Alas, I busted my favorite line in this whole endgame on my way home from work yesterday. You will recall one critical position, which in my home notes is labeled “The Last Crossroads” (and I have now added that title in the original post).
The Last Crossroads
Here I gave three different tries for Black:
61...Nd3, toying with queening the queenside pawns
61...Nd4+ 62.Kb1 Ndb3, forcing the queening of a queenside pawn, and
61...Nd4+ 62.Kb1 Nce2, threatening mate and forcing a draw. This last line is the one that I thought the most correct, and also the most attractive. However, it seems that White has a superior option: after (61...Nd4+ 62.Kb1 Nce2) 63.Ka2 Nc3+ 64.Kxa3 b1/Q
The line that I gave in my original post is 65.Rxb1 Nxb1+ 66.Kb2 Ne6 =. However, this particular position always bothered me, in that sort of nagging way that all too often turns out to be significant. White sort of has a little breather here, because his king isn’t being checked. However, what can he do other than take the queen, right? – because he’s threatened with mate on the move. Wrong! He can under-promote:
65.f8/N+! Kh8
66.Rxb1 Nxb1+
67.Kb2 Nd2
68.Kc3 N2f3
and for the moment Black has preserved his extra knight, but he’s not happy about it. For one thing, White can win the knight back at will by pushing his e-pawn. At the moment, that would also lose the h-pawn, so probably White should start by protecting that by pushing his g-pawn (perhaps preceded by Kd3-e3/e4. None of Black’s pieces can really move (especially once White plays Kd3-e3, tying down both knights). Black may be able to draw if he gets two pawns for one of his knights, but in all these lines it's White who's playing to win.It’s no good trying to avoid this with
65.f8/N+! Kg8
66.h7+ Kf7
67.Rxb1 Nxb1+
68.Kb2
and now Black has to come back with Kg7 to keep the h-pawn from queening, so White gets to take the Nb1. 66...Qxh7 67.Nxh7 is also awful. So it looks like Black would have to go for complicated swindling chances in one of the other tries.
These analytical turnovers are evidence that it is a difficult position. But it seems that most lines lead to draws, under precise play, and it's hard to say what is the best practical choice.
ReplyDeleteAfter 61...Nd4+ 62 Kb1 Nce2 63 Ka2 Nc3+ 64 Kxa3 b1=Q 65 f8=N+ Kh8 66 Rxb1 Nxb1+ 67 Kb2 Nd2 68 Kc3 N2f3, black is fairly safe. Only a few precise moves are needed.
Black threatens an immediate draw with ...Nxe5 70 Kxd4 Nf7 71 Ke5 Nxh6 or 71 h7 Kg7.
69 e6 Nxe6 70 Nxe6 Kh7 and Kxh6 is the most challenging, but is drawn easily because the king is in front of the g-pawn which is not advanced.
Even more clear is to leave the knight on b1 with 67...Nc6.
The second line is lost for black, trying too hard 65...Kg8 goes against common sense. White has 66 h7+ Kf7 67 e6+ which ends up winning both the black knights.
The initial position (move 61) looks drawish. The pawns are blockaded, and if the knights want to they should be able to clean up on the kingside while the white king is on vacation.
61...Nd3 62 Kb1 Nxe5 63 Re1 Nf3 64 Re2 was given in the original post, then ... Ng5 65 Rf2 Kxh6 66 f8=Q Nxf8 67 Rxf8 Ne4 not only attacks the Pg3 leaving a drawn R v N ending, but more directly targets Nd2/c3+ trading to a drawn K+P ending after 68 Rb8.
My preference is for 61...Nd4+ 62 Kb1 Ndb3 where black has at least a draw, I am pretty sure that's all he has.
Incidentally, the white pawns are not too far advanced for the 2N v. P ending, even with the 50 move rule. More precisely, the e+g pawns are at the limit, the f-pawn is too far, and the h-pawn (if it were blockaded by a knight) is won for the 2N's fairly often.
Another thematic position is the ending W Nf8 Ph7 B Kh8, then it doesn't matter where white's king is. If the king is on g6/h6 it is stalemate. Otherwise white's knight cannot move without losing his only hope on h7. Black just plays Kg7-h8.
I'm surprised you didn't look at 61...Nd4+ 62. Kb1
ReplyDeleteNce2 63. Ka2 Nc3+ 64. Kxa3 b1=N+! followed by Ne6, etc. It looks like black should draw that.
@ Anonymous, who advocates 64...b1/N+ (replace the queen in the last diagram with a knight) as a drawing try to avoid the complications examined in this post:
ReplyDeleteI don’t think so. 64...b1/N+ doesn’t force White to give up his rook, so he can play for the win with
65.Kb2! Ne6
66.Rf1 Nf8
67.Rf6!
which will win the Nf8 for just the e-pawn with 68.e6 (since White queens after 67...Nd5/e4 68.e6 Nxf6 69.e7). Once the Nf8 is won, White queens the f-pawn.
The ending in the parentheses above (after, say, 69.e7 N6d7 70.e8/Q+ Nd2 is also fascinating, but mostly in the way that a car accident is. There may be some way that Black can avoid losing, but it's clearly going to be a ton more work than just promoting to a queen on b1.