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When media is streamed over best-effort networks, media data is buffered at the client to protect against playout interruptions due to packet losses and random delays. While the likelihood of an interruption decreases as more data is buffered, the latency that is introduced increases. In this paper we show how adaptive media playout (AMP), the variation of the playout speed of media frames depending on channel conditions, allows the client to buffer less data, thus introducing less delay, for a given buffer underflow probability. We proceed by defining models for the streaming media system and the random, lossy, packet delivery channel. Our streaming system model buffers media at the client, and combats packet losses with deadline-constrained automatic repeat request (ARQ). For the channel, we define a two-state Markov model that features state-dependent packet loss probability. Using the models, we develop a Markov chain analysis to examine the tradeoff between buffer underflow probability and latency for AMP-augmented video streaming. The results of the analysis, verified with simulation experiments, indicate that AMP can greatly improve the tradeoff, allowing reduced latencies for a given buffer underflow probability.