White to play and win.

Material: N for B. The Black Kg8 has 3 legal moves. White has a battery Rd1 and Qd2 on the semi-open d-file. Black has a threat on Nd4 requiring an active response. The Black K-side has dark-square weaknesses. Obviously, the White Bg5 emphasizes the weaknesses, but more subtly, Ng3 and Nd4 can also move to attack them. The White Rg1 faces Kg8, suggesting clearances on the g-file to remove Ng3, Pg4, Bg5, and Pg6. White can open the h-file at will with hxg6. Both Black Bs are loose and Nf6 is merely adequately guarded. White has a tender spot at Pc2, attacked by the battery Rc1 and Qc4, but the 2 White Rs defend the back rank against mate threats, so …Qxc2+ only nets Pc2. Similarly if Ng3 moves White must beware …Nxe4, but without a mate threat at c2, Qd2 protects Bg5.

Candidates (21.): hxg6, Ndf5, Ngf5

21.hxg6 (threatening 22.gxh7+ winning a P)

I gave an analysis as to why Black must recapture with a P, and within a human horizon, Toga readily rejects accepting the sacrificed Nd4 by 21...exd4. Toga also readily shows that 21...hxg6 is inferior to 21...fxg6. I thought the removal of Ph5 and Pf7 would increaes White's attacking chances.

As my candidates indicate, I was aware of the N sacrifices at f5. The fact that this is a puzzle, so something decisive "should" happen next, did not impress me. I would be curious if <anyone> could explain in human terms why they would play a N sacrifice over the board instead of opening the h-file first.

gaining a piece for a pawn. Rybka 3 agrees with it.>

Er, I like your initial move 21.hxg6, so don't think I am not on your side. It is White to move, however, and in this sequence, Black that gains the piece for the P, so I guess Rybka 3 is right.

In fact, according to Toga II 1.3.1, your variation does give White some pull. With best play,

[ply 18/84 time 03:33 value +0.41]

25.b3 Qxd4 26.Qh2 Qxg1 27.Rxg1 Rh8 28.Qd2 Be7 29.Qh6 Bf6 30.Rd1 Rcd8 31.a3 Ke7 32.Ka2 Kf7 33.Kb2 d5 34.Qh5+ Kf8 35.Rg1 dxe4

21 Ngf5 gxf5

but I think black should play 21 ... Kf8 instead of gxf5.

If you get the game line to 24 Nf5, then indeed the better response is 24 ... Bd5 but black is still lost; even though there is a very long continuation where black nearly gains a draw at several points, presumably black would not resign until about move 40.

I'm definitely wondering what is up with Rybka 3 though. It is a lot stronger player than any of my other engines but it's not as easy to use for analysis.

I have found why the engines have trouble with this position - what happens is that 24 ... Qe6 is not as good as 24 ... Bd5. But the continuation from 24 ... Bd5 has a very long sequence where black goes on a king hunt that very neary swindles a draw - there are several moves where white has only one move which keeps his threat alive:

25 Qxf6 Qxa2+ tally ho!
26 Kc1 Rxc2+
27 Kxc2 Rc8+
28 Kd2 Qxb2+
29 Ke1

The king has had no choice

29 ... Qc3+
30 Rd2

This is forced to avoid the draw

30 ... Qc1+

Here white has an option of two moves:

31 Kf2 Qxd2+
32 Kg3 Qf4+
33 Kh3

otherwise draw

33 ... Qxf3+
34 Kh4

otherwise black wins

34 ... Qxf2+
35 Rg3

otherwise draw

35 ... Qh2+
36 Kg5

otherwise draw

37 ... Qd2+
38 Re3

otherwise draw

39 ... Qxe3+

here black has been able to force the exchange of the rook for the queen, with check, and in such a way that white's mate threat is disrupted

40 Nxe3 Be6

However, now white immediately imposes another mate threat

41 Qh6

and indeed the game is lost in this line. In the other line

31 Ke2 Bc4+
32 Kf2

otherwise lose

32 ... Qxd2+
33 Kg3 Qf4+
34 Kh3

otherwise lose or draw

34 ... Qxf3+
35 Kh2 Qf4+
36 Rg3

(or 36 Kh1 which is an even longer tightrope, otherwise draw)

36 ... Qd2+
37 Rg2 Qf4+
38 Kh3

otherwise draw

38 ... Qe3+

this offers the queen to disrupt the mate, it is quicker for white to decline

39 Rg3 Bf1+
40 Kh4

otherwise draw

40 ... Qxg3+
41 Nxg3

again, black is now lost.

