In this paper, we propose a resource-aware solution to achieving reliable and scalable stream diffusion in a probabilistic model, i.e. where communication links and processes are subject to message losses and crashes, respectively. Our solution is resource-aware in the sense that it limits the memory consumption, by strictly scoping the knowledge each process has about the system, and the bandwidth available to each process, by assigning a fixed quota of messages to each process. We describe our approach as gambling in the sense that it consists in accepting to give up on a few processes sometimes, in the hope of better serving all processes most of the time. That is, our solution deliberately takes the risk not to reach some processes in some executions, in order to reach every process in most executions. The underlying stream diffusion algorithm is based on a tree-construction technique that dynamically distributes the load of forwarding stream packets among processes, based on their respective available bandwidths. Simulations show that this approach pays off when compared to traditional gossiping, when the latter faces identical bandwidth constraints.