First, the easy part. White can blockade the queenside pawns with his knight via the maneuver Nf6, Ne4, Nc3, Na2. Then we're left with a symmetrical king and pawns position on the kingside. White's kingside pawns are further advanced, and he can generate extra tempi by shuffling his knight. But is that enough to win?
[Position after 1. Nf6 a5 2. Ne4 a4 3. Nc3 a3 4. Na2 Ke7 5. Kf3 Ke6 6. Ke4]
No, because Black's king can shuffle between d6 and e6. And a pawn advance is no help. Eg, 6...Kd6 7.f5 gxf5 Kxf5 is drawn.
So we return to the original position and try something else. What if White's king stops the queenside pawns, and his knight stops the kingside pawns?
[Position after 1. Kf3 a5 2.Ke4 a4 3. Kd4 a3 4. Kc3 a2 5. Kb2 Ke7]If only the g-pawns, the knight, and Black's king were on the kingside this would be an easy win, but Black's f7-pawn complicates things.
Therefore, the winning strategy is to eliminate the f7-pawn! 6.Nf6 Ke6 7.Ng4 Kf5 (7...f5? or 7...f6? => 8.gxf6!) 8.Nh6+ Kxf4 9.Nxf7 wins.
What a funny-looking winning position! Material is almost equal, but Black is completely lost. White's king will capture the a-pawns, then help his g-pawn promote.
6 comments:
"I'm a thief, and I'll admit it."
You're welcome to anything on my blog at any time. Actually, your explanations of this winning technique are much better than what I wrote. I kind of left it behind as an oddity instead of understanding that there is a general principal.
In the last position of your previous post, I was stumped for a minute on the line 1. ... Nf3 2. Kd3 Ne1 3. Kd2 preventing Nc2. Now if 3. ... Nf3 4. Kd3 repeats the position. Finally I realized that black wins by 3. ... Kf3 4. Kxe1 Ke3.
That's an interesting observation. It follows that if we move the pieces one rank backwards, the position is a draw. After the knight sacrifice the Black king would still win the White pawn... but this time he wouldn't be on the sixth rank and so would draw the resulting K&P vs K ending.
I just checked. Rybka concurs!
fyi, I'm going out of town until Sep 24, so there won't be any new posts this week. Minev's coming with me, so when I get back I plan to shift from knight endings to rook endings.
Enjoy your trip! I hope your posts on rook endings are as good as your posts on knight endings.
Thanks, it was a good trip, but I went out every night and read very little chess. Ahh well. :)
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