A balanced approach to imbalances

[Lyudmil Tsvetkov]

[d]2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1
I think white wins here easily, maybe someone could check. I tried to create as realistic position as possible, it seems that all knights defend well, but black should still lose.

And how wrong you are!

Let's have Stockfish play it against a 2400-Elo engine:

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.23"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. Qb7 {+7.41/16} Nb5 {+6.55/15 5} 2. Qa6 {+4.96/19 19} c6 {+7.00/14 6} 3.
Qbd1 {+6.10/17 16} Nbd5 {+7.44/13 4} 4. Qh2 {+5.37/18 10} Nhf5 {+8.97/13 6}
5. Kf2 {+4.84/18 9} Nbxd4 {+9.25/14 6} 6. b5 {+3.81/18 10} cxb5
{+10.62/14 6} 7. Qdh1 {+2.88/19 4} Ne5 {+11.39/14 8} 8. Qa5 {+1.41/19 13}
Nfg6 {+11.66/13 8} 9. Qa3 {+0.00/18 8} Ngf4 {+13.13/14 11} 10. Qb1
{-2.80/18 1.0} Ncd6 {+12.63/13 4} 11. Qhh1 {-4.90/16 6} Ndc4
{+16.14/13 2.2} 12. Qa8+ {-6.76/18 6} Kf7 {+16.27/15 5} 13. Qhh8
{-9.45/21 9} Nfd3+ {+16.77/14 8} 14. Qxd3 {-10.08/20 2.6} Nxd3+
{+16.87/15 8} 15. Kg1 {-10.78/21 3} Nxf3+ {+16.83/14 5} 16. Kh1
{-5.21/14 2.0} N3d4 {+16.85/14 6} 17. Qhe8+ {-6.70/16 7} Ke6 {+16.94/15 8}
18. Qeb8 {-10.02/20 7} g5 {+17.02/14 8} 19. Qa6+ {-11.85/21 17} Nfd6
{+16.88/10 0.1} 20. Qa2 {-13.11/20 9} Nef5 {+17.04/13 5} 21. Qb1
{-12.00/18 8} N5f4 {+17.15/13 2.2} 22. Qa2 {-14.62/20 5} Ng3+ {+26.27/15 7}
23. Kh2 {-104.13/21 1.9} Nge4 {+26.42/15 8} 24. Kh1 {-104.13/21 31} Kf5
{+31.39/10 0.1} 25. Qba8 {-99.84/18 5} Nf3 {+319.92/16 9} 26. Qd5+
{-99.86/27 5} Nxd5 {+319.93/20 9} 27. Qg2 {-99.88/34 0.1} Nef2+
{+319.94/22 7} 28. Qxf2 {-99.90/70 5} Nxf2+ {+319.95/26 7} 29. Kg2
{-99.92/100 0.1} Nf4+ {+319.96/26 8} 30. Kf1 {-99.94/100 0.2} Ncd2+
{+319.96/26 6} 31. Kxf2 {-99.94/100 0.2} N6e4+ {+319.97/30 9} 32. Ke3
{-99.96/100 0.1} Nc4+ {+319.98/33 5} 33. Kxf3 {-99.98/100 0.1} g4#
{+319.99/42 11}
{Xboard adjudication: Checkmate} 0-1

[d]8/8/5p2/1p3k2/2n1nnp1/5K2/8/8 w - - 0 34
Poor Stockfish... Pickled and packed!

Initially Stockfish sees things your way (+7.41). Queeny already knows better. But Stockfish starts revising its score downward very quickly, as the loss of the first of its Queens comes within the horizon.

Promoting wasn't even necessary. Just go for the throat.

If you want to try it yourself, you can try this with your favorite engine. The recommended opponent is Queeny. It would beat Stockfish probably even with 6 Knights against 3 Queens!

I really do not have the opportunity to test the position against Queeny (although I would have liked to, maybe someone else could try instead), but my impression is that white should win. Stockfish does not even try to exchange a queen for 2 knights, and 9 moves, until Stockfish displays a draw score, are a lot of time for a tactically strong engine, if it knows how to proceed. For me, it would be more difficult, as the position is very peculiar and I am not tactically strong. Still, apart from Qb7, b5 might also be a good start. I am sure white wins that.

On the other hand, this position, if black fares well in any way, might be a testimony that not only undefended pieces, but also the way the pieces are defended among each other is very important. You could gain a couple of pawns' material only based on defence among pieces. And I think it is really the defence among the black knights that matters, making it difficult for white to proceed without a clear plan, rather than the squares those knights take from the queens.

I am astonished by Queeny play, but even more so by its evaluation. At ply 1 it sees itself as enormously winning, while Stockfish does the same for itself. After 9 moves/18 plies Stockfish already sees a draw. Is evaluation that important?

[Lyudmil Tsvetkov]

Interesting, HG, what does Queeny say about the following position:

[d]2bn1bk1/2p1bnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1

Just changed 3 knights for 3 bishops, which by presumption should favour black, control of squares for black should have increased, while mutual defence among pieces decreased. Does Stockfish lose even that?

[hgm]

I am astonished by Queeny play, but even more so by its evaluation. At ply 1 it sees itself as enormously winning, while Stockfish does the same for itself. After 9 moves/18 plies Stockfish already sees a draw. Is evaluation that important?

Well, QueeNy probably mis-evaluates too, in the other direction. To get an engine that tries to execute your plan, I just took one of my engines (Spartacus), and changed the value of the Knight to 5 (Q = 9.5). So it would shy away from the trades you want to make, and keep all its Knights doubly protected.

But the first few Knights would certainly not be worth that much; KQKNN is badly lost for the Knights, as we all know. It is just that with the simplistic sum-of-piece-values evaluations by QueeNy, the reduction of the depreciation that the remaining two Queens suffered (according to the theory of the elephantiasis effect) from the presence of the Knights is accounted in the Knight value. With one or no remaining Queens the Queen side would not get such compensation for removing two Knights, so the Knights would seem much less valuable.

The proper way to implement it would be to add an eval cross term, const * nrOfWhiteQueen * nrOfBlackKnights. But as QueeNy never allows the opponent to trade Q vs 2N, you don't have to worry much about the values for the second and third such trade. The game will never get to the KQKNN (+Pawns) stage, so that QueeNy thinks it would still be bad to trade his last two Knights for Q doesn't hurt it. It just gives a constant overestimate of its own position, by overvaluing his Knights that will be last to go.

