Two Knight Draw...

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Steve Maughan
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Two Knight Draw...

Post by Steve Maughan »

Here's an interesting position which cropped up in CCRL Division 5.

[d]8/4b3/3Np3/8/p1N2k2/P2K4/8/8 b - -

It's black to play. White is a piece up but if black can capture the pawn on a3 it's a draw. None of the top engines seem to understand this.
http://www.chessprogramming.net - Juggernaut & Maverick Chess Engine
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hgm
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Full name: H G Muller

Re: Two Knight Draw...

Post by hgm »

Fruit knows it's a draw:

Code: Select all

 20	 -0.35 	83.4M  	0:32.80	e5 Ne4 Kf5 Ne3+ Ke6 Nc2 Bxa3 Nxa3 Kd5 Nc2 Ke6 Nc3 e4+ Ke3 Ke5 Nxa4 Kd5 Nd4 Kc4 Nb6+ Kc5 Nd7+ Kd6 Nf6 Kc5
 19	 -0.35 	64.3M  	0:25.39	e5 Ne4 Kf5 Ne3+ Ke6 Nc2 Bxa3 Nxa3 Kd5 Nc2 Ke6 Nc3 e4+ Ke3 Ke5 Nxa4 Kd5 Nd4 Kc4 Nb6+ Kc5 Nd7+ Kd6 Nf6
 18	 -0.34 	28.1M  	0:11.50	e5 Ne4 Kf5 Nc3 Bc5 Ne3+ Ke6 Nc2 Bxa3 Nxa3 e4+ Kxe4 Kf6 Nd5+ Ke6 Nf4+ Kf6 Nd3 Ke6 Ne5 Kd6 Nac4+ Kc5 Kd3
 17	 -0.34 	20.6M  	0:08.53	e5 Ne4 Kf5 Nc3 Bc5 Ne3+ Ke6 Nc2 Bxa3 Nxa3 e4+ Kxe4 Kf6 Nd5+ Kg5 Nf4 Kg4 Ne6 Kh5 Kf5 Kh6
 16	 -0.33 	11.7M  	0:04.91	e5 Kd2 Kg5 Nxe5 Kf6 Nec4 Ke6 Ne4 Kd5 Kd3 Bxa3 Nxa3 Kc6 Kd4 Kd7 Kd5 Ke7
 15	 -0.33 	3.74M  	0:01.62	e5 Kd2 e4 Ke1 Kg5 Ke2 Kf6 Nxe4+ Ke6 Kd3 Bxa3 Nxa3 Kd5 Ke3 Ke6 Kd4 Ke7
 14	 -0.33 	2.10M  	0:00.94	e5 Kd2 e4 Ke1 Kg5 Ke2 Kf6 Nxe4+ Ke6 Kd3 Bxa3 Nxa3 Kd5 Ke3 Ke5 Nb5
 13	 -0.33 	1.19M  	0:00.56	e5 Kd2 e4 Ke1 Kg5 Ke2 Kf6 Nxe4+ Kf5 Kd3 Bxa3 Nxa3 Kf4 Nd6 Kf3
 12	 -0.43 	375722	0:00.19	e5 Kd2 e4 Ke1 Bf6 Ke2 Bd4 Nb7 Kg4 Ne3+ Kf4 Nd5+ Ke5 Ne3
 11	 -0.41 	220493	0:00.12	e5 Kd2 e4 Ke1 Bf6 Ke2 Bd4 Nb7 Kg5 Nd8 Kf5 Ne3+ Kf4
 10	 -0.43 	115147	0:00.08	e5 Kd2 e4 Ke1 Kf3 Kf1 Bg5 Nf7 Bf6 Nfe5+ Kf4
  9	 -0.50 	31266  	0:00.03	e5 Kd2 e4 Ke2 e3 Kd3 Kf3 Ne5+ Kf2 Ne4+ Ke1
  8	 -0.50 	18311  	0:00.02	e5 Kd2 e4 Ke2 e3 Kd3 Kf3 Ne5+ Kf2 Ne4+ Ke1
  7	 -0.50 	6958    	0:00.02	e5 Ke2 e4 Kd2 Bf6 Ne3 Bd4
  6	 -0.51 	3810    	0:00.02	e5 Ke2 e4 Kd2 Bf6 Ne3
  5	 -0.49 	2030    	0:00.02	e5 Kd2 e4 Ke2 Bf6
  4	 -0.55 	981      	0:00.00	e5 Kd2 e4 Ke2
  3	 -0.55 	494      	0:00.00	e5 Ke2 e4
  2	 -0.62 	123      	0:00.00	e5 Ne4
  2	 -0.63 	65        	0:00.00	Bf6 Ne3
  1	 -0.60 	41        	0:00.00	Bf6
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tpoppins
Posts: 919
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Location: upstate

Re: Two Knight Draw...

