A novel, biophysically realistic model for early-stage, acetylcholine-mediated retinal waves is presented. In this model, neural excitability is regulated through a slow after-hyperpolarization (sAHP) operating on two different temporal scales. As a result, the simulated network exhibits competition between a desynchronizing effect of spontaneous, cell-intrinsic bursts, and the synchronizing effect of synaptic transmission during retinal waves. Cell-intrinsic bursts decouple the retinal network through activation of the sAHP current, and we show that the network is capable of operating at a transition point between purely local and global functional connectedness, which corresponds to a percolation phase transition. Multielectrode array recordings show that, at this point, the properties of retinal waves are reliably predicted by the model. These results indicate that early spontaneous activity in the developing retina is regulated according to a very specific principle, which maximizes randomness and variability in the resulting activity patterns.