Hikaru completes trilogy with Leela

[lkaufman]

Having played a bullet chess match with LeelaQueenOdds (drawn) and a blitz chess match with LeelaKnightOdds (lost 14 to 2), Hikaru completed the trilogy today by playing a blitz (3'2") match with LeelaRookOdds. Despite taking White in eight of the fourteen games ("rook and move" odds), he lost by 9.5 to 4.5 (seven wins for Leela, two for Hikaru, five draws). Although this was noticeably better than his result at knight odds, Hikaru expected the larger handicap to make more of a difference, and was surprised to lose the match, especially by such a score. One factor was that the bot hardware was upgraded from 4090 to 5090 between the matches, but this was probably just a modest help. Although he claimed to be "on tilt" after many losses, both of his wins came near the end, so that cannot be responsible for the result. I don't believe anyone else has made an even or positive score at rook odds at 3'2" or faster against the current net, so it remains an open question as to whether anyone can surpass Hikaru's score under these conditions. The matches do seem to show that although rook odds is larger than knight odds, it is not so much larger as many might have thought.

[M ANSARI]

Yes, that was very interesting match and you could see Hikaru's frustration at the BOT not playing for the strongest moves when it comes to trading down pieces. The BOT is tuned to play the "trickiest" move rather than the "strongest" move in the position and will avoid trading down pieces unless it is absolutely necessary. This works really well against humans and probably not so well against other engines. The NN of Leela takes advantage of humans fallibility of consistently falling for a tactical trick eventually ... with Queen odds you have a lot of material advantage, so even losing a piece is not fatal ... but with only Rook odds ... you lose a piece and all of a sudden you are facing a 4000 ELO monster with only a small advantage ... no contest.

Here is the link for anyone interested

[towforce]

Yes, that was very interesting match and you could see Hikaru's frustration at the BOT not playing for the strongest moves when it comes to trading down pieces. The BOT is tuned to play the "trickiest" move rather than the "strongest" move in the position and will avoid trading down pieces unless it is absolutely necessary. This works really well against humans and probably not so well against other engines. The NN of Leela takes advantage of humans fallibility of consistently falling for a tactical trick eventually ... with Queen odds you have a lot of material advantage, so even losing a piece is not fatal ... but with only Rook odds ... you lose a piece and all of a sudden you are facing a 4000 ELO monster with only a small advantage ... no contest.

This!

Here is the link for anyone interested

Thank you. I'll take a look at that when time permits.

[lkaufman]

Yes, that was very interesting match and you could see Hikaru's frustration at the BOT not playing for the strongest moves when it comes to trading down pieces. The BOT is tuned to play the "trickiest" move rather than the "strongest" move in the position and will avoid trading down pieces unless it is absolutely necessary. This works really well against humans and probably not so well against other engines. The NN of Leela takes advantage of humans fallibility of consistently falling for a tactical trick eventually ... with Queen odds you have a lot of material advantage, so even losing a piece is not fatal ... but with only Rook odds ... you lose a piece and all of a sudden you are facing a 4000 ELO monster with only a small advantage ... no contest.

Here is the link for anyone interested

I disagree with "and probably not so well against other engines". Even against other engines, the best strategy is to avoid even exchanges if at all plausible. It's better to be down by a 9 to 8 ratio than by a 5 to 4 ratio, for example, regardless of who your opponent is. Our testing shows that at least against bots that are trained on human games, these odds bots are way better than any normal engine in odds play. Probably it is less so against traditional engines, but still clearly true. Against the human-simulating bots, there doesn't seem to be much difference between giving odds to a 2500 human or to a bot that is even (in standard chess) with that 2500 human.

[towforce]

I disagree with "and probably not so well against other engines". Even against other engines, the best strategy is to avoid even exchanges if at all plausible. It's better to be down by a 9 to 8 ratio than by a 5 to 4 ratio, for example, regardless of who your opponent is. Our testing shows that at least against bots that are trained on human games, these odds bots are way better than any normal engine in odds play. Probably it is less so against traditional engines, but still clearly true. Against the human-simulating bots, there doesn't seem to be much difference between giving odds to a 2500 human or to a bot that is even (in standard chess) with that 2500 human.

This is turning out to be an unexpectedly insightful thread!

If the key factor is not human susceptibility to "trickiness", then we have a new way to win games that might otherwise end in a draw.

