Hey <TTD> I saw 20. Neg5, fxg5 and the threats and actually spent more time working out whether 21. Rxd7 or 21.Nxe5 was the stronger continuation.

I went for 21. Rxd7 because after 21. Nxe5, Qf5 white can no longer play 22. Nf7+?, Qxf7 23. Qxf7, Rxc7 and black has three pieces for the queen.

After 21. Rxd7 black is down a rook for a knight and 21...Bf6 won't hold out for much longer because a huge attack is coming.

21. Rxd7, Bf6 22.Qd5, h6 23. Rc1, Re8 (+3.5)

21. Nxe5?, Bd6! 22. Rxd7,Bxe5 23. Qd5, Bf6 24. d4 (+1.0)

My idea of 21 Nxe5, Qf5 22. Nxd7,Bd6 23. Rc1, Bxc7 24. Rxc7, Qxb5 prevents white using the back-rank theme in the puzzle, but does not save his position (+3.5)

White to play and win.

Material: N+P for B. The Black Kh8 is stalemated. White has Rc7 on the 7-th rank, attacked by Rd7, which is in turn supported by Qh3. The White Qa2 controls the a2-g8 diagonal and is in position for mate by Philidor's Legacy, and both Ne4 and Nf3 can reach g5, the usual square on which a N starts in Philidor's Legacy. All White pieces are active, with the exception of Rf1 and possibly Nf3. By contrast, the Black Na5 is out of play, Qh3 is isolated, and Ra8 only defends the back rank.

Candidates (20.): Nfg5, Neg5, Rfc1, Nd6

20.Neg5 (threatening 21.Nxh3 and Philidor's Legacy:

21.Nf7+ Kg8 22.Nh6+ Kh8 [Kf8 23.Qf7#] 23.Qg8+ Rxg8 24.Nf7#)

Black cannot decline the sacrifice, because of conflicting constraints on a feasible move: Qh3 must flee, while maintaining contact with Rd7 and the square f7 critical to Philidor's Legacy. Black must therefore accept the sacrifice of Ng5:

20…fxg5 21.Nxe5, threatening 22.Nxd7 and Philidor's Legacy again

To escape mate, Black must permit 22.Nxd7, so White has won the exchange and a P.

The game line is evaluated at

[ply 15/39 time 00:16 value +4.67]

20.Neg5 fxg5 21.<Rxd7> Bf6 22.Qf7 Qf5 23.Nd2 g4 24.Ne4 Qg6 25.Qxg6 hxg6 26.Rc1 Nb3 27.Rcc7 Nd4 28.Nc3 b6 29.Rxa7 Rc8

The positional 20.Rfc1 should win:

[ply 15/46 time 00:36 value +1.84]

20.<Rfc1> Rf8 21.Rc8 Bd8 22.Nh4 Re8 23.a4 Qg4 24.Kg2 b6 25.Nf3 Qg6 26.Qb2 f5 27.Nxe5 Rxe5 28.Qxe5 fxe4 29.Qxe4

Without the upgrade, the combination is worth less than the positional 20.Rfc1:

[ply 15/43 time 00:14 value +1.70]

<A positive (+) evaluation means advantage for White, while a negative one (-) advantage for Black. If the evaluation is under 1 (so less than +1,00 for White or more than -1,00 for Black) it usually means that the advantage is not decisive [...] More than +1,00 or less than -1,00 it means (usually) decisive advantage or >

No. The valuation is not correct, at least not in any of the engines I'm familar with or have heard mentioned on this site (Fritz, Chessmaster, Toga 2, Crafty, Hiarcs, Rybkka) The numbers are in what I believe are termed "centipawns" in which a value of +1.00 is equal to an advantage of 1 pawn. 0.50 half a pawn. etc. So, a +1 evaluation is like White being up a pawn -- a significant but by no means decisive advantage. A decisive advantage is a judgement call, somewhere between 3.0 and 5.0... somewhere between being up a minor piece and a rook -- although I suppose in the accurate world of high level chess 2.0 (two pawns) is a very big lead.

Glad I cleared that up for myself.

20 eg5 not to go after the queen as much as to divert the black @ f6

21 xd7 to bring the black queen to d7

22 e5!! to threaten a smothered mate after 23 f7+ black's defense,be it at c8,d8,e8,f5 would result in loss of queen.

22...c8 or e8 or f5 23 f7+ g8 24 d6+ and bye-bye blackbird.

