Peer-to-peer (P2P) has become a popular mechanism for video distribution over the Internet, by allowing users to collaborate on locating and exchanging video blocks. The approach LiveShift supports further collaboration by enabling storage and a later redistribution of received blocks, thus, enabling time shifting and video-on-demand in an integrated manner. Video blocks, however, are not always downloaded quickly enough to be played back without interruptions. In such situations, the playback policy defines whether peers (a) stall the playback, waiting for blocks to be found and downloaded, or (b) skip them, losing information. Thus, for the fist time this paper investigates in a reproducible manner playback policies for P2P video streaming systems. A survey on currently-used playback policies shows that existing playback policies, required by any streaming system, have been defined almost arbitrarily, with a minimal scientific methodology applied. Based on this survey and on major characteristics of video streaming, a set of five distinct playback policies is formalized and implemented in LiveShift. Comparative evaluations outline the behavior of those policies under both under- and over-provisioned networks with respect to the playback lag experienced by users, the share of skipped blocks, and the share of sessions that fail. Finally, playback policies with most suitable characteristics for either live or on-demand scenarios are derived.