  Using martingale theory, we compute, in very few lines, exact analytical
expressions for various first-exit-time statistics associated with
one-dimensional biased diffusion. Examples include the distribution for the
first-exit time from an interval, moments for the first-exit site, and
functionals of the position, which involve memory and time integration. As a
key example, we compute analytically the mean area swept by a biased diffusion
until it escapes an interval that may be asymmetric and have arbitrary length.
The mean area allows us to derive the hitherto unexplored cross-correlation
function between the first-exit time and the first-exit site, which vanishes
only for exit problems from symmetric intervals. As a colophon, we explore
connections of our results with gambling, showing that betting on the
time-integrated value of a losing game it is possible to design a strategy that
leads to a net average win.
