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We describe an exciting new application domain for deep reinforcement learning (RL): droplet routing on digital microfluidic biochips (DMFBs). A DMFB consists of a two-dimensional electrode array, and it manipulates droplets of liquid to automatically execute biochemical protocols for clinical chemistry. However, a major problem with DMFBs is that electrodes can degrade over time. The transportation of droplet transportation over these degraded electrodes can fail, thereby adversely impacting the integrity of the bioassay outcome. We demonstrated that the formulation of droplet transportation as an RL problem enables the training of deep neural network policies that can adapt to the underlying health conditions of electrodes and ensure reliable fluidic operations. We describe an RL-based droplet routing solution that can be used for various sizes of DMFBs. We highlight the reliable execution of an epigenetic bioassay with the RL droplet router on a fabricated DMFB. We show that the use of the RL approach on a simple micro-computer (Raspberry Pi 4) leads to acceptable performance for time-critical bioassays. We present a simulation environment based on the OpenAI Gym Interface for RL-guided droplet routing problems on DMFBs. We present results on our study of electrode degradation using fabricated DMFBs. The study supports the degradation model used in the simulator.