Post by tpoppins »

Steve Maughan wrote:White is a piece up but if black can capture the pawn on a3 it's a draw. None of the top engines seem to understand this.
What are the top engines in your neck of woods? ;) Latest SF devbuild sees the draw in one second.

Code: Select all

Analysis by Stockfish 310316 64 POPCNT:

1...e5 2.Ne4 Bf8 3.Nc3 Bc5 4.Kd2 e4 
  +/-  (1.36)   Depth: 7/7   00:00:00  13kN, tb=74
1...e5 2.Ne4 Kf5 3.Ncd6+ Ke6 4.Nb5 Kd5 5.Nec3+ Kc6 6.Ke4 
  +/-  (1.37)   Depth: 8/10   00:00:00  30kN, tb=248
[...]
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Kd4 Bg7+ 5.Kc4 Bf8 6.Kd3 Ke5 7.Nc4+ Kf4 8.Ned6 Be7 9.Kd4 Bf8 10.Kc3 e5 11.Kd3 e4+ 12.Kc2 Be7 
  +/-  (0.71)   Depth: 17/32   00:00:00  1625kN, tb=19256
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Kd4 Bg7+ 5.Kc4 Bf8 6.Kd3 Ke5 7.Nc4+ Kf4 8.Ned6 Be7 9.Kc3 e5 10.Kc2 e4 11.Kd1 Bf8 12.Nb5 Be7 13.Ncd6 Ke5 
  +/=  (0.58)   Depth: 18/32   00:00:00  2025kN, tb=24402
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Nb5 Ke5 5.Ng5 Kf5 6.Nf7 Kf4 7.Nbd6 e5 8.Kc2 Be7 9.Kc3 Bf8 10.Kc4 e4 11.Kc3 Bg7+ 12.Kb4 Bf8 
  +/=  (0.46)   Depth: 19/32   00:00:00  2639kN, tb=31432
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Nb5 Ke5 5.Ng5 Be7 6.Nf7+ Kf4 7.Nfd6 Ke5 8.Nc4+ Kf4 9.Nc3 Bc5 10.Ne2+ Kg5 11.Nd2 Bxa3 12.Kc4 Kf5 13.Nb1 Bb2 
  =  (0.03)   Depth: 20/37   00:00:01  8691kN, tb=145857
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Nb5 Ke5 5.Ng5 Be7 6.Nf7+ Kf4 7.Nfd6 Ke5 8.Nc4+ Kf4 9.Nc3 Bc5 10.Ne2+ Kg5 11.Ke4 Bxa3 12.Nxa3 
  =  (0.00)   Depth: 21/37   00:00:01  10559kN, tb=193516
[...]
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Kd4 Bg7+ 5.Kc4 Bf8 6.Kd3 Ke5 7.Nb5 Be7 8.Nf2 Bc5 9.Nh3 Kf6 10.Kc4 Bxa3 11.Nxa3 
  =  (0.00)   Depth: 75/43   00:01:24  1505MN, tb=24289373
Komodo 9.2 also finds it within seconds, and there's also Komodo 9.42 analysis on Let's Check with same three first plies of the PV above, d=65, eval=0.02. Of the top three engines Houdini 4 Pro took the longest to reach the "=" eval:

Code: Select all

Analysis by Houdini 4 Pro x64 B:

