The starting position shifted one
file to the right is drawn, apparently because White would need an i-file to
operate on.} Na7 2. Kc3 Nb5+ 3. Kd3 Na7 4. Ke4 Nb5 5. Ke5 Na4 (5... Nd6
6. Ke6 Ndc4 7. Bh2+ Kc8 8. Bh1 Nd7 9. Kd5 Ne3+ (9... Ncb6+ 10. Kc6 Nc4 11. Bd5
Nce5+ 12. Kd6 Ng4 13. Bf4 Ndf6 14. Bf3) (9... Na3 10. Bf3 Nb5 11. Bg2 Kd8 (
11... Nc3+ 12. Kc6 Nb8+ 13. Kd6 Nb5+ 14. Kc5 Nc3 15. b5 Na4+ 16. Kd6 Nb6 17.
Bg1 Nc4+ 18. Ke7 Kc7 19. Bh2+ Kc8 20. Bh3+) 12. Kc6 Nd4+ 13. Kb7) 10. Kc6 Nc2
11. Kb5 Na3+ 12. Ka5 Nc4+ 13. Ka6 Nb8+ 14. Ka7 Nd7 15. b5) 6. Kd5 Na3 7. Bh5
Kb7 8. Be8 Nc3+ 9. Kc5 Ne4+ 10. Kd4 Nd6 11. Bh5 Kc6 12. Bf3+ Kb5 13. Kc3 Ka6
14. Kb3 Nab5 15. Bg2 Na7 16. Ka4 Ndc8 17. Bf1+ Kb7 18. b5 Nb6+ 19. Kb4 Kc7 20.
Bh2+ Kd8 21. Ka5 Nac8 22. Ka6 Nd7 23. Kb7 Nc5+ 24. Kc6 Na4 25. Bc7+ 1-0
With a bishop pawn, Black's drawing chances increase, especially if the pawn
can be blocked before it reaches the 5-th rank:
8/2knn3/8/8/2PBB3/2K5/8/8 w - - 0 1
[Event "Bishop Pawn"]
[Site "?"]
[Date "2006.08.21"]
[Round "?"]
[White "BBP"]
[Black "NN"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/2knn3/8/8/2PBB3/2K5/8/8 w - - 0 1"]
[PlyCount "19"]
1. c5 ({Black to move can draw:} 1. -- Kd6 $1 2. Bf2 Nc5 $1 3. Bf3 Nc6 4. Bg3+
Kd7) 1... Nc6 2. Be3 Nde5 3. Bf4 Kd7 4. Kb3 Ke6 5. Ka4 Nd4 6. Ka5 Ndc6+ 7. Ka6
Nd3 8. Be3 Ndb4+ 9. Kb7 Na5+ 10. Kc8 1-0
With a center pawn, Black's drawing chances increase further:
8/3knn2/8/8/3PBB2/4K3/8/8 w - - 0 1
[Event "Queen Pawn"]
[Site "?"]
[Date "2006.08.21"]
[Round "?"]
[White "BBP"]
[Black "NN"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "8/3knn2/8/8/3PBB2/4K3/8/8 w - - 0 1"]
[PlyCount "10"]
1. d5 Nd6 2. Bf3 Nef5+ 3. Kd3 Ke7 4. Kc3 Nb7 {
Black needs to keep White's king from penetrating. Bad is} (4... Kd7 $2 5. Kb4
Kc7 6. Kc5 Kd7 7. Bg4 Ke7 8. Kc6 Nd4+ 9. Kc7 N4b5+ 10. Kb6 Nd4 11. Bh3 Ne4 12.
Bg2 Nd6 13. Bg5+ Kd7 14. Bf6 N4f5 15. Bh3 Ke8 16. Kc7 Kf7 (16... Nb5+ 17. Kc6
Nbd6 18. Bh8 Ke7 19. Bb2 Nc4 20. Bc3 Ng3 21. Bb4+) 17. Be5 Nc4 18. Bh2 Kf6 19.
Kc6 Na5+ 20. Kb6 Nc4+ 21. Kc5 Nd2 22. Bg2 Nb3+ 23. Kb4 Nbd4 24. d6 Ne6 25. Kb5
Nd8 26. Kb6 Ne3 27. Bh3 Nd5+ 28. Ka7 Nc6+ 29. Ka6 Kf7 30. d7) 5. Kb4 Nfd6 {
and the king is kept out.} 1/2-1/2
Against a rook pawn, Black can usually draw by blocking the pawn with a knight,
protected by the other knight. For example, knights on a6 and c7 if the
white pawn is on a5.
Finally, here is a maximal line:
8/K1n5/8/k3n3/8/1B4B1/6P1/8 b - - 0 1
[Event "Maximal loss in 179 moves"]
[Site "?"]
[Date "2006.08.27"]
[Round "?"]
