We study strategic experimentation with two-armed bandits when the risky arm distributes lump-sum payoffs according to a Poisson process with unknown intensity. We characterize the unique symmetric Markov equilibrium of the game, which is in mixed strategies. Asymmetric pure-strategy equilibria are constructed for the special case where there are two players and the arrival of the first lump sum fully reveals the quality of the risky arm. The efficiency of these equilibria depends on the way players share the burden of experimentation. At least for relatively pessimistic beliefs, even the worst asymmetric equilibrium is more efficient than the symmetric one.