  This paper revisits a classical problem of slotted multiple access with
success, idle, and collision events on each slot. First, results of a 2-user
multiple access game are reported. The game was conducted at the University of
Southern California over multiple semesters and involved competitions between
student-designed algorithms. An algorithm called 4-State was a consistent
winner. This algorithm is analyzed and shown to have an optimal expected score
when competing against an independent version of itself. The structure of
4-State motivates exploration of the open question of how to minimize the
expected time to capture the channel for a $n$-user situation. It is assumed
that the system delivers perfect feedback on the number of users who
transmitted at the end of each slot. An efficient algorithm is developed and
conjectured to have an optimal expected capture time for all positive integers
$n$. Optimality is proven in the special cases $n \in \{1, 2, 3, 4, 6\}$ using
a novel analytical technique that introduces virtual users with enhanced
capabilities.