I admit that Stockfish seems especially bad at this; it will never trade Q for 2N even if you offer it such a trade, let alone that it will try to force the opportunity. So time-odds games with QueeNy are actually much more significant, because QueeNy's evaluation is designed to seek such trades, and when you give it superior tactical ability when playing with the Queens, by giving it lots of time to think, against a much less deep searching opponent QueeNy, it will still lose against 7 Knights. It is just to easy to ktep all the Knights twice protected, if you have 7 of them (plus a King). Against 6 Knights, QueeNy can defeat itself even when the Knights get much more time to think. There just seems no way to keep all the Knights twice protected in that case, no matter how much deeper you search than the opponent.

About your position with the Bishops: I cannot try that now, as it is already way past my bed time, but in general Bishops are way poorer at this then Knights. I did try 7 Bishops against 3 Queens in the past several times, and the Bishops are toast! The problem seems to be that to protect each other, they are also in each other's way. The B-pair bonus does not seem so much a bonus for having Bishops on different colors, as well a penalty for having them on the same, where they block each other. With two Bishops you would not know the difference between base-value 3.25 + pair bonus 0.5 and base-value 3.5 + same-color penalty 0.5. But with 4 Bishops on one color you have 6 same-color pairs, which totals to 11, or only 2.75 per Bishop. I never tried with mixed Bishops and Knights. (But that doesn't have to stop you! It is easy enough to play two engines against each other. )

[bob]

I think you left out one of the most fundamental aspect of imbalances, which is Reinhard Scharnagle's 'elephantiasis effect'. The factors you take into account would have a very hard time explaining why 7 Knights are so much stronger than 3 Queens, while any reasonable set of piece values would predict exactly the opposite. Of course I realize this is an extreme situation, which would never occur in practice, but that is just to magnify the effect such that most engines would mis-evaluate it by about 9 Pawns.

This huge value shows that sizable corrections must remain even when you scale it down to realistic imbalances, for instance why the Queen side with Q+R vs R+B+B+N should seek trading the Rooks.

Valuable pieces devaluate in the presence of enemy lower pieces, and each extra lower-valued opponent suppresses its value further, because it interdicts access for it to part of the board.

Funny story. We were playing a one-day-to-be GM back in the early 80's. and we beat him game after game after game. Until one game came along where he simplified and was winning easily. But he wanted a little showmanship, so he promoted a second pawn to a queen, and then a third, but rather than stopping there, he promoted a 4th, and the game was an instant stalemate. He wanted to take the move back, we said "no way."

I think it was Kamsky (who is a good guy, btw) that was playing Crafty back in the middle 90's before hardware got so fast, and he could win maybe one out of every 4 games, maybe. But in one game he did the same as above, except he did not stalemate crafty and won with a ridiculous material advantage.

Edit: memory reminded me it was Kamsky, not Anand. I made the change above.

[lucasart]

[d]2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1
I think white wins here easily, maybe someone could check. I tried to create as realistic position as possible, it seems that all knights defend well, but black should still lose.

And how wrong you are!

Let's have Stockfish play it against a 2400-Elo engine:

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.23"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. Qb7 {+7.41/16} Nb5 {+6.55/15 5} 2. Qa6 {+4.96/19 19} c6 {+7.00/14 6} 3.
Qbd1 {+6.10/17 16} Nbd5 {+7.44/13 4} 4. Qh2 {+5.37/18 10} Nhf5 {+8.97/13 6}
5. Kf2 {+4.84/18 9} Nbxd4 {+9.25/14 6} 6. b5 {+3.81/18 10} cxb5
{+10.62/14 6} 7. Qdh1 {+2.88/19 4} Ne5 {+11.39/14 8} 8. Qa5 {+1.41/19 13}
Nfg6 {+11.66/13 8} 9. Qa3 {+0.00/18 8} Ngf4 {+13.13/14 11} 10. Qb1
{-2.80/18 1.0} Ncd6 {+12.63/13 4} 11. Qhh1 {-4.90/16 6} Ndc4
{+16.14/13 2.2} 12. Qa8+ {-6.76/18 6} Kf7 {+16.27/15 5} 13. Qhh8
{-9.45/21 9} Nfd3+ {+16.77/14 8} 14. Qxd3 {-10.08/20 2.6} Nxd3+
{+16.87/15 8} 15. Kg1 {-10.78/21 3} Nxf3+ {+16.83/14 5} 16. Kh1
{-5.21/14 2.0} N3d4 {+16.85/14 6} 17. Qhe8+ {-6.70/16 7} Ke6 {+16.94/15 8}
18. Qeb8 {-10.02/20 7} g5 {+17.02/14 8} 19. Qa6+ {-11.85/21 17} Nfd6
{+16.88/10 0.1} 20. Qa2 {-13.11/20 9} Nef5 {+17.04/13 5} 21. Qb1
{-12.00/18 8} N5f4 {+17.15/13 2.2} 22. Qa2 {-14.62/20 5} Ng3+ {+26.27/15 7}
23. Kh2 {-104.13/21 1.9} Nge4 {+26.42/15 8} 24. Kh1 {-104.13/21 31} Kf5
{+31.39/10 0.1} 25. Qba8 {-99.84/18 5} Nf3 {+319.92/16 9} 26. Qd5+
{-99.86/27 5} Nxd5 {+319.93/20 9} 27. Qg2 {-99.88/34 0.1} Nef2+
{+319.94/22 7} 28. Qxf2 {-99.90/70 5} Nxf2+ {+319.95/26 7} 29. Kg2
{-99.92/100 0.1} Nf4+ {+319.96/26 8} 30. Kf1 {-99.94/100 0.2} Ncd2+
{+319.96/26 6} 31. Kxf2 {-99.94/100 0.2} N6e4+ {+319.97/30 9} 32. Ke3
{-99.96/100 0.1} Nc4+ {+319.98/33 5} 33. Kxf3 {-99.98/100 0.1} g4#
{+319.99/42 11}
{Xboard adjudication: Checkmate} 0-1

[d]8/8/5p2/1p3k2/2n1nnp1/5K2/8/8 w - - 0 34
Poor Stockfish... Pickled and packed!

Initially Stockfish sees things your way (+7.41). Queeny already knows better. But Stockfish starts revising its score downward very quickly, as the loss of the first of its Queens comes within the horizon.

Promoting wasn't even necessary. Just go for the throat.

If you want to try it yourself, you can try this with your favorite engine. The recommended opponent is Queeny. It would beat Stockfish probably even with 6 Knights against 3 Queens!

