A balanced approach to imbalances

[petero2]

This seems better for black than the other two positions I tested, but it still is not an easy win for QueeNy playing black against TQeeny playing white.

Well, it is quite a feat that QueeNy can win at all against an overwhelmingly superior opponent that agrees on what is good strategy. IMO that proves the situation must have an enormous advantage for the Knights.

Probably. I initially thought the advantage was like KQKN though, where even a quite weak engine playing the stronger side could easily win against an arbitrarily strong opponent. But I no longer think so.

The draws all ended with KNNK. The two games that QueeNy won got to the end game KQKNNNN. Is this endgame generally won for the knights?

Well, as I mentioned somewhere above, QueeNy is stupid and doesn't know that KNNK is draw. So it does not try to avoid a final Q for N+P trade, and is therefore an easy target for an engine that knows this brings a draw. It also does not protect its last Pawn, as decent engines would (e.g. reducing a Pawnless advantage at least by a factor 2). It would be intersting to see if there are positions before KNNK occurrsed that were a theoretical win for the Knights, or would be a win when TQueeny played them out against itself.

The first draw went through KQKNNNN, which is a win in 41% of the cases according to this:
http://www.stmintz.com/ccc/index.php?id=408243. I don't know if this particular case was won though.

The second draw was a long time in the KQpKNNNp endgame with two blocked e pawns. I don't think either side could have won. Selfplay with TQueeny ended in a draw by repetition.

The third draw was in the KQpKNNNpp endgame with white e-pawn and black e and g-pawns. After a while it traded down to KQKNNNp and then quickly to KNNK. Selfplay with TQueeny led to an easily won KNNNK endgame for black.

So in summary I believe this position is won for the knights, but I can not completely rule out the existence of some unknown strategy for the queens that would save the game.

[Lyudmil Tsvetkov]

Testing the imbalance 3Qs vs 5 and 6 rooks respectively. It seems like here elephantiasis is almost non-existent. I am still testing against Queeny, probably I should change the engine, but against the 5 rooks the queens do not have any problems, and even against 6 rooks I am winning some games against Queeny (but its eval here seems to be quite normal). So that, is seems, the 5 rooks, that are numerically stronger than 7 knights and even 7 bishops, and even the 6 rooks, that are even stronger, somehow do not overperform against queens in bigger numbers.

[pgn][Event "Computer chess game"]
[Site "OWNER-PC"]
[Date "2013.10.28"]
[Round "?"]
[White "owner"]
[Black "QN"]
[Result "*"]
[BlackElo "2000"]
[Time "00:06:18"]
[WhiteElo "2400"]
[TimeControl "300"]
[SetUp "1"]
[FEN "rrr1k1rr/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w kq - 0 1"]
[Termination "unterminated"]
[PlyCount "34"]
[WhiteType "human"]
[BlackType "human"]

1. g4 c5 {(c7c5 e2e3 e7e6 c2c4 b7b5 c4b5 b8b5 e3e4 e6e5 g4g5 a8b8 b2b3
d7d6) -3.52/15 18} 2. c4 f6 {(f7f6 d2d4 c5d4 d1d4 c8c6 f2f4 g7g5 f4f5 h7h5
g4h5 h8h5 e2e4 e7e5) -3.57/15 10} 3. h4 h5 {(h7h5 g4g5 f6g5 h4g5 b7b5 c4b5
b8b5 b2b3 h5h4 e2e4 h4h3 d2d4 h3h2 d4d5) -3.21/16 6} 4. g5 fxg5 {(f6g5 h4g5
b7b5 c4b5 b8b5 b2b3 g7g6 f2f4 d7d6 e2e4 e7e6 d2d3 b5b6 a1b2) -3.20/16 6} 5.
hxg5 b5 {(b7b5 b2b3 h5h4 c4b5 b8b5 e2e4 h4h3 d2d4 h3h2 d4d5 d7d6 f2f4 b5b4
a1b1) -3.26/15 8} 6. Qc2 Rc6 {(c8c6 g5g6 b5b4 f2f4 h5h4 h1h3 c6f6 f4f5 e7e5
e2e4 d7d6) -3.12/13 7} 7. b3 bxc4 {(b5c4 b3c4 b8b7 f2f4 c6b6 h1d5 a8b8 a1e5
d7d6 c2g6 e8d8 d2d4 c5d4 e5d4) -3.24/14 15} 8. Qxc6 dxc6 {(d7c6 c2e4 h8h7
e4g6 e8d8 g6c6 h7h6 g5h6 g7h6 c6d5 d8c7 d5c5 c7d7 a1d4 d7e8 b3c4) -5.41/14
4} 9. Qg6+ Kd8 {(e8d8 g6c6 b8c8 c6d5 d8e8 a1e5 g7g6 d5e6 h8h7 e6g8 e8d7
g8h7 c8e8 b3c4 h5h4 h7g6) -11.82/16 19} 10. Qxc6 Rc8 {(b8c8 c6d5 d8e8 a1e5
g7g6 d5e6 h8h7 e6g8 e8d7 e5d5 d7c7 g8e6 c4b3 d5c6 c7d8 c6d7) -M4/15 8} 11.
Qd5+ Ke8 {(d8e8 a1e5 g7g6 d5e6 h8h7 e6g8 e8d7 e5d5 d7c7 g8e6 c4b3 d5c6 c7d8
c6d7) -M3/16 3} 12. Qae5 g6 {(g7g6 d5e6 h8h7 e6g8 e8d7 e5d5 d7c7 g8e6 c4b3
d5c6 c7d8 c6d7) -M3/19 3} 13. Qee6 Rg7 {(g8g7 d5d7 e8f8 d7c8 a8c8 e6c8 f8f7
c8h8 c4b3 a2b3 a7a6 h8c8 g7g8 c8c5) -6.21/17 3} 14. Qdd7+ Kf8 {(e8f8 d7c8
a8c8 e6c8 f8f7 c8h8 c4b3 a2b3 g7g8 h8e5 g8d8 f2f4 h5h4 f4f5 g6f5 e5f5 f7e8
f5c5 d8b8 d2d4 b8b3 c5a7) -6.69/19 9} 15. Qxc8+ Rxc8 {(a8c8 e6c8 f8f7 c8h8
c4b3 a2b3 g7g8 h8e5 g8d8 f2f4 d8d6 f4f5 d6b6 f5g6 b6g6 e5f5 f7g7 f5c5 g7f7
d2d4 g6b6 e2e4 b6b3 c5a7) -7.22/22 4} 16. Qxc8+ Kf7 {(f8f7 c8h8 c4b3 a2b3
g7g8 h8e5 g8d8 f2f4 d8d6 f4f5 g6f5 e5f5 f7g7 f5c5 a7a6 c5e5 g7f7 e5h8 f7g6
h8h6 g6f5 h6h5 e7e5) -7.33/23 3} 17. Qxh8 Rg8 {(g7g8 h8e5 c4b3 a2b3 g8d8
f2f4 d8d6 f4f5 g6f5 e5f5 f7g7 f5c5 a7a6 c5e5 g7f7 e5h8 f7g6 h8h6 g6f5 h6h5
e7e5 d2d3) -7.39/22 6} *
[/pgn]

[pgn][Event "Computer chess game"]
[Site "OWNER-PC"]
[Date "2013.10.28"]
[Round "?"]
[White "owner"]
[Black "QN"]
[Result "1-0"]
[BlackElo "2000"]
[Time "00:35:21"]
[WhiteElo "2400"]
[TimeControl "300"]
[SetUp "1"]
[FEN "rrr1krrr/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w kq - 0 1"]
[Termination "normal"]
[PlyCount "35"]
[WhiteType "human"]
[BlackType "human"]

