Existing routing protocols for multi-hop wireless networks assume an idealised wireless network in which all links in the network are either on or off and where all functioning links are equally good. Such a model interprets the fraction of packets that are dropped due to contention or interference as broken links, which can in turn lead to increased routing traffic and radio contention. This paper introduces a statistical model of estimated link reliability in wireless networks based on sampling attempted and successful packet transmissions in the network. We present a path metric based on the link model to capture the cost of routes in the network. We investigate both the link model and the path metric in an on-demand probabilistic routing protocol called SAMPLE that is inspired by reinforcement learning techniques. Different scenario-based performance evaluations of the protocol in NS-2 are presented. In comparisons with AODV and DSR, SAMPLE exhibits improved performance in both lossy and congested wireless networks.