Thanks HGM. I've certyainly learnt something today. When I looked at the position, I naively believed in the queens and mateial superiority.

DiscoCheck is completely stupid and has no material imbalance eval. With no search, it sees an eval of +770cp for white, and with every depth the score decreases:

Code: Select all

info score cp 785 depth 1 nodes 63 time 0 pv d2a2
info score cp 736 depth 2 nodes 225 time 0 pv d2a2 e7d5
info score cp 752 depth 3 nodes 1421 time 2 pv d2a2 a7c6 a2a6
info score cp 725 depth 4 nodes 3463 time 5 pv b4b5 h6f5 d2a2 c8d6
info score cp 715 depth 5 nodes 11206 time 15 pv b3a2 a7b5 d2d3 b5d6 e4e2
info score upperbound 699 depth 6 nodes 21168 time 21
info score cp 698 depth 6 nodes 29590 time 26 pv f3f4 e7c6 e4g2 c8d6 d2d3 h6f5
info score cp 680 depth 7 nodes 67019 time 51 pv b3a2 e7d5 e4d3 f7d6 d2g2 a7b5 a2b3
info score upperbound 664 depth 8 nodes 106717 time 74
info score cp 670 depth 8 nodes 138494 time 93 pv e4e2 e7d5 e2a6 f7g5 d2d3 a7c6 a6c8 b6c8
info score cp 669 depth 9 nodes 246001 time 162 pv e4d3 c8d6 b3a2 b6c4 d2e1 a7c8 a2a8 h6f5 f3f4
info score upperbound 653 depth 10 nodes 274375 time 178
info score upperbound 637 depth 10 nodes 364145 time 232
info score cp 622 depth 10 nodes 519190 time 327 pv d2h2 e7d5 e4d3 c8d6 h2c2 d5f4 d3d2 b6d5 c2c5 a7b5
info score cp 644 depth 11 nodes 854366 time 535 pv b3c2 h6f5 c2c7 a7b5 c7b8 f7g5 d2a2 f8e6 e4b7 g8f7 f3f4 g5h3 g1g2
info score upperbound 628 depth 12 nodes 1058889 time 645
info score upperbound 612 depth 12 nodes 1162677 time 704
info score upperbound 580 depth 12 nodes 1483559 time 890
info score cp 556 depth 12 nodes 3118236 time 1840 pv f3f4 h6f5 e4h1 a7c6 h1h5 g7g6 h5h1 f5d4 b3h3 c8d6 d2f2 e7f5
info score cp 533 depth 13 nodes 7381773 time 4378 pv f3f4 h6f5 b3h3 a7c6 d2h2 c8d6 e4g2 c6b4 g1h1 f5d4 h3c3 e7c6 h2h5
info score cp 528 depth 14 nodes 10565773 time 6101 pv e4h4 e7f5 h4h5 a7b5 b3c2 b5d4 c2c7 f7e5 d2a2 f8e6 h5e8 g8h7 c7b8 d4f3 g1h1 e6f4 a2c2 f3d4
info score cp 527 depth 15 nodes 13882843 time 7848 pv d2h2 a7b5 h2h5 e7f5 f3f4 b5d4 b3d3 f8e6 h5h2 c8d6 e4g2 b6c4 g1h1 c4e3 g2g6
info score upperbound 511 depth 16 nodes 20926276 time 11432
info score upperbound 495 depth 16 nodes 29947662 time 16149
info score cp 486 depth 16 nodes 38535535 time 20694 pv e4h4 a7b5 h4h5 c8d6 f3f4 e7d5 b3h3 d6e4 d2c1 b5d4 h3d3 f8e6 d3e4 d5f4 h5h2 d4e2 h2e2 f4e2 e4e2
info score cp 480 depth 17 nodes 63234891 time 34155 pv e4h4 a7b5 d2h2 e7f5 h4f2 f5d4 b3a2 f8e6 g1h1 f7g5 h2g2 g5f3 g2f3 d4f3 a2e6 g8f8 f2e2 c8d6
info score upperbound 464 depth 18 nodes 95133530 time 50820
info score cp 477 depth 18 nodes 132669256 time 71453 pv b4b5 h6f5 e4c2 c8d6 c2c7 b6c4 c7c4 d6c4 b3c4 a7c8 d2a2 c8d6 c4b4 e7g6 b5b6 g6h4 g1f2 f8d7 a2a8 d7f8
info score upperbound 445 depth 19 nodes 172339255 time 91906
info score cp 434 depth 19 nodes 204673287 time 108326 pv e4h4 a7b5 d2h2 e7f5 h4f2 f5d4 b3a2 f8e6 g1h1 f7g5 h2g3 h6f7 g3g4 d4f3 f2f1 b5d4 g4h5 c8d6 f1d3
info score cp 423 depth 20 nodes 273303809 time 143787 pv e4h4 a7b5 d2g2 h6f5 h4f6 b6d5 f6a6 b5d4 b3b1 f5h4 g2h3 h4f3 g1h1 f7g5 h3g2 d5b4 b1b4 c8d6 a6a8 e7f5 b4c5
info score upperbound 407 depth 21 nodes 370413608 time 193330

Perhaps a very basic material imbalance would be to look at material and also number of pieces: material is overwhelming positive for white, but number of pieces give black some compeisation. Now the trick is to find the right formula and tune it. Very hard work

[hgm]

Well, number of pieces will certainly have an effect, as having more pieces must mean their average value is smaller for the same total value. But the fundamental effect seems to be lower-valued pieces interdicting board access to higher-valued pieces in a much more efficient way then they higher-valued pieces doing the same to the lower-valued pieces (which can simply be protected). This suggests the material eval has to contain a non-linear term

white_eval += SUM c_ij (B_i * W_j - W_i * B_j)

where i and j run over all piece types, W_i and B_i are the number of white and black pieces of type i, respectively, and c_ij are constants. When the piece values V_i <= V_j, c_ij = 0 because the j-pieces are no threat to protected i-pieces. It is a matter of taste whether you interpret these terms as a depreciation of the value of the higher (white) pieces to V_i - SUM(j) c_ij B_j due to all lower (black) pieces j, or whether you interpret it as an increase of the value of lower pieces to V_i + SUM(j) c_ji B_j when there are higher pieces j to harass.

In principle the c_ij are all independent eval parameters, and could be empirically measured. There are quite a lot of them however, so it would be nice if there was some logic to them, so that all the c_ij could be determined from just a few more basic parameters.