1...e5 2.Ne4 Bxa3 3.Nxa3 Kf5 4.Nc4 Ke6 5.Kc3 
  +/=  (0.65)   Depth: 7/15   00:00:01  3kN
1...e5 2.Ne4 Bxa3 3.Nxa3 Kf5 4.Nc4 Ke6 5.Kc3 a3 6.Nxa3 Kd5 7.Nf6+ Kc5 
  +/=  (0.61)   Depth: 8/16   00:00:01  5kN, tb=1
[...]
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kf4 4.Kd4 Bg7+ 5.Kc4 Bf8 6.Kd3 Ke5 7.Nb5 Kf4 8.Nec3 Be7 9.Ne2+ Ke5 10.Ng3 Kf4 11.Ne4 Bf8 12.Nec3 
  +/=  (0.32)   Depth: 29/60   00:00:46  811MN, tb=3373173
[...]
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kg4 4.Kc4 Kf4 5.Kd4 Bg7+ 6.Kd3 Bf8 7.Nb5 Ke5 8.Ng5 Be7 9.Nf7+ Kf4 10.Nfd6 Bf8 11.Kd2 e5 12.Ke2 e4 13.Kd2 Be7 14.Kd1 Bf6 15.Nc4 Kf3 16.Nd2+ Ke3 17.Nd6 Kd3 18.N2xe4 Bb2 19.Nc5+ Kd4 20.Nxa4 Bxa3 21.Nf7 Kd3 22.Ne5+ Kd4 23.Ng6 Kd3 24.Nb6 Bb2 25.Nf4+ Ke4 26.Nbd5 Be5 
  =  (0.10)   Depth: 30/62   00:01:39  1750MN, tb=8072694
1...Bf8 
  =  (0.05 ++)   Depth: 31/62   00:02:08  2271MN, tb=10855495
1...Bf8 2.Ne4 
  =  (0.16 --)   Depth: 31/62   00:02:13  2378MN, tb=11192922
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kg4 4.Nb5 Kf4 5.Nec3 Be7 6.Ne2+ Kf5 7.Nec3 Kf4 8.Ne2+ 
  =  (0.00)   Depth: 31/62   00:02:38  2809MN, tb=14388602
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kg4 4.Nb5 Kf4 5.Nec3 Be7 6.Ne2+ Kf5 7.Nec3 Kf4 8.Ne2+ 
  =  (0.00)   Depth: 32/62   00:02:55  3096MN, tb=17622937
1...Bf8 2.Ne4 Kf3 3.Ncd6 Kg4 4.Nb5 Kf4 5.Nec3 Be7 6.Ne2+ Kf5 7.Nec3 Kf4 8.Ne2+ 
  =  (0.00)   Depth: 33/62   00:03:10  3348MN, tb=20842590
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BeyondCritics
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Full name: Oliver Roese

Re: Two Knight Draw...

Post by BeyondCritics »

It is not a simple draw. For example this constructed position would be a mate in 52 (Lomonosov):
[d]8/8/3Np3/8/p4k2/N2K4/8/8 b - - 0 1

Generally, if black has only one pawn, which is firmly blocked on or above the "Trotzky Line", it is a sure win, see "https://en.wikipedia.org/wiki/Two_knights_endgame".

I have analyzed the position at home with stockfish without table bases and even after a long time, it shows +4.65 or so. Table base access seems to do a decisive different in analysis quality in this position.
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yurikvelo
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Re: Two Knight Draw...

Post by yurikvelo »

What are the top engines in your neck of woods? ;) Latest SF devbuild sees the draw in one second.
More precise assertion: only Syzygy-6 probing allow engines to recognize it as draw.

Without 6-man Komodo 9.3 eval goes up to +1.57@D=24 and slowly goes down to 0.87 and is stable from D=30+

Without 6-man SF-Dev goes up to +2.09@D=14, 2.53@D=34, 3.84@D=36, 4.75@D=40 and is stable from D=40+

This overvalued score may had pruned really winning lines, earlier in game.
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hgm
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Re: Two Knight Draw...

Post by hgm »

Not true. Fruit doesn't use tablebases of any kind. And it smells the draw from ply 1 on.
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BeyondCritics
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Full name: Oliver Roese

Re: Two Knight Draw...

Post by BeyondCritics »

This position occurs in the main line of fruit after 4...Bxa3(!?) 5.Nxa3 Kd5.
[d] 8/8/8/3kp3/p3N3/N2K4/8/8 w - - 1 6
It is mate in 41, using table bases.
Furthermore it is not obvious what anyone would led to believe, this is a draw, since both black pawns are blocked on or even above the "Trotzky Line".
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yurikvelo
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Re: Two Knight Draw...

