Re: Chained pivot/loop notation: a proposal

[Dan Hoey]

"Josh Purinton" <josh.p...@gmail.com> wrote to suggest that
the neo-Glop-notation position 0.AB/0.0.0.AB.CD.EF/0.CD/0.0.EF be
written in pivot/loop notation as 1L3(L1)(L2).

I have a slightly different suggestion: that the position be written
1L3((L1))((L2)). Why the extra parentheses? Because then we can
add Glop notation to pivot/loop notation by writing it inside single
parentheses, AND we can add pivot/loop notation to Glop notation by
writing it inside single parentheses. The double parenthesis notation
is a simple consequence of the two abbreviations.

So we have the well-known equality ...P0P0 = ...P1 . This could also
be written ...P(2) = ...P(0). In this way the pivot/loop notation
becomes completely as expressive as Glop notation. And we can write
Glop positions like 0.0.0.0.0.0.AB/0.0.0.1<1>.2.AB as (6LA5(2)).

By the way, today I proved the equality ...L(2) = ...L(0). This may
be a much more useful equality, since it can cut down the size of a
game tree right at the root. As with the other equality, it holds in
both normal and misere play.

Dan