From: mzabel@magnus.acs.ohio-state.edu (Mark A Zabel)
Subject: F-SII, Game 2 - Endgame Analysis
Organization: The Ohio State University
Date: Sun, 3 Jan 1993 20:10:48 GMT

     Here's the stuff I promised to post sometime.  Hope it's
worth the reading!

In Fischer-Spassky Game 2, the position after White's (Spassky's)
50th move was the following:

    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |    WHITE: Kc6, Ba7, Be6
    +----+----+----+----+----+----+----+----+           Pa4, Pc4
    | B  |    |    |    |    |    |    | *K |
    +----+----+----+----+----+----+----+----+
    |    | *P | K  |    | B  |    |    |    |    BLACK: Kh7, Nd2, Rb4
    +----+----+----+----+----+----+----+----+           Pa5, Pb6, Pc5
    | *P |    | *P |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    | P  | *R | P  |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    | *N |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+

 Fischer played 50...Nb3?? (Question Marks from Seirawan) and drew.
 The concensus so far seems to be that Fischer should have won with
 50...Nxc4!  The main reason for this seems to be the line:
 51.Bxc4 Rxc4 52.Bxb6 Rxa4 53.Kxc5! Ra2! 54.Kb5 a4 55.Be3 Kg6
 56.Kb4 Kf5 57.Bc1 Ke4 58.Ba3 Kd3 winning, since Kxa4 Kc4
 is ZUGZWANG.  The final statement IS correct, BUT...

 Why does White need the Pawn?  Why not play 58.Bh6 Kd3 59.Bg7
 instead?  The situation at that point looks like:

    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |    WHITE: Kb4, Bg7
    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    | B  |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |    BLACK: Kh7, Ra2
    +----+----+----+----+----+----+----+----+           Pa4
    |    |    |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    | *P | K  |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    | *K |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    | *R |    |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+
    |    |    |    |    |    |    |    |    |
    +----+----+----+----+----+----+----+----+

 I couldn't come up with any winning lines for Black here.
 e.g.  59...Kc2 Bf6 60.Kb1 Bg7 61.Rg2 Bf6 62.Rg4+ Ka3 looks
 like a draw to me.  Also, 58...Kd5 59.Bg7 Rg2 60.Bf6 Rg4+
 61.Ka3 Kb6 62.Be7 Kb5 63.Bd6 Re4 64.Bf8 Re3+ 65.Ka2 Kc4
 seems to be a draw if White keeps his Bishop on the a3-f8
 diagonal, and keeps a3 open for his King should Black
 check with the Rook.  Advancing the Pawn to a3 doesn't seems to
 help either.

 A somewhat analogous position is analysed in Edmar Mednis'
 "questions and Answers On Practical Endgame Play."  The position
is from Campos-Henao, 1976.
     WHITE: Kg2, Bb8, Ph3
     BLACK: Kf4, Rc4, Ph4, Pg5
Here is what GM Mednis has to say about this position.
"... However, there is one class of positions which cannot be
won (R and P against B).  This is where the Pawn has been advanced
too far, with the result that it is both vulnerable and takes away
a key invasion Square from the King. ... It [the position of Campos-
Henao above] turns out to be most frustrating for Black.  The reason
is that after exchange of Black's g-pawn for White's h-pawn a
theoretically drawn position occurs.  R+RP on the 5th or 6th rank vs.
Bishop is drawn if White's pieces are properly placed (as here)
and he defends correctly (something which is not easy to do!).
...This turns out most difficult to do and many analysts have therefore
evaluated Diagram 67 (Campos-Henao) as drawn.  Nevertheless, with a
series of problem-like maneuvers Black can achieve the win.  First
we will follow the game continuation:

     51...Ke4 52.Bd6 Rc2+ 53.Kh1 Kf3 54.Bb8

     This position looks bleak for White but is in fact fully defensible.
Black still cannot play 54...g4 because the position after 55.hxg4
is a theoretical draw.  Moreover, as long as White's Bishop remains
on the h2-b8 diagonal, Black's King cannot get to g3.  Therefore Black
must try to chase White's Bishop away from the present diagonal, but this
can only be done by the combination of Rook and King.  Thus to hope for an
eventual decisive march forward, Black's King must first head
backward..."

As Ross Perot might say, "Now I just find this fascinating!"
Mednis goes on to show a win for Black in Campos-Henao
(54...Rc1+ 55.Kh2 Ke4 56.Kg2 Rc2+ 57.Kh1 Kd5! 58.Kg1 Rc8! 59.Ba7 Ke4
 60.Kf2! Rc7! 61.Bb8 Rb7 62.Bd6 Kd5! 63.Ba3 Rb3! 64.Be7 Rg3!
 65.Kf1 Ke6 66.Bd8 Kf5 and Black wins...whew!), but this method isn't
available in Spassky-Fischer Game 2.  Also, while it is true that the
other side of the board has an asymmetric color complex from the
given example, Mednis states that " R+RP vs. B is drawn if White's
[the defender] pieces are properly placed.  This seems to be the
case in the line given for F_SII Game 2.  White defends on the diagonal
a3-f8 with Black's Pawn on a4 instead of the b8-h2 diagonal with Black's
Pawn on h3 in the given example.

     As I stated in a previous post, I await for this analysis to
be shot full of holes, but I'll be very interested to see what can be
done.  In any event, it seems to me that the move 50...Nb3?? should
at least read 50...Nb3!?  Certainly the position arising after
50...Nc4 is not as easy as Seirawan (and Evans and others who gave
the ZugZwang line) indicate!

-Mark

P.S.  NM Craig Stauffer came up with this idea of defense.  I must
      give credit where credit is due!