Efficient simulations grow a polymer chain in a sequence of steps that occasionally branches out, seeking optimal pathways. The fraction of optimal pathways from among all possible ones has to be evaluated, in order to determine a new chain's ensemble weight and hence its detailed balance acceptance into a multi-chain system. The total number of all possible pathways, however, is huge and has to be sampled. The consequent use of a sampled detailed balance may be questioned. Here it is shown to be exact (at least in the athermal case).