In the bounded delay buffer management problem unit size packets arrive online to be sent over a network link. The objective is to maximize the total weight of packets sent before their deadline. In this paper we are interested in the two-valued variant of the problem, where every packet has either low (1) or high priority weight (α > 1). We show that its randomized competitive ratio against an oblivious adversary is 1 + (α − 1)/(α 2 + α).