1. g4 f6 {(f7f6 h1g2 c7c5 e2e4 e7e5 c2c3 c5c4 d2d4 d7d6 d4d5) +1.54/14 7}
2. b4 h5 {(h7h5 e2e4 h5g4 d1g4 c7c5 b4b5 g7g5) +1.76/15 7} 3. g5 fxg5
{(f6g5 d2d4 g5g4 e2e4 f8f7 c2c4 g8f8 a1b2 f7f2 b2f2 f8f2 e1f2 h8f8 f2g2
c7c6) +2.08/15 7} 4. Qe5 g4 {(g5g4 d2d4 f8f6 e2e4 g8f8 e5g5 b7b5 h1g1 a7a5
a2a3 a5b4 a3b4 f6f2 g1f2 f8f2 e1f2) +2.10/14 4} 5. d4 b5 {(b7b5 c2c3 a7a5
a2a3 a5b4 a3b4 f8f6 e2e4 a8a2 h1g2 c7c6 e5g3) +2.23/14 11} 6. Qd3 a5 {(a7a5
d3b3 h8h6 b4a5 a8a5 e2e4 h5h4 c2c3 c7c6 e5g5) +2.44/12 8} 7. Qhe4 Rf7
{(f8f7 d3b3 e7e6 e5e6 d7e6 b3e6 e8f8 e4d5 f7e7 d5f5 f8e8 f5f7 e8d8 f7e7)
-M3/13 6} 8. Qde3 e6 {(e7e6 e5e6 d7e6 e4c6 e8f8 c6c5 f8e8 e3e6 e8d8 c5g5
f7e7 e6e7) -M3/13 5} 9. d5 Rf6 {(f7f6 d5e6 d7d5 e4d5 c8d8 d5c6 e8f8 e6e7
f8f7 e5e6 f6e6 e3e6) -M3/17 8} 10. dxe6 d5 {(d7d5 e4d5 c8d8 d5c6 e8f8 e6e7
f8f7 e5e6 f6e6 e3e6) -M2/16 9} 11. Q4xd5 Rd8 {(c8d8 d5c6 e8f8 e6e7 f8f7
e5e6 f6e6 e3e6) -M2/19 5} 12. Qc6+ Ke7 {(e8e7 e5c7 d8d7 c7d7 e7f8 d7d6)
-M1/20 4} 13. Qcxc7+ Ke8 {(e7e8 c7c6 e8e7 e5c5 d8d6 c5d6) -M1/20 3} 14.
Qf7+ Rxf7 {(f6f7 e6f7 e8d7 e5e7 d7c8 e3c5) -M1/23 4} 15. exf7+ Kd7 {(e8d7
e5e7 d7c8 e3c5) -M1/23 3} 16. Qe6+ Kc7 {(d7c7 e3c5 c7b7 e6c6) -M1/24 7} 17.
Qc5+ Kb7 {(c7b7 e6c6) +M0/27 4} 18. Qec6# 1-0
[/pgn]

Rooks still defend each other pretty well, and, in large numbers, they even somewhat complement, covering a significant area of the board, however, a major flaw of rooks is that they are not good defenders of the king shelter, in sharp distinction to both minor pieces. So that, objectively, what makes 7Ns and 7Bs so strong in a group is also the fact that they represent an excellent king shelter even in the absence of pawns, while being able to attack at the same time. Rooks are only able to attack, more effeciently than minors, but they do not defend the king well, similarly as queens. So that in all such imbalances the queen side actually plays with a weakened shelter.

[hgm]

QueeNy does not have an adapted Rook value. For this reason it is extremely weak at normal Chess: it immediately sacrifices its Rooks for opponent Knights. It seems you discovered with the Rooks that mutual defense isn't worth all that much.

I have been playing Tqueeny against itself from the position
[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/1Q1QK1Q1 w - - 0 1
20.5 - 4.5 for the Knights

that was supposed to give the Queens a chance due to under-development of the Knights, and spread-out Pawns. I don't know if Tqueeny randomizes, but to make sure I got different games I let white start with 1. f4 (the move it used in the first game), to not be accused of playing an unfavorable move for white, and then forced various Pawn moves for black: a6, b6, ... h6, a5, b5, d5, f5 (well, this one it played by itself in the first game) and h5. The intention was to play 40/5', but by mistake some games got played at 40/20'.

Indeed the Queens won some of the games, but lost all three 40/20' games. So I decided to (re-)play everything at 40/20', to check if at 40/5' tactical inaccuracies still occur that could cost the game.

The resolts were: (+ is a win for the Knights)

Code: Select all

2... 5' 20'
a6   =  +
b6   +  +
c6   +  +
d6   +  +
e6   +  +
f6   +  +
g6   -  +
h6   +  +
a5   =  =
b5   -  +
d5   -  -
f5   +  +
h5   +  +

At 4/20' the Knights thus win 11.5-1.5. 1. f4 d5 was won by the Queens at both time controls, and in both games the d-Pawn immediately falls, giving the Queens total control of the center. So it seems these games are lost because I forced black to make a tactically unsound move, and that the resulting loss of material and center control is more than the Knights can stand. 1... a5 also doesn't seem so good; pushing Pawns blindly by 2 squares is of course risky, because you move them out of the protective cover of other Pawns and Knights.

Indeed even for Tqueeny 40/5' is not enough time to play this perfectly, and tactical errors are more common there than at 40/20', so that at 40/5' the Knights won only 9-4.

So at the level of play exercised by Tqueeny (which seems the best we have at the moment), the position seems to be overwhelmingly won for the Knights.

I posted the games at http://hgm.nubati.net/Tqueeny.pgn .

Btw, I got the impression that Tqueeny is a bit reluctant to march its King towards the center. This might make life more difficult for the Knights than needed.

[hgm]

When an engine that is not elephantiasis-aware plays the Queens, 6 Knights are of course already enough to beat it. If you don't start them too unfavorably::