I discussed this with Larry Kaufman a few years ago. It seems reasonable that weaker pieces would present less of a threat to the same very strong pieces as a slightly less weak piece would do, and that the c_ij should be proportional to the base value of the weaker piece. After all the base value sort of expresses how dangerous the piece is, tactically. So a Queen would suffer more from the presence of two opponent Rooks than from two opponent Knights. How much higher pieces would devaluate by the presence of the same set of lower-valued pieces is less clear; it could be a constant absolute amount (e.g. a Rook would suffer as much from 3 Knights as a Queen would), or a constant fraction of their base value (a Queen would suffer nearly twice as much from 3 Knights as a Rook would, because the Knight interdicts their access to ~20 board squares = 33% of the board, so they might lose 33% of their value).

We sort of came to the conclusion that strong pieces should suffer relatively less than weaker pieces from the same fraction of the board being inaccessible to them, because, being stronger, it would be easier fro them to accomplish what they want to accomplish (e.g. attack unprotected or insufficiently protected pieces, deliver checks) from the part of the board that is not interdicted to them. So it seemed reasonable to have some dependence in-between a constant and a constant fraction, e.g. proportional to the square root of the strong-piece value in absolute terms. I.e.

c_ij = 0 (for V_i <= V_j)
c_ij = C * V_i ^ N * V_j (for V_i > V_j)

with 'master constants' C and N (where the latter is expected to lie between 0 and 1). This would introduce only two parameters, which could be determined empirically (with N = 0.5 as a first guess).

[Lyudmil Tsvetkov]

Well, number of pieces will certainly have an effect, as having more pieces must mean their average value is smaller for the same total value. But the fundamental effect seems to be lower-valued pieces interdicting board access to higher-valued pieces in a much more efficient way then they higher-valued pieces doing the same to the lower-valued pieces (which can simply be protected). This suggests the material eval has to contain a non-linear term

white_eval += SUM c_ij (B_i * W_j - W_i * B_j)

where i and j run over all piece types, W_i and B_i are the number of white and black pieces of type i, respectively, and c_ij are constants. When the piece values V_i <= V_j, c_ij = 0 because the j-pieces are no threat to protected i-pieces. It is a matter of taste whether you interpret these terms as a depreciation of the value of the higher (white) pieces to V_i - SUM(j) c_ij B_j due to all lower (black) pieces j, or whether you interpret it as an increase of the value of lower pieces to V_i + SUM(j) c_ji B_j when there are higher pieces j to harass.

In principle the c_ij are all independent eval parameters, and could be empirically measured. There are quite a lot of them however, so it would be nice if there was some logic to them, so that all the c_ij could be determined from just a few more basic parameters.

I discussed this with Larry Kaufman a few years ago. It seems reasonable that weaker pieces would present less of a threat to the same very strong pieces as a slightly less weak piece would do, and that the c_ij should be proportional to the base value of the weaker piece. After all the base value sort of expresses how dangerous the piece is, tactically. So a Queen would suffer more from the presence of two opponent Rooks than from two opponent Knights. How much higher pieces would devaluate by the presence of the same set of lower-valued pieces is less clear; it could be a constant absolute amount (e.g. a Rook would suffer as much from 3 Knights as a Queen would), or a constant fraction of their base value (a Queen would suffer nearly twice as much from 3 Knights as a Rook would, because the Knight interdicts their access to ~20 board squares = 33% of the board, so they might lose 33% of their value).

We sort of came to the conclusion that strong pieces should suffer relatively less than weaker pieces from the same fraction of the board being inaccessible to them, because, being stronger, it would be easier fro them to accomplish what they want to accomplish (e.g. attack unprotected or insufficiently protected pieces, deliver checks) from the part of the board that is not interdicted to them. So it seemed reasonable to have some dependence in-between a constant and a constant fraction, e.g. proportional to the square root of the strong-piece value in absolute terms. I.e.

c_ij = 0 (for V_i <= V_j)
c_ij = C * V_i ^ N * V_j (for V_i > V_j)

with 'master constants' C and N (where the latter is expected to lie between 0 and 1). This would introduce only two parameters, which could be determined empirically (with N = 0.5 as a first guess).

Hi HG,
thanks a lot for your theoretic conception, it is always good to have more approaches to test their validity, however, going back to the 7 knights and 3 queens position, let's analyse it a bit more objectively.

Do you see anything better for black than:
1.b5 (already threatening Qb7) Nhf5 2.Qda2 Nfd6 3.Qe7 (it takes just 3 moves, if you have the right plan, to exchange a queen for 2 knights) Ne7 4. Qa7 ?

I think this is almost forced and then you get the following position:

[d]5nk1/Q1p1nnp1/1n1n1p2/1P6/3P4/1Q3P2/8/6K1 b - - 0 4

How does Queeny evaluate that?
What about other engines?
I think it is evident white can not lose here, but is also better. It takes just 4 moves to change the picture completely, but you need to have a plan.

[hgm]

Against Stockfish it still wins in a quite straightforward way. Note that you don't just trade Q for 2N, but give up b5 in the process. Which is probably why QueeNy allows it, rather than just give up c7. (It would indeed play the black moves you suggested.) The five Knights just continue to strip you of your remaining Pawns. After one trade you are not home and dry yet. Five Knights still have the advantage over two Queens, especially in combination with Pawns.