I didn't get Wednesday's puzzle (and haven't yet had a chance to look at Thursday's), so I am glad that I noticed the potential for the white queen and knight to double check the black king and to get a smothered mate. The question is, how exactly do you get there?

20. Neg5
(this is the knight to use because the other knight must be able to attack e5).

What happens if black does not take this knight (e.g., moves the queen to g4)? Then white will play Nf6+, Nh6 double+, and then (assuming ...Kh8) white will play Qg8+ followed by smothered mate with Nf7#:

[a) analysis line
20. Neg5 Qg4 (or ... Rxc7)
21. Nf7+ Kg8
22. Nh6+ Kh8 (if ...Kf8, then 23. Qf7#)
23. Qg8+ Rxg8
24. Nf7#]

But if black moves the queen to h5 (to cover the f7 square), then white wins the rook on d7 (and then Nf7+ is again threatened):

[b) analysis line
20. Neg5 Qh5
21. Rxd7 (not 21. Nf7+ because 21 ...Qxf7; 22. Qxf7 Rxc7) 21 ...fxg5
22. Rxe7 and white is a rook up]

Because of all this:

20 ...fxg5 is forced
21. Rxd7 Qxd7
(I suppose that black could decide to not retake here, but after moving the bishop (e.g. to f6), I can't see any good prospects for black, being down the exchange plus a pawn).

22. Nxe5
Now black attacks the queen but more importantly, the smothered mate motif comes up again (i.e., with Nf7+, etc...). White has no time to guard f7 with the remaining rook (...Rf8) because the queen is attacked. Guarding with the queen leads to: 22 ...Qe8
23. Nf7+ Kg8 (if ...Qxf7 then 24. Qxf7)
25. Nd6+ and black loses the queen because of this discovered check.

So this is the entire sequence:

20. Neg5 fxg5
21. Rxd7 Qxd7
22. Nxe5 Qe8
23. Nf7+ Kg8
25. Nd6+

In the end white will end up with the queen plus 2 pawns for two knights (one pawn of course was won in the sequence and white was already up a pawn at the start).

One of the interesting things about this position is that the black bishop makes it impossible to construct an adequate defence.

I have to admit that I initially looked at 21. Nxe5 instead of playing 21. Rd7 first. It almost works that way as well (for instance, smothered mate is again threatened with the remaining knight). Black cannot play ...Rxc7 because 22. Nf7+, etc... Black's other problem is that now the knight and the rook both attack the d7 rook.

But black has 22 ...Qf5 and comes out reasonably okay in comparison to the main line:

[c) analysis line:
20. Neg5 fxg5
21. Nxe5 Qf5
Black's idea here is to guard the f7 square with the queen (e.g., 23. Nf7+ Qxf7; 24. Qxf7 Rxc7).

But also black (seeing that the d7 rook can be captured) is hoping that white will capture on d7 with the knight:

23. Nxd7 Bd6
and now the rook protecting knight must move, after which black can play 24 ...Qxd7 and come out with 2 knights for a rook and pawn in the sequence.

But if white plays:

23. Rxd7 Qxe5
24. Qf7 Bf6 (or ...Bf8)
Then black has managed to again get 2 knights for a rook and a pawn out of the sequence. Things still don't look good for black (black is still a pawn down with a pretty ragged pawn structure and misplaced knight), but it least the position is better in this possible line in comparison to the main sequence.

You wrote: "A decisive advantage is a judgement call, somewhere between 3.0 and 5.0... somewhere between being up a minor piece and a rook -- although I suppose in the accurate world of high level chess 2.0 (two pawns) is a very big lead."

Much weaker than the other alternatives, according to Toga II 1.3.1 (see my prior post for my conventions):

[ply 15/43 time 00:29 value +1.30]

20.<Rxd7> Qxd7 21.Rc1 Rf8 22.a4 b6 23.Qb2 Rc8 24.Rxc8+ Qxc8 25.e3 Nb7 26.Qc3 Qxc3 27.Nxc3 Kg8 28.Nd5 Kf7 29.d4 exd4 30.Nxd4

The problem is that 21.<Neg5> below forces nothing, so Black has time to give his Kh8 some luft:

[ply 15/49 time 00:42 value +1.05]

20.Rxd7 Qxd7 21.<Neg5> h5 22.Ne6 Rc8 23.Nh4 g5 24.Ng6+ Kh7 25.Nxe7 Qxe7 26.d4 exd4 27.Nxd4 Kh8 28.e3 Nc4 29.Rc1 Qc5 30.Qe2 g4