[d]3nk3/2pnpnp1/3nnn2/8/8/8/3PPP2/1Q1QK1Q1 w - - 0 1

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.28"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "TQueeny 64-bit"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "3nk3/2pnpnp1/3nnn2/8/8/8/3PPP2/1Q1QK1Q1 w - - 0 1"]
[SetUp "1"]
1. Qa4 {+14.80/16} g5 {-4.70/17 7} 2. Qg2 {+14.54/19 5} c5 {-4.48/17 6} 3.
d3 {+14.50/20 8} Kf8 {-4.52/16 8} 4. Qa7 {+14.44/22 5} c4 {-4.40/17 8} 5.
dxc4 {+14.44/23 8} Nxc4 {-4.39/18 6} 6. Qh1 {+14.36/24 14} Nde5
{-4.29/17 6} 7. Qaa8 {+14.36/26 5} Kg7 {-4.20/17 6} 8. Qbb8 {+14.36/25 5}
g4 {-4.24/16 9} 9. Qba7 {+14.44/23 5} Ned7 {-4.21/17 6} 10. Qa1
{+14.42/22 11} Nfe5 {-4.26/16 12} 11. Qh2 {+14.44/19 7} Ndf7 {-4.19/16 6}
12. Qg3 {+14.42/20 9} Ndb6 {-4.54/15 7} 13. Qh1 {+14.42/24 9} Kf8
{-4.24/16 6} 14. Qb3 {+14.32/24 12} Ned7 {-4.26/17 26} 15. Qc2
{+14.32/23 5} Nde5 {-4.26/17 6} 16. Qf5 {+14.32/25 6} Ng7 {-4.26/18 6} 17.
Qf4 {+14.32/26 6} Ned7 {-4.25/16 6} 18. Qfh2 {+14.32/22 8} Nf5 {-3.95/17 6}
19. Qb1 {+14.38/21 8} N5d6 {-3.81/17 6} 20. Qf4 {+14.36/23 10} e5
{-3.52/17 6} 21. Qg3 {+14.36/22 5} Nbd5 {-3.40/17 16} 22. Qa2 {+14.28/22 8}
e4 {-3.23/17 6} 23. Qgh2 {+14.12/19 27} Nfe5 {-3.07/17 6} 24. Qa8+
{+14.32/17 5} Kf7 {-3.01/17 6} 25. Qh4 {+14.54/17 6} Ke6 {-2.69/16 6} 26.
Qg2 {+14.56/18 5} N7b6 {-2.59/16 6} 27. Qb8 {+14.24/19 7} e3 {-2.54/15 6}
28. Qgh1 {+13.65/16 9} Nbd7 {-2.29/16 6} 29. Qa8 {+11.79/17 5} Nf5
{-2.46/14 6} 30. Qa6+ {+10.80/18 6} Ncd6 {-2.37/16 9} 31. Qh8
{+14.26/15 2.3} exf2+ {-2.23/15 6} 32. Kxf2 {+13.37/16 5} Nc5 {-2.29/15 6}
33. Qa2 {+11.53/17 9} Nce4+ {-2.26/15 7} 34. Ke1 {+10.68/20 4} g3
{-2.08/16 6} 35. Qa6 {+12.00/16 15} Nde3 {-1.94/16 6} 36. Qhc8+
{+11.63/16 6} Kf7 {-1.07/17 7} 37. Qa7+ {+12.28/15 4} Kg6 {-0.02/17 7} 38.
Qe6 {+8.06/18 3} N5g4 {+0.00/17 7} 39. Qah7+ {+6.42/18 6} Kg5
{+0.00/15 0.1} 40. Qc7 {+5.15/20 4} g2 {+0.00/18 17} 41. Qg1 {+6.18/20 4}
Nb5 {+0.00/17 7} 42. Qd8 {+5.93/23 11} Nc2+ {+0.35/16 6} 43. Kd1
{+5.93/12 0.1} Ncd4 {+0.35/15 7} 44. Qxe4 {+5.97/22 4} Nc3+ {+0.34/16 6}
45. Kc1 {+5.89/23 3} Nxe4 {+0.32/16 6} 46. Qxg2 {+5.89/23 3} Nb3+
{+0.31/16 6} 47. Kb2 {+6.36/22 11} Nbc5 {+0.00/15 7} 48. Qc8 {+6.34/21 22}
Nfd6 {+0.32/15 6} 49. Qc7 {+6.28/23 12} Kg6 {+0.33/16 7} 50. Qa7
{+6.24/24 10} Nc4+ {+0.35/16 7} 51. Kc1 {+6.24/25 13} Ne3 {+0.24/15 7} 52.
Qh3 {+6.16/24 23} Nf5 {+0.32/15 7} 53. Qa2 {+6.16/25 7} Ng5 {+0.36/16 7}
54. Qg2 {+6.16/23 7} Nge4 {+0.32/14 8} 55. Kb2 {+6.24/25 10} Neg3
{+0.31/15 8} 56. Qc6 {+6.28/25 11} Nce4 {+0.31/15 7} 57. Qg8+ {+6.16/20 10}
Kh5 {+0.31/15 7} 58. Qh8+ {+6.16/24 8} Kg5 {+0.25/16 7} 59. Qc1+
{+6.16/23 8} Nge3 {+0.36/16 7} 60. Qg1 {+6.16/25 6} Nfg4 {+0.39/15 7} 61.
Qg8+ {+6.16/23 6} Kf4 {+0.39/14 7} 62. Qe1 {+6.16/23 5} Nd4 {+0.41/13 7}
63. Qf8+ {+6.16/20 9} Ndf5 {+0.40/14 7} 64. Qb8+ {+6.16/23 9} Ne5
{+0.39/14 7} 65. Qeb4 {+6.14/19 6} Ng4 {+0.38/14 7} 66. Q4b5 {+6.16/21 7}
Ned6 {+0.40/14 7} 67. Qa4+ {+6.14/19 8} Nge4 {+0.39/14 7} 68. Ka2
{+6.38/20 6} Nge3 {+0.38/14 7} 69. Qh8 {+6.38/23 6} N5g4 {+0.37/15 7} 70.
Ka1 {+6.38/18 6} Ndc4 {+0.39/16 8} 71. Qb3 {+6.28/21 9} Nce5 {+0.39/16 8}
72. Qf8 {+6.36/21 5} Ngf6 {+0.34/15 8} 73. Qd8 {+6.28/21 4} Nfg4
{+0.37/15 8} 74. Qb1 {+6.36/22 3} Nf7 {+0.38/15 8} 75. Qf8 {+6.36/23 4}
N7d6 {+0.37/16 8} 76. Qh1 {+6.34/23 8} Ke5 {+0.37/15 9} 77. Kb2
{+6.48/15 4} Ngf6 {+0.37/13 9} 78. Qhh8 {+6.34/18 6} Ke6 {+0.39/14 11} 79.
Qh2 {+6.64/16 4} Ned5 {+0.38/14 9} 80. Qh3 {+6.60/15 1.9} Ke5 {+0.38/15 11}
81. Qf3 {+6.28/20 9} Nd4 {+0.39/15 6} 82. Qd3 {+6.26/23 18} Nf4
{+0.37/15 6} 83. Qe7+ {+6.26/19 8} Nde6 {+0.38/16 6} 84. Qd1 {+6.16/24 11}
Nc4+ {+0.40/14 7} 85. Ka1 {+6.16/21 12} N4d5 {+0.38/16 6} 86. Qb7
{+4.92/22 27} N6c5 {+0.29/15 26} 87. Qb8+ {+2.16/18 9} Ke6 {+0.29/15 6} 88.
Qd4 {+1.17/21 15} Ncd6 {+0.36/16 6} 89. e3 {+6.08/20 7} Ncd7 {+0.34/16 6}
90. Qa8 {+6.04/23 7} Ne5 {+0.37/15 6} 91. Qda7 {+6.04/21 9} Nec4
{+0.48/15 6} 92. Qh8 {+6.04/19 6} Ndxe3 {+0.48/14 6} 93. Qd8 {+6.04/22 11}
Ned5 {+0.48/14 7} 94. Qf8 {+5.85/21 29} Ke5 {+0.48/14 6} 95. Qfb8
{+5.09/21 12} Nde3 {+0.48/14 6} 96. Qb3 {+4.86/23 7} Ndf5 {+0.47/13 10} 97.
Qd3 {+4.86/22 16} Nfg4 {+0.48/14 6} 98. Qh7 {+6.02/19 7} Kf4 {+0.50/14 6}
99. Qh8 {+6.02/19 5} Nce5 {+0.50/14 6} 100. Qb3 {+5.95/19 3} Nf3
{+0.50/13 7} 101. Qh3 {+5.67/21 12} Nge5 {+0.49/13 7} 102. Qa4
{+5.07/20 14} N5d4 {+0.50/14 6} 103. Qh6+ {+4.96/19 14} Neg5 {+0.49/15 6}
104. Qaa6 {+4.78/20 2.9} Nef5 {+0.50/13 7} 105. Qf8 {+5.69/16 2.1} Nge6
{+0.50/14 7} 106. Qg8 {+5.69/16 2.2} Nc5 {+0.50/13 7} 107. Qf1 {+4.98/18 3}
Ne3 {+0.50/13 9} 108. Qf8+ {+5.53/13 1.2} Ke4 {+0.49/13 7} 109. Qb1+
{+5.41/15 1.2} Ncd3 {+0.50/14 7} 110. Qb7+ {+5.31/16 3} Nec6 {+0.48/14 7}
111. Qh7+ {+5.09/17 1.4} Nef5 {+0.49/15 7} 112. Qe8+ {+4.80/18 5} Nce5
{+0.50/14 8} 113. Qh3 {+5.01/15 0.7} Nb4 {+0.50/13 11} 114. Kb1
{+4.82/14 0.9} Nd5 {+0.50/13 7} 115. Ka2 {+4.70/15 1.4} Nc3+ {+0.49/12 8}
116. Kb2 {+4.66/15 1.9} Nd5 {+0.49/14 7} 117. Qg8 {+4.24/15 0.6} Nf4
{+0.51/13 7} 118. Qh1 {+5.01/13 0.4} Ne3 {+0.50/12 7} 119. Qgh7+
{+5.09/12 0.5} Ndf5 {+0.49/13 8} 120. Ka2 {+5.15/13 0.8} Nfd5 {+0.49/13 9}
121. Qb7 {+0.06/22 35} Kf4 {+0.49/13 6} 122. Qb2 {+0.10/19 8} N3c4
{+0.50/13 6} 123. Qhc1+ {+0.06/21 13} Nfe3 {+0.49/15 6} 124. Qba1
{+0.02/23 11} Nd3 {+0.51/13 7} 125. Qh1 {+0.02/22 10} Nce5 {+0.51/13 7}
126. Qh6+ {+0.00/21 7} Kg3 {+0.51/13 7} 127. Qah1 {+0.00/24 8} Kf2
{+0.51/13 7} 128. Qa1 {+0.00/24 11} Ke2 {+0.52/13 7} 129. Qh5 {+0.00/25 10}
Kd2 {+0.52/13 7} 130. Qh6 {+0.00/27 6} Ke2 {+0.51/13 7} 131. Qh5
{+0.00/31 8} Kd2 {+0.52/14 7} 132. Qh6 {+0.00/32 8} Nc4 {+0.50/13 7} 133.
Qhh1 {+0.00/26 7} Ke2 {+0.51/14 7} 134. Qah8 {+0.00/25 8} Nce5 {+0.51/13 7}
135. Q1h3 {+0.00/24 7} Kd2 {+0.53/12 7} 136. Q8h6 {+0.00/26 7} Kc2
{+0.53/13 7} 137. Qh7 {-0.98/23 13} Nb4+ {+0.49/14 7} 138. Ka3
{-0.98/24 2.6} Nd2 {+0.50/15 7} 139. Qh2 {-0.98/26 9} N5c4+ {+0.52/14 7}
140. Ka4 {-0.98/12 0.1} Ned5 {+0.52/14 7} 141. Qg7 {-0.98/24 8} Nc3+
{+0.53/15 7} 142. Qxc3+ {-0.98/12 0.1} Kxc3 {+0.53/16 7} 143. Qh8+
{-1.01/25 6} Nde5 {+0.53/16 7} 144. Qh1 {-1.03/25 19} Nd5 {+0.53/15 9} 145.
Qh3+ {-0.98/22 6} Kd4 {+0.54/14 7} 146. Qh8 {-1.03/24 6} Ne4 {+0.54/13 7}
147. Qh4 {-1.03/23 5} Nd2 {+0.54/13 8} 148. Qh8 {-12.98/24 13} Nc5+
{+0.54/13 7} 149. Kb5 {-13.13/25 1.3} Nde4 {+0.54/14 7} 150. Qh4
{-1.03/21 7} Ne7 {+0.54/13 8} 151. Kb6 {-1.01/21 6} Nd5+ {+0.54/13 8} 152.
Kb5 {+0.00/65 14} Nc3+ {+0.55/14 8} 153. Kb4 {-1.03/22 0.7} Ned3+
{+0.54/13 9} 154. Ka5 {-1.03/22 1.8} Kc4 {+0.54/14 10} 155. Qh5
{-1.03/21 2.0} Nd5 {+0.55/14 8} 156. Qg4 {-17.51/22 6} Nb3+ {+15.06/16 8}
157. Ka6 {-99.66/19 1.4} Ndc5+ {+15.52/17 8} 158. Ka7 {-17.36/12 0.1} Nd4
{+15.67/18 10} 159. Qg8 {-99.74/21 2.6} Nf6 {+99.67/16 13} 160. Qf7
{-99.80/21 3} Nb5+ {+99.55/15 8} 161. Ka8 {-99.80/25 16} Kb4 {+99.65/14 12}
162. Qg7 {-99.82/26 10} Nb6+ {+99.83/13 6} 163. Kb8 {-99.84/29 9} Nfd7+
{+99.85/14 7} 164. Qxd7 {-99.86/34 10} Ncxd7+ {+99.87/14 2.0} 165. Kb7
{-99.88/37 10} Kc5 {+99.89/12 0.1} 166. Ka6 {-99.90/42 8} Ne5
{+99.91/10 0.1} 167. Kb7 {-99.86/32 10} Nc6 {+99.93/8 0.1} 168. Ka6
{-99.94/50 8} Nc8 {+99.95/6 0.1} 169. Kb7 {-99.96/100 0.2} Ncd6+
{+99.97/4 0.1} 170. Ka6 {-99.98/100 0.1} Nc7# {+99.99/2 0.1}
{Xboard adjudication: Checkmate} 0-1