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.24"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. b5 Nhf5 2. Qba2 Nfd6 3. Qxe7 Nxe7 {+6.77/16 4} 4. Qxa7 {+1.71/19 3} Nxb5
{+6.77/16 7} 5. Qb8 {+1.47/22 2.0} Nc6 {+8.27/16 5} 6. Qe8 {+1.31/22 4}
Nbxd4 {+8.32/16 8} 7. Qf2 {+0.86/22 21} Nd6 {+8.94/16 4} 8. Qh5
{+0.52/22 13} Nfe6 {+10.41/16 6} 9. Qa2 {+0.46/23 1.1} Kf8 {+10.41/15 4}
10. Qh8+ {+0.44/19 12} Ke7 {+10.92/16 5} 11. f4 {+0.12/21 8} Nb4
{+11.46/15 8} 12. Qb1 {+0.00/25 0.1} N4d5 {+11.63/14 4} 13. f5 {+0.00/27 6}
N4xf5 {+11.75/14 6} 14. Qe1 {-0.73/26 46} Nbc4 {+11.70/14 6} 15. Kh1
{+0.00/22 7} Nce3 {+11.99/14 5} 16. Qa1 {-1.97/18 11} Ned4 {+12.09/14 9}
17. Qg8 {-4.02/21 28} Ne2 {+12.24/14 7} 18. Qaa8 {-4.26/23 0.1} Nfg3+
{+11.28/15 5} 19. Kh2 {-4.18/23 2.5} Nef1+ {+11.26/15 5} 20. Kg2
{-6.12/24 20} Ndf4+ {+11.19/9 0.1} 21. Kf2 {-6.46/24 7} Nde4+ {+11.20/14 3}
22. Qxe4+ {-6.62/24 0.9} Nxe4+ {+11.23/19 7} 23. Kxf1 {-6.74/26 0.1} N2g3+
{+11.37/22 7} 24. Kg1 {-6.68/22 6} Ne6 {+11.51/22 5} 25. Qh8 {-7.03/22 7}
f5 {+11.58/22 7} 26. Kh2 {-7.49/24 0.1} f4 {+12.15/22 7} 27. Qa8
{-10.48/23 12} Nf1+ {+13.03/21 6} 28. Kh3 {-15.79/20 9} Nfd2 {+13.42/22 8}
29. Kg4 {-98.80/23 1.3} f3 {+13.60/22 7} 30. Qa3+ {-111.58/25 0.2} Kf6
{+14.83/22 6} 31. Qa1+ {-99.68/18 28} Kf7 {+18.23/18 0.1} 32. Kf5
{-99.70/17 9} f2 {+18.57/21 10} 33. Qa6 {-99.72/16 0.1} Nd6+ {+18.43/20 7}
34. Kg4 {-99.70/16 5} f1=Q {+19.66/21 8} 35. Qxf1+ {-99.78/19 5} Nxf1
{+26.53/23 11} 36. Kf3 {-99.80/22 0.1} Nd2+ {+27.15/22 15} 37. Ke2
{-99.82/26 0.1} N6e4 {+319.91/21 19} 38. Kd1 {-99.84/29 0.2} g5
{+319.92/21 11} 39. Kc2 {-99.86/34 0.1} g4 {+319.93/26 12} 40. Kb2
{-99.88/57 2.7} g3 {+319.94/28 17} 41. Ka3 {-99.90/100 0.1} g2
{+319.95/26 4} 42. Kb4 {-99.92/100 0.1} g1=Q {+319.96/26 8} 43. Ka3
{-99.94/100 0.1} Qc1+ {+319.97/24 5} 44. Ka4 {-99.96/100 0.2} Qc4+
{+319.98/28 5} 45. Ka3 {-99.98/100 0.1} Qb3# {+319.99/31 4}
{Xboard adjudication: Checkmate} 0-1

[d]8/2p2k2/4n3/8/4n3/Kq6/3n4/8 w - - 6 46
Perhaps more significant is when I let QueeNy also play the Queens, because then we know it will be trying to implement your plan, and strive for a second Q-vs-2N trade. I give it 40 moves/10 min, while the QueeNy playing the Knights only gets 1 min, to make sure the Queens have tactical superiority corresponding to a ~200-Elo stronger engine.

Indeed it puts up a better fight. (Could also be because the Knights play weaker now; against Stockfish I gave them 5 min.)

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.24"]
[Round "-"]
[White "QueeNy 0.16"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/600:40/60"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. b5 Nhf5 2. Qba2 Nfd6 3. Qxe7 Nxe7 4. Qxa7 {-6.91/16 9} Nxb5
{+6.66/14 2.4} 5. Qa6 {-6.77/17 19} Nbd6 {+6.81/10 0.1} 6. Qda2
{-6.96/15 12} Nc6 {+6.92/11 0.1} 7. Qd2 {-7.20/17 15} Nf5 {+8.07/14 1.8} 8.
Qf4 {-7.21/17 13} N7d6 {+7.28/10 0.1} 9. Qa2+ {-7.29/18 16} Kh8
{+7.32/13 0.2} 10. Qfh2+ {-7.28/18 16} Nh7 {+7.39/17 0.2} 11. Kf2
{-7.46/17 16} Ncxd4 {+7.34/9 0.1} 12. Qa7 {-7.33/17 14} Ne6 {+7.38/11 0.1}
13. Qb8+ {-7.43/16 16} Nbc8 {+7.40/15 0.5} 14. Qb3 {-7.45/17 16} Ned4
{+7.38/7 0.1} 15. Qb8 {-7.47/16 8} c5 {+7.44/15 1.9} 16. Qa8 {-7.60/17 10}
g6 {+7.58/9 0.1} 17. Qd5 {-7.67/17 11} c4 {+7.69/12 0.1} 18. Qa5
{-8.04/17 17} N4b5 {+8.04/11 0.2} 19. Qe1 {-8.11/16 11} Kg7 {+8.14/11 0.1}
20. f4 {-8.34/17 10} Nce7 {+8.31/11 0.1} 21. Qeh1 {-8.53/15 10} Nf8
{+8.44/12 0.1} 22. Ke1 {-8.94/16 16} c3 {+9.01/12 0.1} 23. Qc2
{-9.21/16 11} Ne6 {+9.63/14 1.6} 24. Qch2 {-9.93/17 12} Kf7 {+9.87/13 0.1}
25. Qa2 {-10.08/16 14} Nbd4 {+10.21/12 0.1} 26. Qh7+ {-11.25/16 10} Ng7
{+11.48/15 0.3} 27. Qh1 {-12.33/17 21} c2 {+12.41/15 4} 28. Kf2
{-12.84/17 22} Nh5 {+12.88/15 3} 29. Qa3 {-13.15/16 14} N6f5 {+13.03/9 0.1}
30. Qf1 {-13.51/16 19} Nhxf4 {+14.50/15 4} 31. Ke1 {-14.70/17 1:01} Ng3
{+14.86/8 0.1} 32. Qc4 {-15.86/18 18} Nge2 {+14.95/12 0.1} 33. Kd2
{-16.19/18 11} g5 {+16.24/9 0.1} 34. Qaa2 {-16.45/18 17} c1=Q+
{+16.89/10 0.1} 35. Qxc1 {-17.28/20 14} Nxc1 {+20.76/16 4} 36. Kxc1
{-21.10/22 14} g4 {+20.99/21 2.9} 37. Qh2 {-21.14/21 8} g3 {+20.98/20 6}
38. Qh7+ {-21.82/21 11} Ng7 {+21.70/16 0.1} 39. Qh1 {-22.02/21 23} g2
{+22.12/21 8} 40. Qh2 {-22.26/22 17} g1=Q+ {+22.29/20 5} 41. Qxg1
{-22.45/24 58} Nfe2+ {+22.79/22 2.5} 42. Kd1 {-22.40/22 14} Nxg1
{+29.68/20 0.9} 43. Kd2 {-22.66/22 11} f5 {+29.90/18 1.2} 44. Ke3
{-24.09/21 9} Nge2 {+30.13/18 1.2} 45. Kf2 {-30.84/21 9} f4 {+319.91/21 4}
46. Kg2 {-319.91/22 7} Ngf5 {+319.92/19 1.5} 47. Kf1 {-319.93/22 10} Neg3+
{+29.90/12 0.1} 48. Kf2 {-319.93/24 15} Ne4+ {+31.04/12 0.1} 49. Ke1
{-319.94/24 8} f3 {+319.94/15 0.1} 50. Kd1 {-319.95/27 8} f2
{+319.95/17 0.1} 51. Kc1 {-319.96/27 8} f1=Q+ {+319.96/12 0.1} 52. Kb2
{-319.97/27 13} Ne3 {+319.97/12 0.1} 53. Ka2 {-319.98/27 9} Nec2
{+319.98/22 0.1} 54. Kb2 {-319.99/29 8} Qa1# {+319.99/22 0.1}
{Xboard adjudication: Checkmate} 0-1

