  We present microlensing planet OGLE-2017-BLG-0173Lb, with planet-host mass
ratio either $q\simeq 2.5\times 10^{-5}$ or $q\simeq 6.5\times 10^{-5}$, the
lowest or among the lowest ever detected. The planetary perturbation is
strongly detected, $\Delta\chi^2\sim 10,000$, because it arises from a bright
(therefore, large) source passing over and enveloping the planetary caustic: a
so-called "Hollywood" event. The factor $\sim 2.5$ offset in $q$ arises because
of a previously unrecognized discrete degeneracy between Hollywood events in
which the caustic is fully enveloped and those in which only one flank is
enveloped, which we dub "Cannae" and "von Schlieffen", respectively. This
degeneracy is "accidental" in that it arises from gaps in the data.
Nevertheless, the fact that it appears in a $\Delta\chi^2=10,000$ planetary
anomaly is striking. We present a simple formalism to estimate the sensitivity
of other Hollywood events to planets and show that they can lead to detections
close to, but perhaps not quite reaching, the Earth/Sun mass ratio of $3\times
10^{-6}$. This formalism also enables an analytic understanding of the factor
$\sim 2.5$ offset in $q$ between the Cannae and von Schlieffen solutions. The
Bayesian estimates for the host-mass, system distance, and planet-host
projected separation are $M=0.39^{+0.40}_{-0.24}\,M_\odot$,
$D_L=4.8^{+1.5}_{-1.8}\,\kpc$, and $a_\perp=3.8\pm 1.6\,\au$. The two estimates
of the planet mass are $m_p=3.3^{+3.8}_{-2.1}\,M_\oplus$ and
$m_p=8^{+11}_{-6}\,M_\oplus$. The measured lens-source relative proper motion
$\mu=6\,\masyr$ will permit imaging of the lens in about 15 years or at first
light on adaptive-optics imagers on next-generation telescopes. These will
allow to measure the host mass but probably cannot resolve the planet-host
mass-ratio degeneracy.