Post by yurikvelo »

hgm wrote:Not true. Fruit doesn't use tablebases of any kind. And it smells the draw from ply 1 on.
Fruit is not top engines.
Fruit eval favours black, and his "draw" score (starting from line, when eval drops to -0.33) is actually white win
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whereagles
Posts: 565
Joined: Thu Nov 13, 2014 12:03 pm

Re: Two Knight Draw...

Post by whereagles »

I plugged this into SF7 with 5-men syzygy and after 1 hour (two threads at 2.67 GHz) and 250 million TB hits, it still yield +0.09.

Not obvious, even for the mighty fish.
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Ralf Müller
Posts: 127
Joined: Sat Dec 29, 2012 12:07 am

Re: Two Knight Draw...

Post by Ralf Müller »

Cheng 4.39 recognizes is quickly as a draw:

Code: Select all

Neue Partie
8/4b3/3Np3/8/p1N2k2/P2K4/8/8 b - - 0 1

Analysis by Cheng 4.39:

1...e5 2.Se4 
  +-  (2.07)   Tiefe: 2/4   00:00:00
1...e5 
  +-  (1.63)   Tiefe: 3/6   00:00:00
1...e5 
  +-  (1.63)   Tiefe: 3/6   00:00:00
1...e5 2.Kc3 e4 
  +-  (1.63)   Tiefe: 3/6   00:00:00
1...e5 2.Kc3 e4 
  +-  (1.63)   Tiefe: 4/6   00:00:00
1...e5 2.Kc3 e4 3.Kd4 Lf6+ 4.Kd5 
  +-  (1.59)   Tiefe: 4/6   00:00:00
1...e5 2.Kc3 e4 3.Kd4 Lf6+ 4.Kd5 
  +-  (1.59)   Tiefe: 5/7   00:00:00
1...e5 2.Kc3 e4 3.Kb4 Lxd6+ 4.Sxd6 
  +-  (1.60)   Tiefe: 5/7   00:00:00
1...e5 2.Kc3 e4 3.Kb4 Lxd6+ 4.Sxd6 
  +-  (1.60)   Tiefe: 5/7   00:00:00
1...e5 2.Kc3 e4 3.Kb4 Lxd6+ 4.Sxd6 
  +-  (1.60)   Tiefe: 5/7   00:00:00
1...e5 
  +-  (1.77)   Tiefe: 6/9   00:00:00
1...e5 
  +-  (1.77)   Tiefe: 6/9   00:00:00
1...e5 2.Kc3 e4 3.Kb4 Lxd6+ 4.Sxd6 Ke5 
  +-  (1.82)   Tiefe: 6/12   00:00:00  1kN
1...e5 
  +-  (1.49)   Tiefe: 7/14   00:00:00  1kN
1...e5 
  +-  (1.49)   Tiefe: 7/14   00:00:00  1kN
1...e5 
  +-  (1.49)   Tiefe: 7/14   00:00:00  1kN
1...e5 2.Kc3 e4 3.Kd2 Lf6 4.Se3 Ld4 
  ±  (1.36)   Tiefe: 7/14   00:00:00  2kN
1...e5 2.Kc3 e4 3.Kd2 Lf6 4.Se3 Ld4 5.Sdf5 
  ±  (1.37)   Tiefe: 8/14   00:00:00  3kN
1...e5 2.Kc3 e4 3.Kd2 Lf6 4.Se3 Kf3 5.Sf7 Kg3 
  ±  (1.27)   Tiefe: 9/14   00:00:00  6kN
1...e5 
  ±  (1.12)   Tiefe: 10/18   00:00:00  15kN