Even the weak QueeNy manages to cause Stockfish great trouble with only 6 Knights; it manouevres it into this position, from which Tqueeny easily wins, but then unfortunately blunders away the Pawn and finally loses, being outserached more than 10 ply.

[d]8/1Q1n2Q1/5n2/3nnk2/4pnn1/8/8/KQ6 b - - 11 43

So testing against other engines with 7 Knights is really pointless. They are just too much biased against doing Q-for-2N trades, which means a certain loss. Even against 6 Knights.

I really believe KNNNNKQ is usually won. The tablebase might say 41% wins with knights-to-move, after removal of all mate-in-1 and 1. KxQ position, but that is really misleading. There will also be many positions where one of the Knights is doomed, because of the Queen forking or skewering unprotected Knights or King, and positions where an isolated outpost Knight cannot be protected. (Queens are very efficient driving a single Knight to the edge and capturing it there, without King help.)

Most quiet positions, with Knights grouped around the King, are probably won.

[hgm]

If the concern is that the King fortress of the Knights is to strong, you can always start from this position:
[d]nnknnnnn/4pppp/8/8/8/8/4PPPP/4QQQK b
In self-play Tqueeny manages to force two Q-for-2N trades before the Knights get a chance to deploy properly around the King. It doesn't help the Queens side much, however. (And when Stockfish played the Queens, it didn't stand a chance at all.)

