To be clear about this mechanism of a double twist, I've linked Andy's pic below.
/.../
http://igkt.net/sm/index.php?action=dlattach;topic=1870.0;attach=8735;image
Thanks for that. But, the image shows the formation/start,
not the result, which is a
crossing knot vice a
nipping turn.
.:. IMO, the former is more
stable --and equally functional--
than the latter.
The only thing an extra twist does is reduce the constricting force of the nip,
and thereby reduce security.
And of course, given my thoughts above, I disagree;
I see that the
crossing-knot gives more stability to equally adequate
nip, and hence is a better assurance of the overall structure working.
Tie a Figure 8 Stopper, and compare that to a Figure 9 Stopper, a Figure 10 Stopper,
... and a Figure 99 Stopper. Good luck on getting a Figure 99 to jam or otherwise to hold at all.

Acctually, I happen to be focused on stoppers at the moment,
re use in rockclimbing kernmantle (and other) ropes to "back up"
some other structure, to provide an extra security against untying.
And what the
stevedore knot gives in advantage over the
fig.8 stopperis greater security (not really much greater bulk, though more mass):
the extra wraps better grip the SPart, which in turn then retains
nip on the tail. Even so, working with stiff rope can be difficult.
(There is some help in that for the uses I'm focusing on, one will
typically be tying the stopper
around a rope and so have one
extra diameter to stuff within the bending-resistant wraps!)
The standard "half a
fisherman's"
strangle knot (i.e., with just
one overwrap) is too vulnerable to what I call "sympathetic loosening"
in which both ends ease back into the knot and effect a significant
loosening; wheres the
stevedore-like construction puts the wraps
towards locking one end, which in turn nips secure the other;
some other knots seem better at not so readily loosening on
a little relaxation of tension.)
Through this process of extrapolation, I'm comfortable with saying one twist is the point of maximum constriction.
Hmmm, I think that Xarax presented an orientation of a double
(= 2 turns) nipping loop that should give greater nip, and maybe
more stability, to boot. (For myself, I remain leery of these simple
structures, and prefer a *real* knot, such as the
slip-knot.)
--dl*
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