If (and only if) you believe that your engine is stronger than your opponent's engine, then rework it as follows:

1. Evaluate all moves in the usual way

2. Pick the top moves which are roughly equal in eval

3. Evaluate these moves for complexity

3a. Keeps as many pieces on the board as possible

3b. Has as much engagement between opposite coloured pieces as possible

3c. Alternatively, train a separate NN to evaluate a position's complexity (this is 2025 - none of this hand-coding nonsense! )

4. Pick the move with the most complexity

5. The weaker engine will become confused and bewildered, it won't be able to see so far ahead in its game tree, it won't be able to make sense of the large number of interacting chess patterns, and hence will be much more likely to make a bad move

[Father]

[/pgn]

Having played a bullet chess match with LeelaQueenOdds (drawn) and a blitz chess match with LeelaKnightOdds (lost 14 to 2), Hikaru completed the trilogy today by playing a blitz (3'2") match with LeelaRookOdds. Despite taking White in eight of the fourteen games ("rook and move" odds), he lost by 9.5 to 4.5 (seven wins for Leela, two for Hikaru, five draws). Although this was noticeably better than his result at knight odds, Hikaru expected the larger handicap to make more of a difference, and was surprised to lose the match, especially by such a score. One factor was that the bot hardware was upgraded from 4090 to 5090 between the matches, but this was probably just a modest help. Although he claimed to be "on tilt" after many losses, both of his wins came near the end, so that cannot be responsible for the result. I don't believe anyone else has made an even or positive score at rook odds at 3'2" or faster against the current net, so it remains an open question as to whether anyone can surpass Hikaru's score under these conditions. The matches do seem to show that although rook odds is larger than knight odds, it is not so much larger as many might have thought.

Good evening, Mr. Larry Kaufman. Thank you very much for your teachings. I also have a deep gratitude to GM Hikaru Nakamura for teaching us all his combat against bots. I've seen that human super champions play to win. Perhaps I would believe they should play to win, but in the longer term, through long-term strategic maneuvers beyond the algorithm's blind spot. If I had the talent and skill of GM Hikaru Nakamura, I would believe I would give the computers a hard time. But I must be realistic and manage my own inner self. Today I played my first match against LeelaRookOdds and I tied. The time control was 3+2. I wonder... What would my final score be?

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/0xtmjVU3"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "0xtmjVU3"]
[UTCDate "2025.07.02"]
[UTCTime "00:27:20"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 Nf6 2. f4 c5 3. e3 e6 4. Nf3 h6 5. c3 g5 6. Bd3 g4 7. Nh4 b6 8. g3 Bb7 9. O-O Be7 10. Qe2 Nc6 11. Bd2 Qc7 12. Be1 Ba8 13. Nd2 Qb7 14. Ng2 h5 15. a3 O-O 16. Ba6 Qc7 17. Bd3 d5 18. Nh4 Bb7 19. b4 Re8 20. Bf2 c4 21. Bc2 a6 22. Rfc1 b5 23. Bd1 Bd8 24. Nf1 Ne4 25. Nd2 Nd6 26. Nf1 f5 27. Be1 Ne4 28. Nd2 Nd6 29. Nf1 Ne4 30. Nd2 Nd6 31. Nf1 { The game is a draw. } 1/2-1/2[/pgn]

[Father]

[/pgn]

Having played a bullet chess match with LeelaQueenOdds (drawn) and a blitz chess match with LeelaKnightOdds (lost 14 to 2), Hikaru completed the trilogy today by playing a blitz (3'2") match with LeelaRookOdds. Despite taking White in eight of the fourteen games ("rook and move" odds), he lost by 9.5 to 4.5 (seven wins for Leela, two for Hikaru, five draws). Although this was noticeably better than his result at knight odds, Hikaru expected the larger handicap to make more of a difference, and was surprised to lose the match, especially by such a score. One factor was that the bot hardware was upgraded from 4090 to 5090 between the matches, but this was probably just a modest help. Although he claimed to be "on tilt" after many losses, both of his wins came near the end, so that cannot be responsible for the result. I don't believe anyone else has made an even or positive score at rook odds at 3'2" or faster against the current net, so it remains an open question as to whether anyone can surpass Hikaru's score under these conditions. The matches do seem to show that although rook odds is larger than knight odds, it is not so much larger as many might have thought.

Good evening, Mr. Larry Kaufman. Thank you very much for your teachings. I also have a deep gratitude to GM Hikaru Nakamura for teaching us all his combat against bots. I've seen that human super champions play to win. Perhaps I would believe they should play to win, but in the longer term, through long-term strategic maneuvers beyond the algorithm's blind spot. If I had the talent and skill of GM Hikaru Nakamura, I would believe I would give the computers a hard time. But I must be realistic and manage my own inner self. Today I played my first match against LeelaRookOdds and I tied. The time control was 3+2. I wonder... What would my final score be?