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.28"]
[Round "-"]
[White "TQueeny 64-bit"]
[Black "TQueeny 64-bit"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "nnknnnnn/4pppp/8/8/8/8/4PPPP/4QQQK b - - 11 1"]
[SetUp "1"]
1... Nhg6 {+1.75/17 6} 2. h4 {-1.72/17 7} Nac7 {+1.79/18 6} 3. h5
{-1.96/17 7} Nf4 {+1.93/17 10} 4. g3 {-1.99/16 7} N4e6 {+1.86/19 6} 5. f4
{-1.66/17 11} Nfd7 {+1.87/17 6} 6. Qb1 {-2.04/17 15} Ngf6 {+2.18/18 9} 7.
Qf3 {-2.04/16 8} h6 {+2.00/17 14} 8. Qc2 {-1.93/18 6} Nd6 {+2.07/18 6} 9.
f5 {-1.72/18 8} Nef8 {+1.17/17 9} 10. Qgc1 {+0.00/18 6} Nfe8 {+0.01/18 7}
11. Qfc3 {-0.22/19 6} Nbc6 {+0.25/20 6} 12. Qxc6 {-0.22/20 6} Nxc6
{+0.35/21 6} 13. Qxc6 {-0.37/20 6} Kd8 {+0.35/19 6} 14. Qb1 {-0.50/18 14}
e6 {+0.42/19 6} 15. g4 {-0.41/18 6} Ne5 {+0.58/19 6} 16. Qb8+ {-0.57/19 6}
Ke7 {+0.53/22 6} 17. Qxd6+ {-0.53/20 6} Nxd6 {+0.59/23 6} 18. Qxc7+
{-0.59/22 6} Nfd7 {+0.60/23 6} 19. Qc3 {-0.57/22 6} exf5 {+0.59/21 6} 20.
gxf5 {-0.64/22 6} Nxf5 {+0.65/21 6} 21. Qa3+ {-0.77/21 11} Ke6 {+0.67/20 7}
22. Kg1 {-0.74/20 9} g5 {+0.75/19 7} 23. hxg6 {-0.74/21 6} fxg6
{+0.74/20 7} 24. e4 {-0.88/19 8} Nh4 {+1.09/19 9} 25. Qh3+ {-1.17/19 6} Kf7
{+1.46/21 7} 26. Kf1 {-1.44/21 6} g5 {+1.61/21 7} 27. Ke2 {-1.63/21 6} Nf6
{+1.73/20 7} 28. Qh2 {-1.79/20 13} Nfg4 {+1.76/20 7} 29. Qh1 {-1.94/22 6}
h5 {+1.94/21 7} 30. Qd1 {-1.96/20 9} Nhf3 {+2.50/20 7} 31. Qd5+
{-2.76/19 10} Kg7 {+3.14/22 7} 32. Qb7+ {-3.25/21 11} Kg6 {+3.42/23 7} 33.
Kf1 {-3.40/21 8} h4 {+3.59/20 7} 34. Kg2 {-3.35/20 5} Nf6 {+4.25/20 7} 35.
Qb1 {-3.89/19 5} g4 {+8.50/19 8} 36. Kh1 {-5.80/19 6} g3 {+11.30/20 8} 37.
Kg2 {-12.97/19 13} Kh5 {+15.32/18 8} 38. Qb8 {-15.08/17 3} Ne1+
{+17.95/18 10} 39. Kf1 {-20.10/19 8} g2+ {+18.85/18 9} 40. Ke2
{-21.59/16 0.1} N1d3 {+22.00/18 10} 41. Qa7 {-21.21/17 15} Nf4+
{+22.90/17 14} 42. Kd1 {-24.24/18 16} h3 {+24.02/17 8} 43. Qg7
{-28.36/18 24} Neg4 {+28.21/16 18} 44. Kc2 {-28.21/16 16} g1=Q
{+28.39/16 11} 45. Qf7+ {-99.40/16 22} Kh4 {+34.85/15 6} 46. Qf8
{-35.95/14 10} h2 {+99.65/13 6} 47. Qh8+ {-99.42/13 20} N4h5 {+99.89/10 7}
48. Kb3 {-99.70/11 18} Qb6+ {+99.91/9 7} 49. Ka3 {-99.92/9 0.9} h1=Q
{+99.93/8 0.1} 50. Qxf6+ {-99.94/7 0.3} Nhxf6 {+99.95/6 0.1} 51. Ka2
{-99.96/5 0.1} Qhb1+ {+99.97/4 0.1} 52. Ka3 {-99.98/3 0.1} Qa1#
{+99.99/2 0.1}
{Xboard adjudication: Checkmate} 0-1

[Lyudmil Tsvetkov]

QueeNy does not have an adapted Rook value. For this reason it is extremely weak at normal Chess: it immediately sacrifices its Rooks for opponent Knights. It seems you discovered with the Rooks that mutual defense isn't worth all that much.

I have been playing Tqueeny against itself from the position
[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/1Q1QK1Q1 w - - 0 1
20.5 - 4.5 for the Knights

that was supposed to give the Queens a chance due to under-development of the Knights, and spread-out Pawns. I don't know if Tqueeny randomizes, but to make sure I got different games I let white start with 1. f4 (the move it used in the first game), to not be accused of playing an unfavorable move for white, and then forced various Pawn moves for black: a6, b6, ... h6, a5, b5, d5, f5 (well, this one it played by itself in the first game) and h5. The intention was to play 40/5', but by mistake some games got played at 40/20'.

Indeed the Queens won some of the games, but lost all three 40/20' games. So I decided to (re-)play everything at 40/20', to check if at 40/5' tactical inaccuracies still occur that could cost the game.

The resolts were: (+ is a win for the Knights)

Code: Select all

2... 5' 20'
a6   =  +
b6   +  +
c6   +  +
d6   +  +
e6   +  +
f6   +  +
g6   -  +
h6   +  +
a5   =  =
b5   -  +
d5   -  -
f5   +  +
h5   +  +

At 4/20' the Knights thus win 11.5-1.5. 1. f4 d5 was won by the Queens at both time controls, and in both games the d-Pawn immediately falls, giving the Queens total control of the center. So it seems these games are lost because I forced black to make a tactically unsound move, and that the resulting loss of material and center control is more than the Knights can stand. 1... a5 also doesn't seem so good; pushing Pawns blindly by 2 squares is of course risky, because you move them out of the protective cover of other Pawns and Knights.

Indeed even for Tqueeny 40/5' is not enough time to play this perfectly, and tactical errors are more common there than at 40/20', so that at 40/5' the Knights won only 9-4.

So at the level of play exercised by Tqueeny (which seems the best we have at the moment), the position seems to be overwhelmingly won for the Knights.

I posted the games at http://hgm.nubati.net/Tqueeny.pgn .

Btw, I got the impression that Tqueeny is a bit reluctant to march its King towards the center. This might make life more difficult for the Knights than needed.

You started from another position - with queens on b1 and g1 instead of a1 and h1. I think a1 and h1, replacing the rooks and providing some symmetry, are more natural locations. Even with this position your results were not absolutely convincing, but you initially claimed the position is fully lost for the queens, which, even with your tests, is not confirmed.
There is also the highly relevant possibility that TQueeny does not handle optimally the queen side in terms of evaluation.

[Lyudmil Tsvetkov]

When an engine that is not elephantiasis-aware plays the Queens, 6 Knights are of course already enough to beat it. If you don't start them too unfavorably::