[White "BBP"]
[Black "NN"]
[Result "1-0"]
[Annotator "bourzutschky,marc"]
[SetUp "1"]
[FEN "8/K1n5/8/k3n3/8/1B4B1/6P1/8 b - - 0 1"]
[PlyCount "356"]
1... Nb5+ 2. Kb7 $1 Kb4 3. Bg8 $1 Nd6+ 4. Kc7 $1 Nb5+ 5. Kb6 Nc4+ 6. Kc6 $1 Ne3
7. Be1+ $1 Nc3 8. g3 $1 Nc2 9. Bd2 $1 Nd4+ 10. Kd7 $1 Nf3 11. Bf4 $1 Ne4 12.
Ke7 $1 Kc3 13. Bf7 $1 Kd4 14. Bh5 $1 Ne5 15. Ke6 $1 Nc5+ 16. Kf5 $1 Nc6 17. Be2
$1 Ne7+ 18. Kg4 $1 Nd7 19. Bg5 $1 Ne5+ 20. Kh3 $1 Nf5 21. Ba6 $1 Nd3 22. Bd8 $1
Nc5 23. Bc8 $1 Ke5 24. Bc7+ $1 Ke4 25. Bb6 Ne7 26. Bg4 $1 Nd3 27. Ba7 $1 Nc6
28. Bg1 Nd4 29. Bc8 Nc5 30. Bf2 $1 Ke5 31. Be3 $1 Ke4 32. Bf4 Nc6 33. Bc7 Ne7
34. Bg4 $1 Nd3 35. Bd7 $1 Ne5 36. Ba4 Nd5 37. Bc2+ $1 Kd4 38. Bb8 $1 Nc6 39.
Bd6 $1 Ne5 40. Bb1 Nf3 41. Bb8 $1 Ke3 42. Bf5 $1 Nf6 43. Kg2 $1 Ke2 44. Bc8 $1
Ne1+ 45. Kh3 Nf3 46. Ba6+ Ke3 47. Kg2 $1 Ne1+ 48. Kf1 Nc2 49. Bf4+ Kf3 50. Be2+
$1 Ke4 51. Kf2 Nd4 52. Ba6 $1 Nd7 53. Bb7+ $1 Kd3 54. Bg2 Ne6 55. Bf1+ $1 Ke4
56. Bd6 Nd4 57. Bh3 Nf5 58. Ba3 $1 Ne5 59. Bg2+ $1 Kd3 60. Bb7 $1 Nc4 61. Bf8
$1 Nfd6 62. Ba6 $1 Ke4 63. Kg2 Kd4 64. Kh2 $1 Ke5 65. Kh3 $1 Kd5 66. Be7 $1 Ne4
67. Bb7+ $1 Kd4 68. Bd8 $1 Ke3 69. Ba8 Nf2+ 70. Kg2 $1 Ng4 71. Bb7 Kd4 72. Bc7
Nce5 73. Bb6+ Kd3 74. Kf1 Ne3+ 75. Kf2 N3g4+ 76. Ke1 Nc4 77. Ba6 Nge5 78. Kf2
Ke4 79. Bb7+ Kd3 80. Ba7 Ne3 81. Ba6+ Ke4 82. Ke2 N3c4 83. Bb7+ Kf5 84. Kf2 Nd6
85. Ba6 Ne8 86. Kg2 Nf6 87. Bb7 Nfd7 88. Bd4 Nf7 89. Kh3 Nfe5 90. Be3 Nf6 91.
Bc5 Ke6 92. Kh4 Nfd7 93. Bd4 Kf5 94. Bc3 Nf6 95. Ba5 Ke6 96. Bb6 Kf5 97. Bd8
Kg6 98. Kh3 Nfg4 99. Be7 Kh5 100. Bc5 Nc4 101. Bg1 Nce5 102. Bc8 Kg5 103. Bc5
Kh5 104. Bf5 Kg5 105. Be4 Nd7 106. Be7+ Ndf6 107. Bb7 Nf2+ 108. Kg2 N2g4 109.
Bc8 Ne5 110. Kh3 Nd3 111. Bd8 Ne5 112. Be6 Kg6 113. Bc7 Ne4 114. Kg2 Kf6 115.
Ba2 Ng5 116. Bd8+ Kf5 117. Bb1+ Kg4 118. Bc2 Nd7 119. Bc7 Ne6 120. Bd6 Nf6 121.
Bd3 Ng5 122. Bf4 Nf7 123. Bc4 Ng5 124. Ba6 Kf5 125. Bc8+ Kg6 126. Bc1 Nfe4 127.
g4 Kf7 128. Bb7 Kg6 129. Ba6 Kf6 130. Bb2+ $1 Ke6 131. Bc4+ Ke7 132. Bd3 Ke6
133. Kf1 Kd5 134. Ke2 Ne6 135. Kf3 N6g5+ 136. Ke3 Nc5 137. Bf5 Nce6 138. Bb1
Nf7 139. Ba2+ Kd6 140. Ke4 Ke7 141. Kf3 Ned8 142. Kg3 Ne6 143. Kh4 Neg5 144.
Bb3 Ne6 145. Bc3 Kd6 146. Bd2 Ke7 147. Kh5 Kf6 148. Bc3+ Ke7 149. Kg6 Nf8+ 150.
Kf5 Nh6+ 151. Kg5 Nf7+ 152. Kf4 Ne6+ 153. Kf5 Nd6+ 154. Kg6 Nf4+ 155. Kh7 Ne4
156. Ba1 Ne6 157. Kg6 Nf8+ 158. Kh5 Ne6 159. Be5 Kf7 160. Bd5 N4g5 161. Kh6 Nh3
162. Bg3 Kf6 163. Bc6 Ke7 164. Be4 Kf6 165. Bb1 Ke7 166. Ba2 Ng1 167. g5 Nf3
168. g6 $1 Nfd4 169. Bh4+ Kd6 170. Bf6 Nf5+ 171. Kh5 $1 Kd7 172. Bb3 Kd6 173.
Ba4 Ne7 174. g7 $1 Ng8 175. Bc3 Nf4+ 176. Kg4 Ne6 177. Bb3 Ke7 178. Kf5 Nh6+
179. Kg6 $1 1-0
-Marc