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Subject: Frank Phillips' KNNKP position revisited ...

Author: GuyHaworth

Date: 16:06:50 09/18/03



Frank's position last week is really 'on the edge' in terms of winability.
Maximising DTM can throw away the draw for Black, but it does take time.


The endgame query service at http://chess.jaet.org/cgi-bin/dtx shows that:

[D] 8/4k3/8/8/4Kp1p/5N1N/8/8 w

requires 1. Kxf4 to retain the win, ignoring the 50-move rule.


Then Dwe are into KNNKP with DTZ = 51, but this means that the winner requires
51 moves, and (given the nature of KNNKP endgames) Black is forced to play 52.
... h3 but only on ply 103.

White therefore needs to see Black wasting 2 moves in DTZ terms - "Depth to
Zeroing (move-count)".


In the line I followed, White and Black subset their moves as follows:
White play SZ'Z50-Z-C-
    i.e. White first 'guards' DTZ, leaving only moves beating the 50-move rule
         If there are none, White plays SZ-, minimising DTZ
         Next, White minimises DTZ50 from the remaining moves
           DTZ50 == DTZ unless the win can be thwarted by a 50-move draw claim
         In fact, for some time, DTZ50 is 'draw' so White considers all moves
         Next, White minimises DTZ from the remaining moves
         If DTZ > moves_left as here initially, SZ'Z50-Z- == SZ-
         Lastly, White minimises DTC from the remaining moves

[ SZ' == SZ<degree sign> in my normal notation ]

Black has the 50-move rule on its side and plays a simpler strategy:
Black plays SM+Z+
    i.e. Black first maximises DTM(ate) and then DTZ
    Of course, this gives White the chance it needs.
    Black should though play SZ50+ hre to defend its 50-move draw

The play then went like this:

a)  Black wasted 1 move of DTZ-depth on moves 2b and 5b
      Therefore, from move 6w, White knows it can complete phase 1 'in time'
      However, White knows that DTZ50 still says 'draw'
      Therefore, a later phase can still be forced to be longer than 50m
b)  If Black could have changed strategy to SZZ50+ ...
      It could still have got its 50-move draw as late as move 20b
c)  However, at move 20b, Black drops 11 moves of depth in DTZ50 terms ...
      ... allowing White to complete phase 1 in 49m and avoid a draw-claim

The "SZ+" part of Black's move-subsetting strategy is hardly relevant.  The
"SM+" part usually picks a unique move for Black.

Black does not retain the draw with SM+Z50+ either.

Black had a choice of 2 moves only twice - on moves 16 and 17.  I would expect
these to hand White the win in a similar way.

g



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