[d]3nk3/2pnpnp1/3nnn2/8/8/8/3PPP2/1Q1QK1Q1 w - - 0 1

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.28"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "TQueeny 64-bit"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "3nk3/2pnpnp1/3nnn2/8/8/8/3PPP2/1Q1QK1Q1 w - - 0 1"]
[SetUp "1"]
1. Qa4 {+14.80/16} g5 {-4.70/17 7} 2. Qg2 {+14.54/19 5} c5 {-4.48/17 6} 3.
d3 {+14.50/20 8} Kf8 {-4.52/16 8} 4. Qa7 {+14.44/22 5} c4 {-4.40/17 8} 5.
dxc4 {+14.44/23 8} Nxc4 {-4.39/18 6} 6. Qh1 {+14.36/24 14} Nde5
{-4.29/17 6} 7. Qaa8 {+14.36/26 5} Kg7 {-4.20/17 6} 8. Qbb8 {+14.36/25 5}
g4 {-4.24/16 9} 9. Qba7 {+14.44/23 5} Ned7 {-4.21/17 6} 10. Qa1
{+14.42/22 11} Nfe5 {-4.26/16 12} 11. Qh2 {+14.44/19 7} Ndf7 {-4.19/16 6}
12. Qg3 {+14.42/20 9} Ndb6 {-4.54/15 7} 13. Qh1 {+14.42/24 9} Kf8
{-4.24/16 6} 14. Qb3 {+14.32/24 12} Ned7 {-4.26/17 26} 15. Qc2
{+14.32/23 5} Nde5 {-4.26/17 6} 16. Qf5 {+14.32/25 6} Ng7 {-4.26/18 6} 17.
Qf4 {+14.32/26 6} Ned7 {-4.25/16 6} 18. Qfh2 {+14.32/22 8} Nf5 {-3.95/17 6}
19. Qb1 {+14.38/21 8} N5d6 {-3.81/17 6} 20. Qf4 {+14.36/23 10} e5
{-3.52/17 6} 21. Qg3 {+14.36/22 5} Nbd5 {-3.40/17 16} 22. Qa2 {+14.28/22 8}
e4 {-3.23/17 6} 23. Qgh2 {+14.12/19 27} Nfe5 {-3.07/17 6} 24. Qa8+
{+14.32/17 5} Kf7 {-3.01/17 6} 25. Qh4 {+14.54/17 6} Ke6 {-2.69/16 6} 26.
Qg2 {+14.56/18 5} N7b6 {-2.59/16 6} 27. Qb8 {+14.24/19 7} e3 {-2.54/15 6}
28. Qgh1 {+13.65/16 9} Nbd7 {-2.29/16 6} 29. Qa8 {+11.79/17 5} Nf5
{-2.46/14 6} 30. Qa6+ {+10.80/18 6} Ncd6 {-2.37/16 9} 31. Qh8
{+14.26/15 2.3} exf2+ {-2.23/15 6} 32. Kxf2 {+13.37/16 5} Nc5 {-2.29/15 6}
33. Qa2 {+11.53/17 9} Nce4+ {-2.26/15 7} 34. Ke1 {+10.68/20 4} g3
{-2.08/16 6} 35. Qa6 {+12.00/16 15} Nde3 {-1.94/16 6} 36. Qhc8+
{+11.63/16 6} Kf7 {-1.07/17 7} 37. Qa7+ {+12.28/15 4} Kg6 {-0.02/17 7} 38.
Qe6 {+8.06/18 3} N5g4 {+0.00/17 7} 39. Qah7+ {+6.42/18 6} Kg5
{+0.00/15 0.1} 40. Qc7 {+5.15/20 4} g2 {+0.00/18 17} 41. Qg1 {+6.18/20 4}
Nb5 {+0.00/17 7} 42. Qd8 {+5.93/23 11} Nc2+ {+0.35/16 6} 43. Kd1
{+5.93/12 0.1} Ncd4 {+0.35/15 7} 44. Qxe4 {+5.97/22 4} Nc3+ {+0.34/16 6}
45. Kc1 {+5.89/23 3} Nxe4 {+0.32/16 6} 46. Qxg2 {+5.89/23 3} Nb3+
{+0.31/16 6} 47. Kb2 {+6.36/22 11} Nbc5 {+0.00/15 7} 48. Qc8 {+6.34/21 22}
Nfd6 {+0.32/15 6} 49. Qc7 {+6.28/23 12} Kg6 {+0.33/16 7} 50. Qa7
{+6.24/24 10} Nc4+ {+0.35/16 7} 51. Kc1 {+6.24/25 13} Ne3 {+0.24/15 7} 52.
Qh3 {+6.16/24 23} Nf5 {+0.32/15 7} 53. Qa2 {+6.16/25 7} Ng5 {+0.36/16 7}
54. Qg2 {+6.16/23 7} Nge4 {+0.32/14 8} 55. Kb2 {+6.24/25 10} Neg3
{+0.31/15 8} 56. Qc6 {+6.28/25 11} Nce4 {+0.31/15 7} 57. Qg8+ {+6.16/20 10}
Kh5 {+0.31/15 7} 58. Qh8+ {+6.16/24 8} Kg5 {+0.25/16 7} 59. Qc1+
{+6.16/23 8} Nge3 {+0.36/16 7} 60. Qg1 {+6.16/25 6} Nfg4 {+0.39/15 7} 61.
Qg8+ {+6.16/23 6} Kf4 {+0.39/14 7} 62. Qe1 {+6.16/23 5} Nd4 {+0.41/13 7}
63. Qf8+ {+6.16/20 9} Ndf5 {+0.40/14 7} 64. Qb8+ {+6.16/23 9} Ne5
{+0.39/14 7} 65. Qeb4 {+6.14/19 6} Ng4 {+0.38/14 7} 66. Q4b5 {+6.16/21 7}
Ned6 {+0.40/14 7} 67. Qa4+ {+6.14/19 8} Nge4 {+0.39/14 7} 68. Ka2
{+6.38/20 6} Nge3 {+0.38/14 7} 69. Qh8 {+6.38/23 6} N5g4 {+0.37/15 7} 70.
Ka1 {+6.38/18 6} Ndc4 {+0.39/16 8} 71. Qb3 {+6.28/21 9} Nce5 {+0.39/16 8}
72. Qf8 {+6.36/21 5} Ngf6 {+0.34/15 8} 73. Qd8 {+6.28/21 4} Nfg4
{+0.37/15 8} 74. Qb1 {+6.36/22 3} Nf7 {+0.38/15 8} 75. Qf8 {+6.36/23 4}
N7d6 {+0.37/16 8} 76. Qh1 {+6.34/23 8} Ke5 {+0.37/15 9} 77. Kb2
{+6.48/15 4} Ngf6 {+0.37/13 9} 78. Qhh8 {+6.34/18 6} Ke6 {+0.39/14 11} 79.
Qh2 {+6.64/16 4} Ned5 {+0.38/14 9} 80. Qh3 {+6.60/15 1.9} Ke5 {+0.38/15 11}
81. Qf3 {+6.28/20 9} Nd4 {+0.39/15 6} 82. Qd3 {+6.26/23 18} Nf4
{+0.37/15 6} 83. Qe7+ {+6.26/19 8} Nde6 {+0.38/16 6} 84. Qd1 {+6.16/24 11}
Nc4+ {+0.40/14 7} 85. Ka1 {+6.16/21 12} N4d5 {+0.38/16 6} 86. Qb7
{+4.92/22 27} N6c5 {+0.29/15 26} 87. Qb8+ {+2.16/18 9} Ke6 {+0.29/15 6} 88.
Qd4 {+1.17/21 15} Ncd6 {+0.36/16 6} 89. e3 {+6.08/20 7} Ncd7 {+0.34/16 6}
90. Qa8 {+6.04/23 7} Ne5 {+0.37/15 6} 91. Qda7 {+6.04/21 9} Nec4
{+0.48/15 6} 92. Qh8 {+6.04/19 6} Ndxe3 {+0.48/14 6} 93. Qd8 {+6.04/22 11}
Ned5 {+0.48/14 7} 94. Qf8 {+5.85/21 29} Ke5 {+0.48/14 6} 95. Qfb8
{+5.09/21 12} Nde3 {+0.48/14 6} 96. Qb3 {+4.86/23 7} Ndf5 {+0.47/13 10} 97.
Qd3 {+4.86/22 16} Nfg4 {+0.48/14 6} 98. Qh7 {+6.02/19 7} Kf4 {+0.50/14 6}
99. Qh8 {+6.02/19 5} Nce5 {+0.50/14 6} 100. Qb3 {+5.95/19 3} Nf3
{+0.50/13 7} 101. Qh3 {+5.67/21 12} Nge5 {+0.49/13 7} 102. Qa4
{+5.07/20 14} N5d4 {+0.50/14 6} 103. Qh6+ {+4.96/19 14} Neg5 {+0.49/15 6}
104. Qaa6 {+4.78/20 2.9} Nef5 {+0.50/13 7} 105. Qf8 {+5.69/16 2.1} Nge6
{+0.50/14 7} 106. Qg8 {+5.69/16 2.2} Nc5 {+0.50/13 7} 107. Qf1 {+4.98/18 3}
Ne3 {+0.50/13 9} 108. Qf8+ {+5.53/13 1.2} Ke4 {+0.49/13 7} 109. Qb1+
{+5.41/15 1.2} Ncd3 {+0.50/14 7} 110. Qb7+ {+5.31/16 3} Nec6 {+0.48/14 7}
111. Qh7+ {+5.09/17 1.4} Nef5 {+0.49/15 7} 112. Qe8+ {+4.80/18 5} Nce5
{+0.50/14 8} 113. Qh3 {+5.01/15 0.7} Nb4 {+0.50/13 11} 114. Kb1
{+4.82/14 0.9} Nd5 {+0.50/13 7} 115. Ka2 {+4.70/15 1.4} Nc3+ {+0.49/12 8}
116. Kb2 {+4.66/15 1.9} Nd5 {+0.49/14 7} 117. Qg8 {+4.24/15 0.6} Nf4
{+0.51/13 7} 118. Qh1 {+5.01/13 0.4} Ne3 {+0.50/12 7} 119. Qgh7+
{+5.09/12 0.5} Ndf5 {+0.49/13 8} 120. Ka2 {+5.15/13 0.8} Nfd5 {+0.49/13 9}
121. Qb7 {+0.06/22 35} Kf4 {+0.49/13 6} 122. Qb2 {+0.10/19 8} N3c4
{+0.50/13 6} 123. Qhc1+ {+0.06/21 13} Nfe3 {+0.49/15 6} 124. Qba1
{+0.02/23 11} Nd3 {+0.51/13 7} 125. Qh1 {+0.02/22 10} Nce5 {+0.51/13 7}
126. Qh6+ {+0.00/21 7} Kg3 {+0.51/13 7} 127. Qah1 {+0.00/24 8} Kf2
{+0.51/13 7} 128. Qa1 {+0.00/24 11} Ke2 {+0.52/13 7} 129. Qh5 {+0.00/25 10}
Kd2 {+0.52/13 7} 130. Qh6 {+0.00/27 6} Ke2 {+0.51/13 7} 131. Qh5
{+0.00/31 8} Kd2 {+0.52/14 7} 132. Qh6 {+0.00/32 8} Nc4 {+0.50/13 7} 133.
Qhh1 {+0.00/26 7} Ke2 {+0.51/14 7} 134. Qah8 {+0.00/25 8} Nce5 {+0.51/13 7}
135. Q1h3 {+0.00/24 7} Kd2 {+0.53/12 7} 136. Q8h6 {+0.00/26 7} Kc2
{+0.53/13 7} 137. Qh7 {-0.98/23 13} Nb4+ {+0.49/14 7} 138. Ka3
{-0.98/24 2.6} Nd2 {+0.50/15 7} 139. Qh2 {-0.98/26 9} N5c4+ {+0.52/14 7}
140. Ka4 {-0.98/12 0.1} Ned5 {+0.52/14 7} 141. Qg7 {-0.98/24 8} Nc3+
{+0.53/15 7} 142. Qxc3+ {-0.98/12 0.1} Kxc3 {+0.53/16 7} 143. Qh8+
{-1.01/25 6} Nde5 {+0.53/16 7} 144. Qh1 {-1.03/25 19} Nd5 {+0.53/15 9} 145.
Qh3+ {-0.98/22 6} Kd4 {+0.54/14 7} 146. Qh8 {-1.03/24 6} Ne4 {+0.54/13 7}
147. Qh4 {-1.03/23 5} Nd2 {+0.54/13 8} 148. Qh8 {-12.98/24 13} Nc5+
{+0.54/13 7} 149. Kb5 {-13.13/25 1.3} Nde4 {+0.54/14 7} 150. Qh4
{-1.03/21 7} Ne7 {+0.54/13 8} 151. Kb6 {-1.01/21 6} Nd5+ {+0.54/13 8} 152.
Kb5 {+0.00/65 14} Nc3+ {+0.55/14 8} 153. Kb4 {-1.03/22 0.7} Ned3+
{+0.54/13 9} 154. Ka5 {-1.03/22 1.8} Kc4 {+0.54/14 10} 155. Qh5
{-1.03/21 2.0} Nd5 {+0.55/14 8} 156. Qg4 {-17.51/22 6} Nb3+ {+15.06/16 8}
157. Ka6 {-99.66/19 1.4} Ndc5+ {+15.52/17 8} 158. Ka7 {-17.36/12 0.1} Nd4
{+15.67/18 10} 159. Qg8 {-99.74/21 2.6} Nf6 {+99.67/16 13} 160. Qf7
{-99.80/21 3} Nb5+ {+99.55/15 8} 161. Ka8 {-99.80/25 16} Kb4 {+99.65/14 12}
162. Qg7 {-99.82/26 10} Nb6+ {+99.83/13 6} 163. Kb8 {-99.84/29 9} Nfd7+
{+99.85/14 7} 164. Qxd7 {-99.86/34 10} Ncxd7+ {+99.87/14 2.0} 165. Kb7
{-99.88/37 10} Kc5 {+99.89/12 0.1} 166. Ka6 {-99.90/42 8} Ne5
{+99.91/10 0.1} 167. Kb7 {-99.86/32 10} Nc6 {+99.93/8 0.1} 168. Ka6
{-99.94/50 8} Nc8 {+99.95/6 0.1} 169. Kb7 {-99.96/100 0.2} Ncd6+
{+99.97/4 0.1} 170. Ka6 {-99.98/100 0.1} Nc7# {+99.99/2 0.1}
{Xboard adjudication: Checkmate} 0-1