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/0xtmjVU3"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "0xtmjVU3"]
[UTCDate "2025.07.02"]
[UTCTime "00:27:20"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 Nf6 2. f4 c5 3. e3 e6 4. Nf3 h6 5. c3 g5 6. Bd3 g4 7. Nh4 b6 8. g3 Bb7 9. O-O Be7 10. Qe2 Nc6 11. Bd2 Qc7 12. Be1 Ba8 13. Nd2 Qb7 14. Ng2 h5 15. a3 O-O 16. Ba6 Qc7 17. Bd3 d5 18. Nh4 Bb7 19. b4 Re8 20. Bf2 c4 21. Bc2 a6 22. Rfc1 b5 23. Bd1 Bd8 24. Nf1 Ne4 25. Nd2 Nd6 26. Nf1 f5 27. Be1 Ne4 28. Nd2 Nd6 29. Nf1 Ne4 30. Nd2 Nd6 31. Nf1 { The game is a draw. } 1/2-1/2[/pgn]

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/LzcC6Qch"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "LzcC6Qch"]
[UTCDate "2025.07.02"]
[UTCTime "02:34:15"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 d6 2. f4 f5 3. e3 e6 4. Nf3 h6 5. c3 g5 6. g3 g4 7. Nh4 Kf7 8. Bd3 d5 9. Kf1 h5 10. Bd2 Be7 11. Be1 b6 12. Rg1 c5 13. Qe2 Nf6 14. Rg2 Rg8 15. Kg1 Bb7 16. a3 Qd7 17. Nd2 Nc6 18. Ba6 Ba8 19. Bd3 c4 20. Bc2 b5 21. Nf1 a5 22. Bd1 Na7 23. Qc2 Bc6 24. Kh1 Nc8 25. Kg1 Nd6 26. Kh1 Nc8 27. Kg1 Nd6 28. Kh1 Qd8 29. Kg1 Bd7 30. Kh1 Bc6 31. Kg1 Nd7 32. Kh1 Ne4 33. Kg1 Qa8 34. Kh1 Qd8 35. Kg1 Qa8 36. Kh1 Nb6 37. Kg1 Qb7 38. Kh1 Qa8 39. Kg1 Qb7 40. Kh1 Nd7 41. Kg1 Nd6 42. Kh1 Ne4 43. Kg1 a4 44. Kh1 Ke8 45. Qe2 Kd8 46. Rc1 Kc7 47. Rc2 Qb8 48. Kg1 Kb6 49. Kh1 Ka6 50. Rc1 Kb6 51. Qc2 Ndf6 52. Kg1 Ne8 53. Kh1 N8d6 54. Kg1 Nb7 55. Kh1 Na5 56. Kg1 Nb3 57. Rb1 Nd6 58. Kh1 Ne4 59. Kg1 Nd6 60. Kh1 Bd7 61. Kg1 Na5 62. Kh1 Nc6 63. Rc1 Ne4 64. Kg1 Na5 65. Kh1 Nc6 66. Kg1 Na5 67. Kh1 Nb3 68. Rb1 Na5 69. Kg1 Nb3 70. Kh1 Kb7 71. Kg1 Nd6 72. Kh1 Na5 73. Rc1 Nb3 74. Rb1 Ka6 75. Kg1 Ne4 76. Kh1 Na5 77. Rc1 Nb3 78. Rb1 Nf6 79. Kg1 Na5 80. Rc1 Nc6 81. Kh1 Ne4 82. Kg1 Na5 83. Kh1 Nf6 84. Kg1 Ne4 85. Kh1 { The game is a draw. } 1/2-1/2[/pgn]

[Father]

[/pgn]

Having played a bullet chess match with LeelaQueenOdds (drawn) and a blitz chess match with LeelaKnightOdds (lost 14 to 2), Hikaru completed the trilogy today by playing a blitz (3'2") match with LeelaRookOdds. Despite taking White in eight of the fourteen games ("rook and move" odds), he lost by 9.5 to 4.5 (seven wins for Leela, two for Hikaru, five draws). Although this was noticeably better than his result at knight odds, Hikaru expected the larger handicap to make more of a difference, and was surprised to lose the match, especially by such a score. One factor was that the bot hardware was upgraded from 4090 to 5090 between the matches, but this was probably just a modest help. Although he claimed to be "on tilt" after many losses, both of his wins came near the end, so that cannot be responsible for the result. I don't believe anyone else has made an even or positive score at rook odds at 3'2" or faster against the current net, so it remains an open question as to whether anyone can surpass Hikaru's score under these conditions. The matches do seem to show that although rook odds is larger than knight odds, it is not so much larger as many might have thought.