[d]8/4nk2/8/8/3nn3/8/1Kn5/q7 w - - 0 55
All you have proven is that the position you set up was not tactically quiet, but that the Queens had a space advantage, and a pin on one of the Knights, which gave them an above-average advantage. But it could not save them...

[Lyudmil Tsvetkov]

Against Stockfish it still wins in a quite straightforward way. Note that you don't just trade Q for 2N, but give up b5 in the process. Which is probably why QueeNy allows it, rather than just give up c7. (It would indeed play the black moves you suggested.) The five Knights just continue to strip you of your remaining Pawns. After one trade you are not home and dry yet. Five Knights still have the advantage over two Queens, especially in combination with Pawns.

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.24"]
[Round "-"]
[White "Stockfish 4 64 SSE4.2"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/300"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. b5 Nhf5 2. Qba2 Nfd6 3. Qxe7 Nxe7 {+6.77/16 4} 4. Qxa7 {+1.71/19 3} Nxb5
{+6.77/16 7} 5. Qb8 {+1.47/22 2.0} Nc6 {+8.27/16 5} 6. Qe8 {+1.31/22 4}
Nbxd4 {+8.32/16 8} 7. Qf2 {+0.86/22 21} Nd6 {+8.94/16 4} 8. Qh5
{+0.52/22 13} Nfe6 {+10.41/16 6} 9. Qa2 {+0.46/23 1.1} Kf8 {+10.41/15 4}
10. Qh8+ {+0.44/19 12} Ke7 {+10.92/16 5} 11. f4 {+0.12/21 8} Nb4
{+11.46/15 8} 12. Qb1 {+0.00/25 0.1} N4d5 {+11.63/14 4} 13. f5 {+0.00/27 6}
N4xf5 {+11.75/14 6} 14. Qe1 {-0.73/26 46} Nbc4 {+11.70/14 6} 15. Kh1
{+0.00/22 7} Nce3 {+11.99/14 5} 16. Qa1 {-1.97/18 11} Ned4 {+12.09/14 9}
17. Qg8 {-4.02/21 28} Ne2 {+12.24/14 7} 18. Qaa8 {-4.26/23 0.1} Nfg3+
{+11.28/15 5} 19. Kh2 {-4.18/23 2.5} Nef1+ {+11.26/15 5} 20. Kg2
{-6.12/24 20} Ndf4+ {+11.19/9 0.1} 21. Kf2 {-6.46/24 7} Nde4+ {+11.20/14 3}
22. Qxe4+ {-6.62/24 0.9} Nxe4+ {+11.23/19 7} 23. Kxf1 {-6.74/26 0.1} N2g3+
{+11.37/22 7} 24. Kg1 {-6.68/22 6} Ne6 {+11.51/22 5} 25. Qh8 {-7.03/22 7}
f5 {+11.58/22 7} 26. Kh2 {-7.49/24 0.1} f4 {+12.15/22 7} 27. Qa8
{-10.48/23 12} Nf1+ {+13.03/21 6} 28. Kh3 {-15.79/20 9} Nfd2 {+13.42/22 8}
29. Kg4 {-98.80/23 1.3} f3 {+13.60/22 7} 30. Qa3+ {-111.58/25 0.2} Kf6
{+14.83/22 6} 31. Qa1+ {-99.68/18 28} Kf7 {+18.23/18 0.1} 32. Kf5
{-99.70/17 9} f2 {+18.57/21 10} 33. Qa6 {-99.72/16 0.1} Nd6+ {+18.43/20 7}
34. Kg4 {-99.70/16 5} f1=Q {+19.66/21 8} 35. Qxf1+ {-99.78/19 5} Nxf1
{+26.53/23 11} 36. Kf3 {-99.80/22 0.1} Nd2+ {+27.15/22 15} 37. Ke2
{-99.82/26 0.1} N6e4 {+319.91/21 19} 38. Kd1 {-99.84/29 0.2} g5
{+319.92/21 11} 39. Kc2 {-99.86/34 0.1} g4 {+319.93/26 12} 40. Kb2
{-99.88/57 2.7} g3 {+319.94/28 17} 41. Ka3 {-99.90/100 0.1} g2
{+319.95/26 4} 42. Kb4 {-99.92/100 0.1} g1=Q {+319.96/26 8} 43. Ka3
{-99.94/100 0.1} Qc1+ {+319.97/24 5} 44. Ka4 {-99.96/100 0.2} Qc4+
{+319.98/28 5} 45. Ka3 {-99.98/100 0.1} Qb3# {+319.99/31 4}
{Xboard adjudication: Checkmate} 0-1

[d]8/2p2k2/4n3/8/4n3/Kq6/3n4/8 w - - 6 46
Perhaps more significant is when I let QueeNy also play the Queens, because then we know it will be trying to implement your plan, and strive for a second Q-vs-2N trade. I give it 40 moves/10 min, while the QueeNy playing the Knights only gets 1 min, to make sure the Queens have tactical superiority corresponding to a ~200-Elo stronger engine.

Indeed it puts up a better fight. (Could also be because the Knights play weaker now; against Stockfish I gave them 5 min.)

