On optimally reducing search costs for placing replicas in Symphony P2P networks Peer-to-peer (P2P) overlay networks are widely employed in distributed systems. Furthermore, the number of hops required by a node for searching an object is the fundamental search cost of a P2Pnetwork. Hence, since placing replicas can efficiently reduce such a cost of the whole system, how todeploy replicas to reduce it as much as possible becomes a critical problem of P2P networks. In this study, the authors investigate this centre problem for the randomised P2P network `Symphony’. Particularly, the authors present a stochastic analysis on optimal replica placements, in terms of number of total hops, as well as proposing an optimal replica placement algorithm to perform a simulation study on this issue. Both the theoretical and experimental results show that locations of optimal replica placements in Symphony are not necessarily closest to the target node in the identifier space. Hence, based on the results, the authors evaluate one existing simple but experimentally efficient replica placement strategy, which exactly allocates replicas at nodes closest to the target node, to provide some guidelines on designing more efficient strategy applicable to the real-world Symphony.