Wednesday, January 4, 2012

You're going to need a couple hints for this one....

This blog's very own Frederick Rhine is the author of today's study (cribbed once again from the terrific HHdbIV).

Frederick Rhine
Chess Life, 2002
White to play and draw 

There was a Karpov-Kasparov game in 1991 that reached the pawnless ending KBNN vs. KR.  The game was drawn, and subsequent research confirmed that this ending is theoretically drawn in the general case.  (The rook can sacrifice itself for the bishop, after which KNN vs. K is drawn.)

Black is threatening checkmate in the above position: do whatever it takes to stop Black!  But kindly do it in the right order.


Frederick Rhine said...

Interesting factoid: Staunton wrote in 1847 that in the general case BNN v. R was drawn, while BBN v. R was a win for the pieces. Fine, Soltis, and Benko (reviser of Fine's Basic Chess Endings) all asserted, much later, that both endings were drawn. Computers showed that Staunton was right, the others were wrong.

Keith Ammann said...

1.Qe8+ Bxe8
Gets the light-square bishop off the sixth rank.

2.Ne5+ Bxe5 3.Rh6+!
Or 2...Kb5 3.Rxb2+! Either way, the queen is skewered.

Bill Brock said...

Good try.

But what about 1.Qe8+ Bxe8 2.Ne5+ Kb5?

Keith Ammann said...

Hmm . . . on second thought, that's not enough:


OK, now I see why you said, "Do it in the right order." Take 2:

1.Ne5+ Bxe5
1...Kb5?? 2.Rxb2+ Nb3 3.Rxc4! Qxe3 4.Rxb3+! Qxb3 5.Qh1

2.Qe8+ Bxe8 3.Rh6+ Bd6 4.Rxd6+! Kxd6 5.Nxc4+ Nxc4 6.Rxb6+ Ke5
6...Nxb6+ 7.Kd8 and the bishop can't be saved without causing stalemate.

Frederick Rhine said...

Good job, Keith! I love the final position in the main line, where Black has three minor pieces against a lone king, yet it's a draw. Before I discovered that position (and made it into this problem) I would not have believed that such a thing was possible.

Bill Brock said...

Could we turn the theme into a White win?

Something like....

4r1K1/3k4/2N3B1/8/6N1/8/8/8 b - - 0 1

Frederick Rhine said...

You mean in that position White has to play 1.Bxe8+, and then 1...Kxe8 2.Nf6#? Maybe, if we could find a way of reaching that position. It's a "White to Play and Win" problem as it stands, but obviously a trivial one. I had a thought like that myself at one point, but couldn't conceive how to do it.