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The wrong bishop
December 26, 2003 |
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You probably know that a bishop and a pawn will generally
win against a lone king, even if the bishop doesn't control
the queening square of the pawn. A tempo move or two will
dislodge the defending king and the promotion is inevitable.
However there is one important exception. This is when
the pawn is on the edge of the board and the bishop does
not control the promotion square. Here's an example.
In this position White cannot win. The black king simple
shuffles between the squares g8 and h8 (or between h8 and
g7) and cannot be dislodged, only stalemated. Try it out:
1.Be6+ Kh8 2.h7 is stalemate, as is 1.Kh5 Kh8 2.h7 Kg7
3.Bc2 Kh8 4.Kh6. Black must commit a dreadful blunder in
order to lose, e.g. 1.Kh5 Kf8?? 2.Bh7! Kf7 3.Kg5 Ke7 4.Kg6
Kf8 5.Kf6 and White will queen the pawn. But of course
nobody but a world-class patzer will play move the king
to f8.
This ending with the "wrong coloured bishop"
has been know to chess players for a long time. Here's
a study from the 17th century
Gioacchino Greco, Le Iev des Eschets
1621
Black to play and draw
At first sight it looks incredible that Black can draw
this position. After all his opponent has two connected
passed pawns. But it can be done, with just a few sharp
strokes: 1...Ra1+ 2.Rf1 Rxf1+! 3.Kxf1 Bh3!! 4.gxh3
and the position is a theoretical wrong bishop draw, even
though White has two pawns on the h-file. Naturally
4.Kf2 will not help, since Black simply plays 4...Bxg2!
with the same draw to follow.
The rule of the wrong bishop draw is simple. The endgame
king, bishop and pawn vs king is always a draw when
-
the pawn is on the a or h-file and the bishop does
not control the promotion square;
- the defending king can reach the promotion square in
time to defend it.
For a long time this simple piece of chess knowledge eluded
chess playing computers. They simply couldn't calculate
all the way to the promotion, and without specific instructions
on how to handle the position they would often take a wrong
decision. During the eighties, when the first programs
were being told about the wrong bishop draw, I devised
a test position to find out if they could handle the endgame
correctly.
White to play and draw
As an astute chess player you will immediately know what
to do: 1.Kxc5! h5 2.Kd5 h4 3.Ke4 h3 4.Kf3 h2 5.Kg2
Kb7 6.Kh1 ½-½. But for the computers
at the time it was too difficult. They would inevitably
take the bishop and lose the game, e.g. 1.Kxe5?? h5 2.Kf4
Ne6+ 3.Kg3 Kb7 4.Kh4 Ng7 and Black wins. The temptation
was simply too great, they went astray for the following
reasons:
-
a bishop is valued higher than a knight, especially
in open endgame positions;
-
Kxe5 centralises the king, while Kxc5 doesn't
- if it takes the knight the black pawn advances all
the way to h2, where it gets a lot of bonus points for
being one square away from promotion. After taking the
bishop it remains
Naturally any sensible computer would take the bishop,
unless of course it was told to do otherwise. Which seemed
to be the case in the following game.
Human (2265) – Cray Blitz
Mississippi State Championship, 1982
Black to play
Naturally the computer immediately saw the trick and played
1...Rxf3!+ 2.Kxf3 Bd5+ 3.Ke3 Bxa8. With
a piece and a pawn down the human player was reduced to
trying a swindle: 4.a5?! Could it work,
would the program take the free pawn offer? Nope, Cray
Blitz avoided the pittfall and played 4...Be4!,
winning the game comfortably after 5.Kd2 Kd4! 6.Kc1
b5! 7.Kb2 Kc4 8.a6 b4 9.Ka2 Kc3 with a mate announcement
in six.
At the time this was celebrated as the first instance
of practical chess knowledge, implemented into a computer,
leading to a victory when otherwise a draw would be expected.
But some time later I obtained the computer logs and discussed
the position with Harry Nelson of the Cray team. It turned
out that Cray Blitz had simply searched deep enough to
see the promotion after 4...Be4, while it found no queen
on the board after 4...bxa5. It is that simple.