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.24"]
[Round "-"]
[White "QueeNy 0.16"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/600:40/60"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. b5 Nhf5 2. Qba2 Nfd6 3. Qxe7 Nxe7 4. Qxa7 {-6.91/16 9} Nxb5
{+6.66/14 2.4} 5. Qa6 {-6.77/17 19} Nbd6 {+6.81/10 0.1} 6. Qda2
{-6.96/15 12} Nc6 {+6.92/11 0.1} 7. Qd2 {-7.20/17 15} Nf5 {+8.07/14 1.8} 8.
Qf4 {-7.21/17 13} N7d6 {+7.28/10 0.1} 9. Qa2+ {-7.29/18 16} Kh8
{+7.32/13 0.2} 10. Qfh2+ {-7.28/18 16} Nh7 {+7.39/17 0.2} 11. Kf2
{-7.46/17 16} Ncxd4 {+7.34/9 0.1} 12. Qa7 {-7.33/17 14} Ne6 {+7.38/11 0.1}
13. Qb8+ {-7.43/16 16} Nbc8 {+7.40/15 0.5} 14. Qb3 {-7.45/17 16} Ned4
{+7.38/7 0.1} 15. Qb8 {-7.47/16 8} c5 {+7.44/15 1.9} 16. Qa8 {-7.60/17 10}
g6 {+7.58/9 0.1} 17. Qd5 {-7.67/17 11} c4 {+7.69/12 0.1} 18. Qa5
{-8.04/17 17} N4b5 {+8.04/11 0.2} 19. Qe1 {-8.11/16 11} Kg7 {+8.14/11 0.1}
20. f4 {-8.34/17 10} Nce7 {+8.31/11 0.1} 21. Qeh1 {-8.53/15 10} Nf8
{+8.44/12 0.1} 22. Ke1 {-8.94/16 16} c3 {+9.01/12 0.1} 23. Qc2
{-9.21/16 11} Ne6 {+9.63/14 1.6} 24. Qch2 {-9.93/17 12} Kf7 {+9.87/13 0.1}
25. Qa2 {-10.08/16 14} Nbd4 {+10.21/12 0.1} 26. Qh7+ {-11.25/16 10} Ng7
{+11.48/15 0.3} 27. Qh1 {-12.33/17 21} c2 {+12.41/15 4} 28. Kf2
{-12.84/17 22} Nh5 {+12.88/15 3} 29. Qa3 {-13.15/16 14} N6f5 {+13.03/9 0.1}
30. Qf1 {-13.51/16 19} Nhxf4 {+14.50/15 4} 31. Ke1 {-14.70/17 1:01} Ng3
{+14.86/8 0.1} 32. Qc4 {-15.86/18 18} Nge2 {+14.95/12 0.1} 33. Kd2
{-16.19/18 11} g5 {+16.24/9 0.1} 34. Qaa2 {-16.45/18 17} c1=Q+
{+16.89/10 0.1} 35. Qxc1 {-17.28/20 14} Nxc1 {+20.76/16 4} 36. Kxc1
{-21.10/22 14} g4 {+20.99/21 2.9} 37. Qh2 {-21.14/21 8} g3 {+20.98/20 6}
38. Qh7+ {-21.82/21 11} Ng7 {+21.70/16 0.1} 39. Qh1 {-22.02/21 23} g2
{+22.12/21 8} 40. Qh2 {-22.26/22 17} g1=Q+ {+22.29/20 5} 41. Qxg1
{-22.45/24 58} Nfe2+ {+22.79/22 2.5} 42. Kd1 {-22.40/22 14} Nxg1
{+29.68/20 0.9} 43. Kd2 {-22.66/22 11} f5 {+29.90/18 1.2} 44. Ke3
{-24.09/21 9} Nge2 {+30.13/18 1.2} 45. Kf2 {-30.84/21 9} f4 {+319.91/21 4}
46. Kg2 {-319.91/22 7} Ngf5 {+319.92/19 1.5} 47. Kf1 {-319.93/22 10} Neg3+
{+29.90/12 0.1} 48. Kf2 {-319.93/24 15} Ne4+ {+31.04/12 0.1} 49. Ke1
{-319.94/24 8} f3 {+319.94/15 0.1} 50. Kd1 {-319.95/27 8} f2
{+319.95/17 0.1} 51. Kc1 {-319.96/27 8} f1=Q+ {+319.96/12 0.1} 52. Kb2
{-319.97/27 13} Ne3 {+319.97/12 0.1} 53. Ka2 {-319.98/27 9} Nec2
{+319.98/22 0.1} 54. Kb2 {-319.99/29 8} Qa1# {+319.99/22 0.1}
{Xboard adjudication: Checkmate} 0-1

[d]8/4nk2/8/8/3nn3/8/1Kn5/q7 w - - 0 55
All you have proven is that the position you set up was not tactically quiet, but that the Queens had a space advantage, and a pin on one of the Knights, which gave them an above-average advantage. But it could not save them...

I post again the position after move 4 of white:

[d]5nk1/Q1p1nnp1/1n1n1p2/1P6/3P4/1Q3P2/8/6K1 b - - 0 4

Does Queeny really capture here the white pawn on b5, sacrificing a knight, as b5 is defended by the queen on b3?

[hgm]

Oops, my mistake! Seems I played 2. Qba2 in stead of 2. Qda2, when entering the moves of your proposed plan. So the Pawn was not defended. The game QueeNy-QueeNy was cheating anyway, as it turned out that pondering was on. So the Knights side was not having nearly as much disadvantage of the time odds as was intended.

I now replayed the game with ponder off, 40 min for the Queens, 4 min for the Knights. Because I let QueeNy play from the very beginning there, it did actually play Qda2, and not the faulty move I entered. This makes life indeed a bit harder, as 5 Knights vs 2 Queens is in fact rather close to equality. Black will have to play accurately, and at 1 sec per move becomes prone to tactical mistakes.

