Is the following Knight sac in the Sicilian Najdorf justified? [FEN ""]
 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. Bg5 e6 7. f4 Nbd7 8. Qf3 h6 9. Bxf6    Nxf6 10. O-O-O Qb6 11.e5 Nd7 12. Bc4 dxe5 13. Nxe6
I ran this through Stockfish at 15 minutes per move. What I have found is that the sacrifice is sound and wins.  But for a 'won' game, it is about the hardest road I have ever seen.  The evaluation of the position is less than a pawn advantage for White up through move 25 or so.

The sacrifice leads to opportunities for White, but both sides are walking the razor's edge.



[FEN "r1b1kb1r/1p1n1pp1/pq2p2p/4p3/2BN1P2/2N2Q2/PPP3PP/2KR3R w kq - 0 1"]

1.Nxe6 fxe6 2.Qh5+ Kd8 3.Qf7 Qe3+ 4.Kb1 Qxf4 5.Qxe6 Qf6 6.Qh3 Bc5 7.Rhf1 
Qc6 8.Bd5 Qg6 9.Bxb7 Ra7 10.Be4 Qe8 11.Nd5 Rf8 12.Qh4+ g5 13.Qxh6 Rxf1 14.
Rxf1 Bb7 15.Qxg5+ Kc8 16.h4 Qd8 17.Qg3 Bxd5 18.Bxd5 Kb8 19.h5 Rc7 20.Rd1 
Ka7 21.Be4 Qf6 22.Qg4 Nb6 23.Qf5 Qg7 24.a3 Be3 25.g4 Bf4 26.Rd6 Nc4 27.Rg6
Qd7 28.Qxd7 Rxd7 29.Bd3 Nd2+ 30.Ka2 e4 31.Be2 Kb8 32.g5 Nf3 33.Rg8+ Kc7 
34.g6 Kd6 35.Rh8 Nh4 36.Bxa6 Be5 37.Re8 e3 38.b4 Nf5 39.Rf8 Ra7 40.Bd3 Nd4
41.h6 Nxc2 42.Kb1 Nxa3+ 43.Kc1 Re7 44.h7 Nc4 45.Rd8+ Kc7 46.Rg8 Nb6 47.
h8=Q Bxh8 48.Rxh8 e2 49.Bxe2 Kd6 50.Kd2 Rg7 51.Bd3 Nd5 52.Rd8+ Ke5 53.b5 
Nb6 54.Rf8 Ke6 55.Ke3 Rb7 56.Kf4 Ra7 57.Kg5 Ke5 58.Kh6 Rd7 59.Rf5+ Kd4 60.
g7 Rd8 61.Rf8 Rd6+ 62.Bg6 Kc5 63.g8=Q Kxb5 64.Qb3+ Kc6 65.Qc3+ Kb7  66.Rf7+
Nd7 67.Qc5 Rd1 68.Re7 Rh1+ 69.Kg7 Rh7+ 70.Bxh7 Ka6 71.Bd3+ Kb7 72.Rxd7+ 
Kb8 73.Qf8#



The general method of White's win isn't a Tal-like knockout, but instead we find that Black cannot hold onto the Kingside pawns. They drop off allowing White connected outside passers.    Black has plenty of resources however.  In return, Black gets a passer on the e-file that will be a real threat.  Black also eats two of the three pawns on the Queenside. I think this passer is one too many, and it's going to kill him.

After 2. Qh5+, Black's King is stuck in the middle of the board. This will be a
lodestone that will haunt Black for the rest of the game.  Yet another example of
what happens when the weak f7 square is exploited.  This is really the lesson of
this sacrifice - "Weaken the f7 square and you might just get some traction."

3. Qf7 and the White Queen is in Black's business.

After move 5, we see White's side is orderly, his two minor pieces are developed,
his King is secure, and his Rooks are ready to leap into action.  Charitably
speaking, one of Blacks minor pieces is developed.  His Rooks are still in the
box, and one Bishop is entombed.  Black is trying to trade off the Queens.
If he does, he wins.  When one has a material advantage, it's generally best to
trade off pieces. Of course, White is having none of it.