The point of these tightrope variations is that although black doesn't actually win, it is a tightrope where white must play very precisely to avoid losing or drawing.

Now to the human player, it's tricky, but to the computer, having a lot of lines which become draws is a sure way to burn up a ton of computer cycles and not be able to rule in or out continuations, so the search cannot get very deep.

So it's not surprising to me that engines can choke on some of the lines here.

And as far as for a human playing over the board? I doubt that the "correct" move (21 Ngf5) would win if black was any of stronger engines mentioned in this kibitzing - unless the human was a strong GM, otherwise too much time would get lost avoiding the traps.

I agree with your implication that engines are not totally trustworthy here, although I now believe that 21.Ngf5 is indeed the "right" move.

I am dumbfounded that anyone could find 21.Ngf5 over the board when a good "safe" alternative like 21.hxg6 is available."

I have also found that using Rybka 3 in the Shredder interface (my usual interface) is probably not the best way to use Rybka 3; I have just started analyzing this problem in Aquarium and although it is still preferring 21 hxg6 in the deep analysis mode, it was able to recognize 21 Ngf5 as a good move very quickly in game analysis mode, and it has already annotated 24 ... Qe6?! and 24 ... Bd5 !?

Correct. My take on the best play for both sides is:

21. Ngf5 Kf8 22. hxg6 hxg6 23. Nxe7 Kxe7 24. Nf5 gxf5 25. gxf5 Qxc2 26. Qxc2 Rxc2

If you want to plug it into Rybka and analyze for mistakes, it might confirm it.

<zenpharaohs: I have just started analyzing this problem in Aquarium and although it is still preferring 21 hxg6 in the deep analysis mode, it was able to recognize 21 Ngf5 as a good move very quickly in game analysis mode, and it has already annotated 24 ... Qe6?! and 24 ... Bd5 !?>

Stockfish 14 says:

21. Ngf5

(21. Ngf5 (♘g3-f5 g6xf5 ♗g5xf6 ♗e7xf6 ♕d2-h6 f5xe4 ♘d4-f5 ♗b7-d5 ♖d1xd5 ♕c4xc2+ ♔b1-a1 ♖d8-d7 f3xe4 ♖d7-c7 ♖d5-d1 ♗f6-h8 ♕h6-g5+ ♔g8-f8 a2-a3 f7-f6 ♕g5-h6+ ♔f8-g8 ♕h6-e3 ♕c2-c5 ♕e3-d2 b5-b4 a3xb4 ♕c5-c2 ♕d2xc2 ♖c7xc2 ♘f5-e7+ ♔g8-g7 ♘e7xc8 ♖c2xc8 ♖d1xd6 ♖c8-b8 g4-g5 f6xg5 ♖g1xg5+ ♔g7-f7 ♖d6-h6 ♗h8-f6 ♖g5-f5 ♖b8-b6 ♖h6xh7+ ♔f7-g8 ♖h7-d7 ♖b6-e6 ♔a1-a2 ♗f6-e7 ♔a2-b3 ♗e7-f6 ♖d7-a7 ♗f6-e7 ♖a7-b7 ♗e7-f6 ♔b3-c4 ♗f6-d8 ♖b7-b8 ♖e6-e8 ♔c4-d5) +8.10/35 256)

Black threatens Qxd4 and exd4.

A quick scan yields lines like 21.Ngf5 gxf5 22.gxf5 Qxd4 23.Bxf6+ Kf8 24.Qh6+ Ke8 25.Rxd4.

Or 22... exd4 23.Bh6+ (23.Bxf6+ Kf8 24.Rg8+ Kxg8 25.Qh6 Qxc2+ 26.Ka1 Qxd1+ and mate next) 23... Kh8 24.Qg5 Qxc2+ 25.Ka1 Qxd1+ 26.Rxd1 Rg8 27.Qd2 looks good for White in spite of the material deficit.

Or 22... Kf8 23.Ne6+ fxe6 24.Bxf6 Bxf6 25.Qh6+ Ke7 26.Qxh7+ and mate in two.