Today all top programs know about the wrong bishop ending
and will solve each of the above endings instantly. For
instance here is Fritz 8 avoiding the temptation after
4.a5?! in the above position:
Not for a single cycle does the program consider 4...bxa5,
it immediately goes to 4...Be4 and tries to work out just
how many pawns this is worth (17, it turns out). Our test
position above is solved in 0:00:00 seconds (1.Kxc5!),
as is the Greco study, as you can see in the picture below.
A test for humans
The following study was shown to us around 1982 by GM
Klaus Darga (we did not have an author at the time). In
the meantime I have found three different sources, the
one given below being the oldest.
J. Vancura, Ceske Slovo 1922
White to play and win
After the lengthy lecture on wrong bishops you will probably
know exactly what this study is all about. Please try to
solve it yourself – and keep a record of the time
you require to find the one correct move in the above position
(all others lead to a draw). You can then compare your
performance to the following players:
-
GM Isván Bilek, whom I showed
the position during the Microcomputer World Chess Championship
in Budapest in 1983. He gave me a wrong line, then
reexamined the position together with an IM colleague
and, moving piece on the board, found the correct move
in a total of 15 minutes.
- The
Polgar infants Sophie and Judit, also in
1983. Sophie was eight at the time, and Judit was almost
seven years old. While eating apples and cake they tossed
the pieces around the board, coming up with the correct
solution ("Sooo simple!?") in 22 minutes.
Susan Polgar with her little sisters in Hungary
in 1983
-
A day earlier I had shown the position to the 14-year-old
Zsuzsa Polgar. She sat in front of
the board, never touched a piece, glanced up occasionally
at me, and then, after 17 minutes dictated the entire
solution correctly.
- In the same year there was a Computer Chess World
Championship in New York, and the guest of honour was
ex world champion Mikhail Botvinnik.
One day he visited the Bell Laboratories and at one stage
sat in the chess club section of the cafeteria, waiting
for a lecture to begin. I set up the four pieces on the
board in front of Botvinnik, and he simply looked at
the position. After a minute or two he said "White
win?", and when I nodded he showed me a wrong line.
I made the refuting move and he set up the pieces in
the original position. Then he sat there without moving
until, with a wry little smile, he executed the correct
first move.
Mikhail Botvinnik (right) with Ken Thompson at
the Computer WCh 1983
- On the day after the Computer Chess World Championship
I showed the position to the new title winner Cray
Blitz. The program, running on a 80 mega-flop
machine (80 million floating point operations per second)
spent 13 seconds considering a wrong key move –
with a logical +4.032 score. Then, at ten ply, it switched
to the correct move and displayed +10.878. Mikhail Botvinnik
saw this all happen and was not very happy to see a computer
solve the position so effectively by pure brute force,
without the chess knowledge he so ardently advocated.
Click
here to see the solutions to all puzzles.
The page contains all the unsolved problems. It includes
a link to a Javascript board on which you can can replay
the moves of each solution and download the positions.
On the Javascript page you will find all the positions
quoted in our 2003 Christmas Puzzle section, including
the ones for which solutions are already given in the text.
Frederic Friedel
Tommy's Christmas Repton
Amazing, just fifteen minutes after we had posted yesterday's
puzzle section we got the first email with the solution
of screen one (i.e. the password for screen two). We also
received a few questions on some details of this fascinating
game. There is little to say, except: figure it out for
yourself. All we can do is give you some vocabulary. The
mysterious object in screen two is an "egg",
what hatches out of it is a "monster". What that
does you can find out for yourself.
To upgrade your Repton to screen two simply download the
following file, repton1.rep (8537 bytes long) and save
it in the subdirectory Christmas Repton\data\maps\, overwriting
the previous repton1.rep file there.
The new file contains the first and second levels. The
latter can be accessed either by solving level one or by
entering the password you get when you solve level one
(click File – Enter password). If you have not started
to play the game yet you can download the whole thing (121
KB) and follow the instructions given at the bottom of
our Chistmas
Day page. Note that this now contains two levels, so
you don't have to retrieve the above file to upgrade.
 We
remind you that you can get the latest Repton game in a
new version (just completed a week ago) from the Superior
Interactive site. Click on the logo on the right and download
a trial version. For $19.95 you can get a key that upgrades
it to the full version.
We will be providing new levels for Tommy's Christmas
Repton on a daily basis until the end of our Christmas
Puzzle week. Please make a note of the passwords, especially
the last one you get. You can send them in, together with
your comments, to take part in our Puzzle contest in which
you can win some interesting prizes.
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