1...e5 2.Kc3 e4 3.Kd2 Kf3 4.Se5+ Kg2 5.Sef7 Kf3 6.Kc3 Lf6+ 7.Kc4 
  ±  (1.11)   Tiefe: 10/18   00:00:00  18kN
1...e5 2.Ke2 e4 3.Kd1 Lf6 4.Kc2 Le7 5.Kc3 e3 6.Kd3 Kf3 7.Se5+ Kg2 
  ±  (1.23)   Tiefe: 11/19   00:00:00  40kN
1...e5 
  ±  (1.08)   Tiefe: 12/20   00:00:00  58kN
1...e5 2.Ke2 e4 3.Kf2 Lh4+ 4.Kf1 Lf6 5.Ke1 Lh4+ 6.Kd1 Lf6 7.Kc2 Le7 8.Kc3 e3 
  ±  (1.17)   Tiefe: 12/20   00:00:00  66kN
1...e5 
  ±  (1.02)   Tiefe: 13/21   00:00:00  99kN
1...e5 
  ±  (0.87)   Tiefe: 13/21   00:00:00  124kN
1...e5 2.Ke2 e4 3.Kf2 e3+ 4.Ke2 Lf8 5.Kf1 Kf3 6.Se5+ Kg3 7.Sef7 Lxd6 8.Sxd6 Kf3 
  ±  (0.80)   Tiefe: 13/21   00:00:00  142kN
1...e5 2.Ke2 e4 3.Kf2 e3+ 4.Ke2 Lf8 5.Kf1 Kf3 6.Se5+ Kg3 7.Sef7 Lxd6 8.Sxd6 Kf3 9.Kg1 
  ±  (0.71)   Tiefe: 14/22   00:00:00  198kN
1...e5 2.Ke2 e4 3.Kf2 e3+ 4.Ke2 Lf8 5.Kf1 Kf3 6.Se5+ Kg3 7.Sef7 Lxd6 8.Sxd6 Kf3 9.Ke1 e2 10.Sf5 
  ²  (0.65)   Tiefe: 15/23   00:00:00  304kN
1...e5 2.Ke2 e4 3.Kf1 Lf8 4.Kf2 Le7 5.Ke1 Lf8 6.Kd2 Le7 7.Ke2 e3 8.Kd3 Lf8 9.Se4 e2 
  ±  (0.72)   Tiefe: 16/24   00:00:00  556kN
1...e5 
  ²  (0.57)   Tiefe: 17/27   00:00:00  764kN
1...e5 2.Ke2 e4 3.Kf1 Lf8 4.Kf2 Le7 5.Ke1 Lf8 6.Kd2 Le7 7.Ke2 e3 8.Kf1 Lf8 9.Ke1 Kf3 10.Se5+ Kg2 
  ±  (0.77)   Tiefe: 17/27   00:00:00  867kN
1...e5 
  ²  (0.62)   Tiefe: 18/27   00:00:00  1040kN
1...e5 
  ²  (0.47)   Tiefe: 18/27   00:00:01  1972kN
1...e5 
  =  (0.17)   Tiefe: 18/27   00:00:01  2478kN
1...e5 2.Ke2 Kg5 3.Sxe5 Kf6 4.Sec4 Ke6 5.Sb5 Lxa3 6.Sc7+ Kf6 7.Sxa3 Ke5 8.Sc4+ Kf4 9.Sd5+ Ke4 10.Kf2 Kxd5 11.Sa3 Ke5 
  =  (0.05)   Tiefe: 18/27   00:00:01  2994kN
1...e5 2.Ke2 Kg5 3.Sxe5 Kf6 4.Sec4 Ke6 5.Sb5 Lxa3 6.Sc7+ Kf6 7.Sxa3 Ke5 8.Sc4+ Kf4 9.Sd5+ Ke4 10.Kf2 Kxd5 11.Se3+ Ke5 12.Ke2 a3 
  =  (0.05)   Tiefe: 19/29   00:00:01  3711kN
1...e5 2.Ke2 Kg5 3.Sxe5 Kf6 4.Sec4 Ke6 5.Sb5 Lxa3 6.Sc7+ Kf6 7.Sxa3 Ke5 8.Sc4+ Kf4 9.Sd5+ Ke4 10.Kf2 Kxd5 11.Sd2 Ke6 12.Ke2 Ke5 
  =  (0.05)   Tiefe: 20/29   00:00:02  4813kN
1...e5 2.Ke2 Kg5 3.Sxe5 Kf6 4.Sec4 Ke6 5.Sb5 Lxa3 6.Sc7+ Kf6 7.Sxa3 Ke5 8.Sc4+ Kf4 9.Sd5+ Ke4 10.Kf2 Kxd5 11.Se3+ Kc5 12.Sd1 a3 13.Sc3 Kd4 
  =  (0.05)   Tiefe: 21/31   00:00:03  6435kN

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