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Subject: Some definitions of DTM, DTC etc ...

Author: GuyHaworth

Date: 09:54:42 01/16/06

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DTM == Depth to Mate:
    an SM-/SM+ line by definition minimaxes DTM

DTC == Depth to Conversion, i.e., to force-change and/or mate
    DTC =< DTM
    an SC-/SC+ line by definition minimaxes DTC
    in such a line, 'moves to mate' may be <> DTM ... it all depends

DTZ == Depth to (Move-count) Zeroing (move),
    i.e. to P-push and/or force-change and/or mate
    DTZ =< DTC =< DTM
    an SZ-/SZ+ line by definition minimaxes DTZ

DTZ50 = DTZ except when the defender can invoke a draw under the 50-move rule
    it is assumed the defender will invoke a draw if the chance occurs
    DTZ50 >= DTZ if the game remains decisive
    an SZ50-/SZ50+ line by definition minimaxes DTZ50

In a recent paper by MB, JTamplin and self, we show that there are positions
where no SC-, SM- or SZ-optimal move can retain the win in the presence of a
50-move rule.  We also showed the impact of the 50-move rule on 6-man P-less
endgames with respect to the number of delayed wins (SZ50 > SZ) and the number
of denied wins (SZ50 = draw when the position is otherwise decisive).

g

g





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