Good evening, Mr. Larry Kaufman. Thank you very much for your teachings. I also have a deep gratitude to GM Hikaru Nakamura for teaching us all his combat against bots. I've seen that human super champions play to win. Perhaps I would believe they should play to win, but in the longer term, through long-term strategic maneuvers beyond the algorithm's blind spot. If I had the talent and skill of GM Hikaru Nakamura, I would believe I would give the computers a hard time. But I must be realistic and manage my own inner self. Today I played my first match against LeelaRookOdds and I tied. The time control was 3+2. I wonder... What would my final score be?

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/0xtmjVU3"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "0xtmjVU3"]
[UTCDate "2025.07.02"]
[UTCTime "00:27:20"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 Nf6 2. f4 c5 3. e3 e6 4. Nf3 h6 5. c3 g5 6. Bd3 g4 7. Nh4 b6 8. g3 Bb7 9. O-O Be7 10. Qe2 Nc6 11. Bd2 Qc7 12. Be1 Ba8 13. Nd2 Qb7 14. Ng2 h5 15. a3 O-O 16. Ba6 Qc7 17. Bd3 d5 18. Nh4 Bb7 19. b4 Re8 20. Bf2 c4 21. Bc2 a6 22. Rfc1 b5 23. Bd1 Bd8 24. Nf1 Ne4 25. Nd2 Nd6 26. Nf1 f5 27. Be1 Ne4 28. Nd2 Nd6 29. Nf1 Ne4 30. Nd2 Nd6 31. Nf1 { The game is a draw. } 1/2-1/2[/pgn]

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/LzcC6Qch"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "LzcC6Qch"]
[UTCDate "2025.07.02"]
[UTCTime "02:34:15"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 d6 2. f4 f5 3. e3 e6 4. Nf3 h6 5. c3 g5 6. g3 g4 7. Nh4 Kf7 8. Bd3 d5 9. Kf1 h5 10. Bd2 Be7 11. Be1 b6 12. Rg1 c5 13. Qe2 Nf6 14. Rg2 Rg8 15. Kg1 Bb7 16. a3 Qd7 17. Nd2 Nc6 18. Ba6 Ba8 19. Bd3 c4 20. Bc2 b5 21. Nf1 a5 22. Bd1 Na7 23. Qc2 Bc6 24. Kh1 Nc8 25. Kg1 Nd6 26. Kh1 Nc8 27. Kg1 Nd6 28. Kh1 Qd8 29. Kg1 Bd7 30. Kh1 Bc6 31. Kg1 Nd7 32. Kh1 Ne4 33. Kg1 Qa8 34. Kh1 Qd8 35. Kg1 Qa8 36. Kh1 Nb6 37. Kg1 Qb7 38. Kh1 Qa8 39. Kg1 Qb7 40. Kh1 Nd7 41. Kg1 Nd6 42. Kh1 Ne4 43. Kg1 a4 44. Kh1 Ke8 45. Qe2 Kd8 46. Rc1 Kc7 47. Rc2 Qb8 48. Kg1 Kb6 49. Kh1 Ka6 50. Rc1 Kb6 51. Qc2 Ndf6 52. Kg1 Ne8 53. Kh1 N8d6 54. Kg1 Nb7 55. Kh1 Na5 56. Kg1 Nb3 57. Rb1 Nd6 58. Kh1 Ne4 59. Kg1 Nd6 60. Kh1 Bd7 61. Kg1 Na5 62. Kh1 Nc6 63. Rc1 Ne4 64. Kg1 Na5 65. Kh1 Nc6 66. Kg1 Na5 67. Kh1 Nb3 68. Rb1 Na5 69. Kg1 Nb3 70. Kh1 Kb7 71. Kg1 Nd6 72. Kh1 Na5 73. Rc1 Nb3 74. Rb1 Ka6 75. Kg1 Ne4 76. Kh1 Na5 77. Rc1 Nb3 78. Rb1 Nf6 79. Kg1 Na5 80. Rc1 Nc6 81. Kh1 Ne4 82. Kg1 Na5 83. Kh1 Nf6 84. Kg1 Ne4 85. Kh1 { The game is a draw. } 1/2-1/2[/pgn]

Good evening, Mr. Larry Kaufman. I'm afraid I won't be able to catch GM Hikaru Nakamura in this short march.

