  Several dozen hypervelocity star (HVS) candidates have been reported based on
the second data release of Gaia (Gaia DR2). However, it has been proven that
the radial velocities of some Gaia HVS candidates are not reliable. In this
paper, we employ refined astrometric criteria to re-examine Gaia DR2, arriving
at a more reliable sample of HVS and high velocity star candidates than those
found by previous authors.We develop a method called Binary Escape Probability
Analysis to identify some HVS candidates. This method allows us to work with
stars having only two epochs of measured radial velocity. These stars were
usually discarded in previous similar studies. A scrutiny of our final results
sheds light on selection effects present in our studies, which we propose to be
the focus of future studies. In total, we find three late-type (2 G-type and 1
K-type) HVS and 21 high velocity star candidates, 3 and 11 of which are new,
respectively. Judging by their historical trajectories, which we calculate, all
three HVS candidates could not have had Galactic center origins. Further
monitoring is required to confirm their status.
