  The Event Horizon Telescope (EHT), a global sub-millimeter wavelength very
long baseline interferometry array, is now resolving the innermost regions
around the supermassive black holes Sgr A* and M87. Using black hole images
from both simple geometric models and relativistic magnetohydrodynamical
accretion flow simulations, we perform a variety of experiments to assess the
promise of the EHT for studying strong gravity and accretion physics during the
stages of its development. We find that (1) the addition of the LMT and ALMA
along with upgraded instrumentation in the "Complete" stage of the EHT allow
detection of the photon ring, a signature of Kerr strong gravity, for predicted
values of its total flux; (2) the inclusion of coherently averaged closure
phases in our analysis dramatically improves the precision of even the current
array, allowing (3) significantly tighter constraints on plausible accretion
models and (4) detections of structural variability at the levels predicted by
the models. While observations at 345 GHz circumvent problems due to
interstellar electron scattering in line-of-sight to the galactic center, short
baselines provided by CARMA and/or the LMT could be required in order to
constrain the overall shape of the accretion flow. Given the systematic
uncertainties in the underlying models, using the full complement of two
observing frequencies (230 and 345 GHz) and sources (Sgr A* and M87) may be
critical for achieving transformative science with the EHT experiment.
