When media is streamed over the Internet, a best-effort packet delivery network, buffers are used at the client to average the performance of the network over time. While large buffers are attractive because they provide immunity to correspondingly larger channel variations, they also lead to longer delays at the client. Adaptive playout strategies mitigate this tradeoff by varying the rate at which media is played according to the fullness of the client buffer. This work extends previous analysis of delay vs. buffer underflow performance of adaptive media playout schemes. Previous analyses have assumed deterministic packet interrarrival times, or have assumed that all packets arrive correctly and ignore the issue of retransmission. In this paper our channel model incorporates both random interarrival times and random packet errors. We present methods to find average playout rates and buffer underflow probabilities for three scenarios which include: short media clips, long programs streamed at the maximum available bandwidth, and long programs streamed at 90% of the maximum available bandwidth, allowing room for retransmissions.