The Behting study is sound
By John Nunn
Back in August, ChessBase
published the famous Behting study, which is often used as a demonstration
that computers can’t solve all positions.
K. K. Behting, Baltische Schachblätter 1908
White to play and draw
The intended solution is 1 Kc6! g1Q 2 Nxh4, followed by 3
Nhf3, with a positional draw as Black cannot make progress.
However, I suggested that there might be an alternative solution to this study,
and this provoked several people to look at the position more closely. The proposed
alternative ran 1 Ng7+ Kg5 2 Nf3+ Kg4 3 Nf5 h3 4 Ke4 g1Q 5 Nxh6+ Kh5
6 Nxg1 h2 7 Nf3 h1Q 8 Nf5 Kg4, reaching a key position.
It isn’t easy to see how Black can break down White’s fortress,
but to definitely resolve the issue, endgame tablebase expert Marc Bourzutschky
constructed the seven-man tablebase with Q+P vs 2N+P. This showed that Black
can break down the defence, and while the winning line isn’t especially
deep, there are some surprising features. One important point is that while
the ending of Q vs 2N is generally drawn, if the knights are badly placed defending
one another then the queen can often win – indeed the queen may still
win even if the defender has an extra pawn.
There was then a discussion involving several endgame experts, such as Noam
Elkies, Harold van der Heijden and John Beasley, before it was discovered that
the key winning idea had already been given by Arapd Rusz in 2010. Finally,
Peter Stephenson sent some detailed analysis giving the win in more depth. The
analysis which follows is based on these contributions, but any mistakes are
From the diagram position, one side line runs 9 N5d4 Kg3 10 Ke3 (10 Ne2+ Kf2
11 Ned4 Kg2 and 10 Nf5+ Kf2 11 N5d4 Kg2 transpose to the main line below) 10...Qh6+
11 Ke4 Qf4+ 12 Kd5 Qf7+ 13 Ke5 Qe7+ 14 Kf5 Qa7 15 Ke5 Qa8 and now White is in
an unpleasant zugzwang. His king must move, allowing ...Kf4 followed by ...Ke4,
and Black’s king penetrates.
The main line runs 9 Ne3+ Kg3 10 Nf5+ Kf2 11 N5d4 and this
is where the key idea comes in.
11...Kg2!! This is the move I had missed when I first looked
at the position. Black’s surprising triangulation, which in addition unpins
the knight, leaves White without a good reply:
12 Nf5 Qb1+ 13 Kf4 Kf2 14 Ng5 Qb8+ 15 Kg4 Ke2 16 Ne4 Qf8 17 Kf4 Kd3 and
Black’s king enters.
12 Kf4 Qh7 13 Ke3 (13 Nf5 Kf2 14 N5d4 Qd3 15 Ke5 transposes) 13...Qd3+
14 Kf4 Kf2 15 Ke5 c3 16 dxc3 Ke3 wins, since Black’s king enters and
the white knights are badly placed.
12 Ke3 Qb1! 13 Kf4 Qh7 14 Ke3 Qd3+ transposes to line 2.
12 Ne5 Kg3+ 13 Ndf3 Qb1+ 14 Ke3 Qf1 15 Kd4 Kf4 16 Kc3 Qb1 17 Kxc4 Ke4 is
12 Kd5 Kg3 13 Kxc4 is perhaps the most surprising line. Black simply gives
up his pawn in order to activate his pieces. Although White doesn’t
appear too badly off, he cannot save the game and the tablebase shows that
Black can now mate in 50 moves. The main line starts 13...Qf1+ 14 Kd5 Kf4
15 Ne5 Qg2+ 16 Ndf3 Qg8+ 17 Kd4 Qa8 18 Kc4 Ke4 and again we have the typical
penetration by the king, while the knights are paralysed since they can
only defend each other.
Thus Behting’s 1908 study has, after just over a century, been proved
correct and ChessBase can continue to use it to humiliate computers until the
day dawns when they can finally solve it.
Dr John Nunn is a director of Gambit
Publications, one of the world’s leading chess publishers. Gambit
was founded in 1997, and in the past 15 years has published over 170
chess books in English and more than 50 in German. Several of its titles
have won awards in different countries, most recently the English Chess
of the Year Prize for Nunn’s Chess Endings Volume
1 and Volume
2. Nunn’s recently published Understanding
Chess Middlegames is already a bestseller and has been reprinted
after only two months on sale.
Gambit has exciting plans to bring its books to a wider audience by
means of electronic publishing. There are already 15
Gambit titles available for the Kindle e-book reader, with more
to follow in the coming months. Additionally, Gambit will be producing
an app, initially for the iPad, which will enable readers to play over
electronic versions of Gambit books on-screen.
John is also an avid amateur astronomer, as you can see from the latest
images he sent us recently. He made them using a remote telescope of
This image, captured by John in a 70-minute exposure using the T21
telescope of iTelescope.net, is a rather difficult target, as all the galaxies
are quite faint. The galaxies in this cluster are believed to be about 200 million
light-years away, a figure based on the red shift of the galaxies involved.
You can click on the image to get a larger version, and then endeavor to count
the number of galaxies.
John has labelled the more prominent members in the above picture. "I
don't recall having seen the odd double galaxy NGC750/751 before," he says,
"and could only find very few good amateur pictures on the Internet. The
best I could locate is here,
an image using a lengthy exposure of some 20 hours. Is this two galaxies in
the process of merging, or is it something else? Maybe some of our readers can
help by finding more images or information?"
Addendum: Appeals for assistance on our news
page are always answered, including the most obscure ones. Jeremy
Treadwell of Bakersfield, CA, wrote: "The two galaxies are said
to be connected by luminous filaments. You can find more info on them here
(PDF file). These types of double-galaxies are actually common, though I understand
the term is highly subjective. For something really cool, look up WILD's triple
To which John Nunn writes:
It is interesting to see a paper from 1956 (the year after I was born) and
the comparison between an image (left) taken with the Palomar
200-inch telescope, the largest in the world at the time, and one taken
with a modern 12.5 inch RCOS telescope, a high-end amateur instrument costing
just about $20,000.