  We study the group Russian roulette problem, also known as the shooting
problem, defined as follows. We have $n$ armed people in a room. At each chime
of a clock, everyone shoots a random other person. The persons shot fall dead
and the survivors shoot again at the next chime. Eventually, either everyone is
dead or there is a single survivor. We prove that the probability $p_n$ of
having no survivors does not converge as $n\to\infty$, and becomes
asymptotically periodic and continuous on the $\log n$ scale, with period 1.