[pgn] [Event "casual blitz game"]
[Site "https://lichess.org/creeqcTK"]
[Date "2025.07.02"]
[White "Catecan"]
[Black "LeelaRookOdds"]
[Result "1/2-1/2"]
[GameId "creeqcTK"]
[UTCDate "2025.07.02"]
[UTCTime "03:41:16"]
[WhiteElo "2082"]
[BlackElo "2000"]
[BlackTitle "BOT"]
[Variant "From Position"]
[TimeControl "180+2"]
[ECO "?"]
[Opening "?"]
[Termination "Normal"]
[FEN "1nbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQk - 0 1"]
[SetUp "1"]
[Annotator "lichess.org"]

1. d4 g6 2. f4 d5 3. Nf3 Bg7 4. e3 c5 5. c3 Qc7 6. Bd3 Nh6 7. Qe2 O-O 8. O-O Ng4 9. Re1 Rd8 10. a3 b6 11. Nbd2 Nd7 12. Ba6 Bxa6 13. Qxa6 c4 14. Qa4 Rc8 15. Qc2 Bh6 16. Nf1 f5 17. Re2 Ngf6 18. g3 Ne4 19. Rg2 Ndf6 20. Bd2 g5 21. Be1 g4 22. Nh4 e6 23. Kh1 Bf8 24. Kg1 Kf7 25. Kh1 Be7 26. Kg1 h5 27. Kh1 Rg8 28. Kg1 Nd6 29. Kh1 Rb8 30. Kg1 Qb7 31. Kh1 a5 32. Kg1 b5 33. Kh1 Qa6 34. Kg1 Rg8 35. Kh1 Nd7 36. Kg1 Nb6 37. Kh1 Nd7 38. Kg1 Nb6 39. Kh1 Qa8 40. Kg1 Bd8 41. Kh1 Be7 42. Kg1 Ke8 43. Kh1 Rg7 44. Kg1 Kf7 45. Kh1 Qc8 46. Kg1 Na4 47. Kh1 Qa8 48. Kg1 Qc8 49. Kh1 Qa8 50. Kg1 Bf6 51. Kh1 Bd8 52. Kg1 Be7 53. Kh1 Bf6 54. Kg1 Qe8 55. Kh1 Qa8 56. Kg1 Qb7 57. Kh1 Be7 58. Kg1 Nb6 59. Kh1 Qa8 60. Kg1 Ke8 61. Kh1 Kf7 62. Kg1 Qg8 63. Kh1 Bf6 64. Kg1 Qe8 65. Kh1 Qg8 66. Kg1 Qe8 67. Kh1 a4 68. Kg1 Nd7 69. Qe2 Qg8 70. Rc1 Ke8 71. Rc2 Kd8 72. Kh1 Ke8 73. Kg1 Nf8 74. Kh1 Bd8 75. Kg1 Rh7 76. Kh1 Bf6 77. Kg1 Be7 78. Kh1 Rg7 79. Kg1 Qh7 80. Kh1 Bf6 81. Kg1 Nd7 82. Kh1 Nb8 83. Kg1 Nc6 84. Kh1 Ne7 85. Kg1 Nc6 86. Kh1 Qg8 87. Kg1 Be7 88. Kh1 Bf6 89. Kg1 Be7 90. Kh1 Kd7 91. Kg1 Ne4 92. Kh1 Nf6 93. Kg1 Ke8 94. Kh1 Nd7 95. Kg1 Bf6 96. Kh1 Kf8 97. Kg1 Na5 98. Kh1 Ke7 99. Kg1 Nb3 100. Kh1 Kf8 101. Kg1 Na5 102. Kh1 Ke7 103. Kg1 Nb3 104. Kh1 Bxh4 105. gxh4 Nf6 106. Bg3 Na1 107. Rc1 Nb3 108. Rc2 Kd7 109. Qe1 Ne4 110. Kg1 Nd6 111. Kh1 Ne4 112. Kg1 Kd6 113. Kh1 Kc7 114. Kg1 Kd6 115. Kh1 Ke7 116. Kg1 Kd7 117. Kh1 Ke8 118. Kg1 Ke7 119. Kh1 Kd8 120. Nd2 Nf6 121. Nf1 Kc8 122. Kg1 Kd7 123. Kh1 Kc7 124. Kg1 Kd7 125. Kh1 { The game is a draw. } 1/2-1/2[/pgn]