6... Bc5  Black must develop. Now his Bishop matters and he can activate his Rook.

Up to move 9, White harasses the Black Queen developing a Rook with tempo, then
picks up the loose b pawn.  This allows Black Queen Rook to enter the game, but
now Black as 2 isolated pawns to defend.

10... Qe8 To this point, Black has managed to swap his King's and Queen's positions!
White's Rooks control two open files and has a big grip on the center.  The Rook on
d1 is a monster, holding the center, pointing at the exposed Black King while pinning
the Knight in the process.  Remember, if Black can't use the Knight, it does not really
exist, and thus White is, after a fashion, not down any material.

11... Rf8 challenges White's f Rook.  The cost is terrible - the remaining pawns
on the kingside.  12. Qh4+ is frightening, exposing Black's folly.  At this point, it's
worth pointing out how the computer is very particular with tempo.  Instead of an
immediate Rook trade White throws a
check first - again hitting the misplaced King and cause Black to further weaken himself.
Amusingly (for White) the Black Knight is still immobile.  If he moves it to,
say b6, Rf8 wins. 
I would be interested to see peoples' alternatives to 11... Rf8.

15. Qxg5+ White scoops up the other pawn, with tempo, adding insult to injury.
The immediate 16. h4 is the signal Black's in for a long day.

17... Bxd5 Black has finally completed his development though White has the
open file and the majority of the center.

20. Rd1 Back to the center, now pressuring the Queen.

23. Qf5 White now offers the Queen trade which is declined.  This is another point
in the game where a variation could be helpful.

Through move 26, Black's defensive play is quite good.  He's a tempo from picking up the
pawn on g4.  White's 27. Rg6 supports g4 again with tempo.  This move does
three things: it threatened the Black Q, defends g4, and frees the White Q to run if
Black were to play Ne3.

Through move 29, the Queens drop off, Black claims the d file, and White blocks it
with his Bishop, simultaneously preventing a nasty Knight fork on d2.  Such economy!

30... e4 Black has threats, too.  Black's play is a great lesson on how not to give up.
White is one bad move from losing this game.

31... Nf3 wins the g pawn?  Nope, White checks with tempo allowing the jammed pawn
to move out of danger.  Again, seeing alternatives to 31...Kb8 would be interesting.

35...Nh4 looks goofy as it allows the a-pawn to drop off.  But it's lights-out if White
is allowed to play h6.  In that case, White wins the Black Bishop and threatens a
discovered check with g7.  Economy!

You might think Black should just resign. And maybe he should.  Now let's look at the
defensive resources that are available to him.

First, Black's e3 hits White where he isn't.  That pawn is scary.  Only the Bishop
is saving White.  Black attacks it. If the Bishop is driven off the a6-f1 diagonal,
Black wins or draws.

41. h6 computers are cool under fire.

41... Nxc2 if Bxc2, White loses.  Now the threat is Nxb4+ where white's defending
Bishop drops off, and it's mayhem that favors Black.

42. Kb1 the Bishop needs help.  White must now pay the Butcher's Bill.

44. h7 White pours on the pressure, but Black's Bishop and Rook combo is very effective.

44... Nc4 is hard to understand.  Perhaps it is one of those moves that moves a bad
evaluation out one move.  Some thought here is needed.

49... Kd6 is a great example of an inhuman computer move, where the machine is making choices about fractions of pawns.  The alternative is 49... Rxe2 50. g7 Rg1 51. g8=Q Rxg8 52. Rxg8 and Black has lost the exchange for a pawn.  I would like to know why Black played 48... e2 at all.

Finally, to answer the OP's question, is the sacrifice justified?  That's a value judgement.  If I played this as White, and won, it would easily be the hardest win in my 'career'. A win is good, but this game is a hard, risky win. If one is willing to walk the razor's edge and one is good at managing one's clock, a point's a point.

This could be one of those games where one side has to play MUCH better in order to hold. That is, maybe White has to play like a master to hold, but Black can play like an 'Expert' to draw.  That is, whoever missteps first, loses, and White has more land-mines to avoid.

If anyone has alternate variations they'd like me to run, let me know.