  \emph{Contention Resolution} is a fundamental symmetry-breaking problem in
which $n$ devices must acquire temporary and exclusive access to some
\emph{shared resource}, without the assistance of a mediating authority. For
example, the $n$ devices may be sensors that each need to transmit a single
packet of data over a broadcast channel. In each time step, devices can
(probabilistically) choose to acquire the resource or remain idle; if exactly
one device attempts to acquire it, it succeeds, and if two or more devices make
an attempt, none succeeds. The complexity of the problem depends heavily on
what types of \emph{collision detection} are available. In this paper we
consider \emph{acknowledgement-based protocols}, in which devices
\underline{only} learn whether their own attempt succeeded or failed; they
receive no other feedback from the environment whatsoever, i.e., whether other
devices attempted to acquire the resource, succeeded, or failed.
  Nearly all work on the Contention Resolution problem evaluated the
performance of algorithms \emph{asymptotically}, as $n\rightarrow \infty$. In
this work we focus on the simplest case of $n=2$ devices, but look for
\underline{\emph{precisely}} optimal algorithms. We design provably optimal
algorithms under three natural cost metrics: minimizing the expected average of
the waiting times ({\sc avg}), the expected waiting time until the first device
acquires the resource ({\sc min}), and the expected time until the last device
acquires the resource ({\sc max}).