Even the weak QueeNy manages to cause Stockfish great trouble with only 6 Knights; it manouevres it into this position, from which Tqueeny easily wins, but then unfortunately blunders away the Pawn and finally loses, being outserached more than 10 ply.

[d]8/1Q1n2Q1/5n2/3nnk2/4pnn1/8/8/KQ6 b - - 11 43

So testing against other engines with 7 Knights is really pointless. They are just too much biased against doing Q-for-2N trades, which means a certain loss. Even against 6 Knights.

I really believe KNNNNKQ is usually won. The tablebase might say 41% wins with knights-to-move, after removal of all mate-in-1 and 1. KxQ position, but that is really misleading. There will also be many positions where one of the Knights is doomed, because of the Queen forking or skewering unprotected Knights or King, and positions where an isolated outpost Knight cannot be protected. (Queens are very efficient driving a single Knight to the edge and capturing it there, without King help.)

Most quiet positions, with Knights grouped around the King, are probably won.

This is already exaggerated. 6Ns can never win against 3 Qs, even from your position with only central pawns. But the player with the Qs needs not push its pawns forward: you leave all of the where they are to protect the king, the king stays precisely where it is, and only the queens move. No chance for the knights here.
You see, it is all about piece defence, in the final position you posted the 6 knights defend each other some 10 times in all, that is tremendous, something you will never watch in a real game.

[Lyudmil Tsvetkov]

If the concern is that the King fortress of the Knights is to strong, you can always start from this position:
[d]nnknnnnn/4pppp/8/8/8/8/4PPPP/4QQQK b
In self-play Tqueeny manages to force two Q-for-2N trades before the Knights get a chance to deploy properly around the King. It doesn't help the Queens side much, however. (And when Stockfish played the Queens, it didn't stand a chance at all.)

