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| This is the fourth-roll position that occurred in the sequence discussed in this thread. The diagram on the left shows the board before Blue plays his 51. The diagram on the right shows the best play, D (Down) = 14/8.
This position illustrates one of the more subtle rules of Nactation: When you have a choice in a roll of non-doublets, for purposes of Nactation, you must play the larger number first. With this 51, that means moving 14/9 first, and then moving 9/8. The resulting Nactation has both dice being played down, and thus the play belongs in the D (Down) family. Were it acceptable in Nactation to play the smaller die first, then the move could also be nactated as 14/13, 13/8. The first part, 14/13, is a move on the far side of the board, while 13/8 is a move played down. If the Nactation were allowed (which it is not), this latter play would belong in the Z (Reverse split) family. To prevent the clutter and ambiguity that can arise when one play is allowed to be a member of more than one family, Nack wisely created the higher-die-first rule. Now consider the “convenience clause” that allows S to be used as a stand-in for Z. For reasons of history, we are probably stuck with it. As Nack points out, players are now comfortable with 21S, 41S and 51S. But can you see the parallel to the higher-die-first situation? The convenience clause allows precisely what the higher-die-first rule is designed to prevent: the potential ambiguity and confusion that can arise when one play is allowed to belong to more than one family. When Nactation was used only to describe very early opening moves it was a reasonable decision to allow S to be used as a substitute for Z. Now that Nactation has been extended for use into middle and end-games, however, we have situations where S and Z are the Nactations for plays that do not split in the traditional sense at all, and do not even necessarily move a checker in the rear quadrant. It is not always trivial to discern whether the S family is empty, and therefore can be used in place of Z. A fair appraisal should admit that if we could erase history, and start from scratch, S would probably not be allowed as a substitute for Z. Whether it is too late to change is a matter upon which fair-minded people can disagree. Mike |