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Subject: Re: With Diagram (Attn Steve Lim) (more discussion)

Author: Robert Hyatt

Date: 09:22:03 12/09/03

Go up one level in this thread


Here is how to discover how to win this.

The game is really two sub-games.  First, remove the black pawns and
white king.  See what you can do to prevent the black king from eating
all your pawns.  You will find that zugzwang is a critical factor.

IE with just the three white pawns and white king and black king, it
is an easy mate by tables.  But it isn't quite as easy really, because
the white king can't march up the board to help.  If it does, you have
to remember that in the _real_ game the black pawns on the other side of
the board will run if the white king leaves their "square" (square of the
pawn).

IE try a4 Kd7 c4 Kc7 a5 Kb7 c5.  Now what does black do?

Kc6?  a6 and it is over.  Ka6? c6 and it is over.

So here, black does not want to move.  White brings up the
other pawn and forces a queen. So when black doesn't want to
move on the queen-side, he moves on the king-side.  And the
reverse plays out.  But the issue here is that white moves
first, and every move he plays puts black into a move and lose
situation.  Eventually black gets zugged on both sides and
has to push a pawn white white eats, and once the king-side
black pawns are gone, the white king comes to the queenside
and the game is over.

It is cute.  I once write a special evaluator for this, but
never quite got it all finished.  The idea was to recognize
the zug positions on both sides, and if the same side gets
zugged on _both_ sides of the board, he loses.  That can be
forced on black with perfect play.  Otherwise you can reach
positions where either side can move and not lose on one side
of the board and it is a draw.  And if white screws up twice,
black can zug white on both sides and actually win.

That's a simplistic description, but note the plan of a/c pawns
advancing, then the b-pawn is available to chuck a tempo if white
ends up in zugzwang because black defends against the pawns
correctly.  There are some well-known drawn positions, such as
where the pawns are at (say) a5, b4 and c5 with the black king
at b5.  The pawns are stuck with no support.  While black can
go to a6/c6 with no problems.  So you _never_ reach that
position with white or you are screwed into at least a draw.

More if you are interested.




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