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.28"]
[Round "-"]
[White "TQueeny 64-bit"]
[Black "TQueeny 64-bit"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "nnknnnnn/4pppp/8/8/8/8/4PPPP/4QQQK b - - 11 1"]
[SetUp "1"]
1... Nhg6 {+1.75/17 6} 2. h4 {-1.72/17 7} Nac7 {+1.79/18 6} 3. h5
{-1.96/17 7} Nf4 {+1.93/17 10} 4. g3 {-1.99/16 7} N4e6 {+1.86/19 6} 5. f4
{-1.66/17 11} Nfd7 {+1.87/17 6} 6. Qb1 {-2.04/17 15} Ngf6 {+2.18/18 9} 7.
Qf3 {-2.04/16 8} h6 {+2.00/17 14} 8. Qc2 {-1.93/18 6} Nd6 {+2.07/18 6} 9.
f5 {-1.72/18 8} Nef8 {+1.17/17 9} 10. Qgc1 {+0.00/18 6} Nfe8 {+0.01/18 7}
11. Qfc3 {-0.22/19 6} Nbc6 {+0.25/20 6} 12. Qxc6 {-0.22/20 6} Nxc6
{+0.35/21 6} 13. Qxc6 {-0.37/20 6} Kd8 {+0.35/19 6} 14. Qb1 {-0.50/18 14}
e6 {+0.42/19 6} 15. g4 {-0.41/18 6} Ne5 {+0.58/19 6} 16. Qb8+ {-0.57/19 6}
Ke7 {+0.53/22 6} 17. Qxd6+ {-0.53/20 6} Nxd6 {+0.59/23 6} 18. Qxc7+
{-0.59/22 6} Nfd7 {+0.60/23 6} 19. Qc3 {-0.57/22 6} exf5 {+0.59/21 6} 20.
gxf5 {-0.64/22 6} Nxf5 {+0.65/21 6} 21. Qa3+ {-0.77/21 11} Ke6 {+0.67/20 7}
22. Kg1 {-0.74/20 9} g5 {+0.75/19 7} 23. hxg6 {-0.74/21 6} fxg6
{+0.74/20 7} 24. e4 {-0.88/19 8} Nh4 {+1.09/19 9} 25. Qh3+ {-1.17/19 6} Kf7
{+1.46/21 7} 26. Kf1 {-1.44/21 6} g5 {+1.61/21 7} 27. Ke2 {-1.63/21 6} Nf6
{+1.73/20 7} 28. Qh2 {-1.79/20 13} Nfg4 {+1.76/20 7} 29. Qh1 {-1.94/22 6}
h5 {+1.94/21 7} 30. Qd1 {-1.96/20 9} Nhf3 {+2.50/20 7} 31. Qd5+
{-2.76/19 10} Kg7 {+3.14/22 7} 32. Qb7+ {-3.25/21 11} Kg6 {+3.42/23 7} 33.
Kf1 {-3.40/21 8} h4 {+3.59/20 7} 34. Kg2 {-3.35/20 5} Nf6 {+4.25/20 7} 35.
Qb1 {-3.89/19 5} g4 {+8.50/19 8} 36. Kh1 {-5.80/19 6} g3 {+11.30/20 8} 37.
Kg2 {-12.97/19 13} Kh5 {+15.32/18 8} 38. Qb8 {-15.08/17 3} Ne1+
{+17.95/18 10} 39. Kf1 {-20.10/19 8} g2+ {+18.85/18 9} 40. Ke2
{-21.59/16 0.1} N1d3 {+22.00/18 10} 41. Qa7 {-21.21/17 15} Nf4+
{+22.90/17 14} 42. Kd1 {-24.24/18 16} h3 {+24.02/17 8} 43. Qg7
{-28.36/18 24} Neg4 {+28.21/16 18} 44. Kc2 {-28.21/16 16} g1=Q
{+28.39/16 11} 45. Qf7+ {-99.40/16 22} Kh4 {+34.85/15 6} 46. Qf8
{-35.95/14 10} h2 {+99.65/13 6} 47. Qh8+ {-99.42/13 20} N4h5 {+99.89/10 7}
48. Kb3 {-99.70/11 18} Qb6+ {+99.91/9 7} 49. Ka3 {-99.92/9 0.9} h1=Q
{+99.93/8 0.1} 50. Qxf6+ {-99.94/7 0.3} Nhxf6 {+99.95/6 0.1} 51. Ka2
{-99.96/5 0.1} Qhb1+ {+99.97/4 0.1} 52. Ka3 {-99.98/3 0.1} Qa1#
{+99.99/2 0.1}
{Xboard adjudication: Checkmate} 0-1

This is a biassed position: knights gain much from play on one side, the queens from larger span of pawns.

[hgm]

And you don't think the fact that the Knights are totally undeveloped, do not protect each other, and that the black King is wide in the open is sufficient compensation for that? (Not to mention that the Queens have a material advantage of +650 cP in terms of naive piece-value counting...)

The spread-out / undeveloped case was treated 3 postings earlier. It did not help the Queens much. But you cannot have it both ways: the King out in the open AND spread out Pawns. Or do you really want to start with the black King on e6 before a closed Pawn rank, to give those poor Queens a chance?

You started from another position - with queens on b1 and g1 instead of a1 and h1. I think a1 and h1, replacing the rooks and providing some symmetry, are more natural locations.

I always used this position as starting position for Charge of the Light Brigade. Are you claiming that it would make any difference whether the Queens start on the b/g file rather than the a/h file? If so, the position would not be quiet...

But you are right, it would have been better to force different games by shuffling the Queens on the back rank (7*6*5/1*2*3 = 35 possibilities). Then I would not have had to force possibly losing moves on black. You do that, then.

You do realize that the losses are not really from this position, but just because I forced a move on black that created another position that happened to be lost? That with inaccurate play a fully won position can be lost is hardly news.

And last, but not least: you claimed this position was an easy win for the Queens. Which one of us was closer to the truth? I think this absolutely convincingly shows that you were wrong. Which is all that matters.

Even with this position your results were not absolutely convincing, but you initially claimed the position is fully lost for the queens, which, even with your tests, is not confirmed.
There is also the highly relevant possibility that TQueeny does not handle optimally the queen side in terms of evaluation.

[petero2]

I don't know if Tqueeny randomizes

It only randomizes if you set the strength parameter to less than 1000, which I guess you did not do. I don't know how the strength setting would affect play in these imbalances though, so I suggest not to change it.

So at the level of play exercised by Tqueeny (which seems the best we have at the moment), the position seems to be overwhelmingly won for the Knights.

I think it would also be interesting to modify stockfish, which is more than 300 elo stronger than texel, to understand this imbalance. Then it could be tested if TQueeny is still able to win with the knights, and if stockfish wins against itself with the knights.

Btw, I got the impression that Tqueeny is a bit reluctant to march its King towards the center. This might make life more difficult for the Knights than needed.

This may be the case. A bit simplified, texel has a scale factor for king safety that goes to zero in the end game. In TQueeny I modified the calculation of this factor so that it gets much smaller for the knight side, thus encouraging it to centralize its king and not be as much concerned about queens attacking squares close to the king. I did not tune this though, so it is possible that TQueeny is still too afraid to centralized the king.

Texel, and hence TQueeny, also has a text interface, which among other things prints the evaluation score. For example:

Code: Select all

$ ./tqueeny txt
Eval: 0.00
    +----+----+----+----+----+----+----+----+
    | *R | *N | *B | *Q | *K | *B | *N | *R |
    +----+----+----+----+----+----+----+----+
    | *P | *P | *P | *P | *P | *P | *P | *P |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |  P |  P |  P |  P |  P |  P |  P |  P |
    +----+----+----+----+----+----+----+----+
    |  R |  N |  B |  Q |  K |  B |  N |  R |
    +----+----+----+----+----+----+----+----+
Enter move (white):setpos nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1
Eval: -1.41
    +----+----+----+----+----+----+----+----+
    | *N | *N | *N | *N | *K | *N | *N | *N |
    +----+----+----+----+----+----+----+----+
    | *P | *P | *P | *P | *P | *P | *P | *P |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |  P |  P |  P |  P |  P |  P |  P |  P |
    +----+----+----+----+----+----+----+----+
    |  Q |    | .. |  Q |  K |    | .. |  Q |
    +----+----+----+----+----+----+----+----+
Enter move (white):setpos nnnn1nnn/pppppppp/6k1/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1
Eval: -1.17
    +----+----+----+----+----+----+----+----+
    | *N | *N | *N | *N |    | *N | *N | *N |
    +----+----+----+----+----+----+----+----+
    | *P | *P | *P | *P | *P | *P | *P | *P |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. | *K | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |  P |  P |  P |  P |  P |  P |  P |  P |
    +----+----+----+----+----+----+----+----+
    |  Q |    | .. |  Q |  K |    | .. |  Q |
    +----+----+----+----+----+----+----+----+
Enter move (white):setpos nnnn1nnn/pppppppp/8/4k3/8/8/PPPPPPPP/Q2QK2Q w - - 0 1
Eval: -1.49
    +----+----+----+----+----+----+----+----+
    | *N | *N | *N | *N |    | *N | *N | *N |
    +----+----+----+----+----+----+----+----+
    | *P | *P | *P | *P | *P | *P | *P | *P |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | *K |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |    | .. |    | .. |    | .. |    | .. |
    +----+----+----+----+----+----+----+----+
    | .. |    | .. |    | .. |    | .. |    |
    +----+----+----+----+----+----+----+----+
    |  P |  P |  P |  P |  P |  P |  P |  P |
    +----+----+----+----+----+----+----+----+
    |  Q |    | .. |  Q |  K |    | .. |  Q |
    +----+----+----+----+----+----+----+----+
Enter move (white):

The reported scores are from white's perspective. The Kg6 position has the worst evaluation for black, because the king is not much closer to the center than it is on e8, but it has no pawn shield. The Ke5 positions is about equal to the Ke8 position. Apparently the value of the pawn shield is about equal to the value of centralizing the king.

The Ke5 position is of course totally lost for black because the queens will inflict serious damage before the king has a chance to get to safety. A more ambitious king safety evaluation should also take knight shields into account.