Author: Frank Phillips
Date: 01:33:34 09/19/03
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On September 18, 2003 at 19:06:50, GuyHaworth wrote: > >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 Thanks for the analysis. Not as simple as it first appears. I have added an evaluation term to devalue two knights, but having been caught out before am reluctant to just say its a draw. And of course, even the draw is quite balletic. Frank
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