Still, the Knights win:

Code: Select all

[Event "Computer Chess Game"]
[Site "MAKRO-PC"]
[Date "2013.10.24"]
[Round "-"]
[White "QueeNy 0.16"]
[Black "QueeNy 0.16"]
[Result "0-1"]
[TimeControl "40/2400"]
[FEN "2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1"]
[SetUp "1"]

{--------------
. . n . . n k .
n . p . n n p .
. n . . . p . n
. . . . . . . .
. P . P Q . . .
. Q . . . P . .
. . . Q . . . .
. . . . . . K .
white to play
--------------}
1. b5 {-5.77/16} Nhf5 {+5.81/14 7} 2. Qda2 {-5.85/18 48} Nfd6 {+5.95/16 5}
3. Qxe7 {-6.07/18 54} Nxe7 {+6.17/17 5} 4. Qxa7 {-6.49/19 1:07} Ned5
{+5.78/16 6} 5. Qaa2 {-5.85/17 40} Nf4 {+5.91/15 5} 6. Kf2 {-6.10/17 1:16}
g5 {+5.95/15 4} 7. Ke3 {-6.08/16 32} N8g6 {+6.03/13 3} 8. Kf2
{-6.25/17 1:02} Ne7 {+6.33/15 4} 9. Qbc2 {-6.24/17 1:00} Nbd5 {+6.34/15 4}
10. Qab1 {-6.74/17 34} f5 {+6.55/14 4} 11. Qcb3 {-6.83/17 1:06} g4
{+6.80/15 6} 12. Qe1 {-6.95/16 45} Kf8 {+7.03/14 4} 13. Qh1 {-6.90/17 46}
Ng5 {+7.00/14 6} 14. Qh6+ {-5.68/16 42} Kf7 {+6.68/14 4} 15. b6
{-5.70/17 1:03} Ngh3+ {+6.60/14 14} 16. Kg3 {-5.80/18 57} Ne2+ {+5.81/14 5}
17. Kh2 {-5.77/18 40} Nhf4 {+5.50/14 3} 18. fxg4 {-5.90/18 1:03} fxg4
{+5.76/15 6} 19. b7 {-5.92/18 40} Nxb7 {+5.93/15 6} 20. Qh7+ {-5.79/19 36}
Ke6 {+5.86/17 4} 21. Qe4+ {-5.85/19 43} Kf6 {+5.78/18 9} 22. Qxb7
{-5.99/20 1:01} g3+ {+5.91/17 6} 23. Kh1 {-6.14/22 57} g2+ {+5.99/17 3} 24.
Qxg2 {-7.02/22 37} Nxg2 {+5.93/18 4} 25. Qa6+ {-7.25/25 56} Kg5
{+7.06/22 5} 26. Qxe2 {-7.18/25 1:06} Nge3 {+7.31/22 7} 27. Kg1
{-7.23/24 1:02} Kf4 {+7.34/21 4} 28. Qd3 {-7.27/24 43} Kf3 {+7.42/22 6} 29.
Qh7 {-7.40/26 1:01} Ke2 {+7.35/22 5} 30. Qh5+ {-7.41/24 43} Kd3
{+7.36/22 4} 31. Kf2 {-7.40/25 44} N7f5 {+7.36/21 5} 32. Qe2+
{-7.38/26 1:14} Kc3 {+7.41/21 6} 33. Qb5 {-7.37/24 1:25} Nxd4 {+7.48/20 5}
34. Qa5+ {-7.43/26 1:12} Kc2 {+7.40/21 7} 35. Qa7 {-7.46/24 47} Kd3
{+7.38/21 5} 36. Qa6+ {-7.48/27 1:19} Nc4 {+7.38/22 6} 37. Qb7
{-7.39/25 1:00} c6 {+7.46/22 5} 38. Qb1+ {-7.39/25 50} Nc2 {+7.37/23 8} 39.
Qd1+ {-7.38/25 2:00} Kc3 {+7.44/21 8} 40. Kf3 {-7.48/23 53} Nd2+
{+7.41/21 12} 41. Kf2 {-7.57/24 1:17} c5 {+7.50/20 6} 42. Qh1 {-7.53/23 35}
Nf4 {+7.52/20 4} 43. Qa8 {-7.49/23 45} Nd3+ {+7.48/20 5} 44. Ke2
{-7.85/23 37} Ndb4 {+7.47/19 4} 45. Qg8 {-7.43/24 1:04} Nd4+ {+7.45/20 4}
46. Ke3 {-7.58/23 34} c4 {+7.52/21 5} 47. Kf2 {-14.09/24 1:09} Nbc2
{+13.87/20 4} 48. Qb8 {-14.20/25 47} N4b3 {+14.15/23 3} 49. Qf4
{-14.29/26 49} Kb2 {+14.30/22 5} 50. Qc7 {-14.37/25 47} c3 {+14.41/22 4}
51. Ke2 {-14.48/25 1:04} Nc1+ {+14.35/22 8} 52. Kf2 {-14.53/24 43} Ndb3
{+14.47/21 3} 53. Qc8 {-14.70/23 47} Na2 {+14.84/21 4} 54. Qh8
{-15.06/25 1:03} Ncd4 {+14.97/23 20} 55. Ke3 {-15.20/25 44} Nb4
{+15.06/22 3} 56. Qe5 {-320.00/100 4:16} Nbc6 {+15.18/21 3} 57. Qh2+
{-15.23/24 1:02} c2 {+15.27/21 3} 58. Kd3 {-15.35/23 1:04} Kb1
{+15.24/20 5} 59. Qxc2+ {-15.35/23 44} Nxc2 {+15.57/27 4} 60. Kc4
{-16.33/29 1:42} Kb2 {+16.08/25 5} 61. Kd3 {-16.38/28 33} N2b4+
{+16.43/25 7} 62. Ke4 {-16.35/28 31} Kc3 {+16.49/24 4} 63. Ke3
{-16.48/28 40} Nd3 {+16.48/24 4} 64. Ke4 {-16.57/28 1:04} Ne7 {+16.47/24 7}
65. Kf3 {-16.57/29 40} Kd4 {+16.49/23 5} 66. Kg4 {-319.81/28 44} Ke5
{+16.66/24 4} 67. Kf3 {-319.81/29 46} Nd5 {+319.88/25 5} 68. Kg3
{-319.86/30 52} Kf5 {+319.92/27 5} 69. Kf3 {-319.91/32 47} Nd4+
{+319.92/27 6} 70. Kg3 {-319.92/34 1:04} Kg5 {+319.93/28 5} 71. Kh3
{-319.93/35 43} N5f4+ {+319.94/30 6} 72. Kg3 {-319.93/35 49} Kh5
{+319.95/31 6} 73. Kh2 {-319.95/42 50} Nde2 {+319.96/37 5} 74. Kh1
{-319.94/45 44} Ne5 {+319.97/43 6} 75. Kh2 {-319.98/59 53} Nf3+
{+319.98/47 5} 76. Kh1 {-319.99/71 47} Ng3# {+319.99/52 6}
{Xboard adjudication: Checkmate} 0-1

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