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Old March 3rd 04, 07:07 PM
Dr A. N. Walker
 
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Default Difficult ending

I wonder if the collected wisdom of "r.g.c.a" can throw any new
light on the following ending:

White: Kb3, Nh3, Pg4;
Black: Ke4, Bc5, Pa3, f4 [to play].

White has just played Ng1-h3 in response to Bf8-c5. The game
[from the 4NCL] finished in a rather banal way: 1 ... f3? 2
Ng5+ Kf4 3 Nxf3 and the draw very soon followed. It is clear
that once the f-pawn is below the g-pawn, NxfP draws at once,
as the g-pawn deflects the B from the defence of a3. Also
clear is 1 ... Be7? 2 g5 [threat Nxf4] f3 3 g6 and draws as
the B is deflected from the defence of g5.

So is this an "obvious" draw, as I [White] thought at
the time? No; for example, 1 ... Bf8 2 g5? f3 3 g6 Kf5 4 g7
Bxg7 5 Kxa3 Bd4 and the N is trapped. So 1 ... Bf8 2 Ka2 Ke3
[2 ... Kf3? 3 g5 and Nxf4] 3 Kb3 f3 4 Ka2 [g5 is still premature]
Kd3 [4 ... Kd2? 5 Ng5 f2 6 Ne4+ draws] 5 Kb3 Kd4 6 Ka2 Kc4
[6 ... Kc3 7 Ng5] 7 Ng5?! f2 8 Ne4 f1N is unclear [at least to
me]. But White can switch from shuffling the K to shuffling the
N. Black can make this difficult by Bc5 or Be7.

If White *is* eventually forced to push the g-pawn, then
after an eventual ... Bxg7, Kxa3 we reach the 5-man tablebases,
which show that White "usually" loses if the N is on h3, f2, or
d3, but draws if it is on d1; there is a mutual zugzwang with
WKc4, Nd1, BKe4, Bd4, Pf3. But can the push be forced? And
can Black control where the N is? Or can Black simply abandon
the a-pawn to free the bishop? Or what?

Well, I've spent far too long on this ending already, so
thought I'd exercise other people's brains/computers as well ....

--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.

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