We introduce a method for serving models that estimate reach and demographics of cross-device online audiences. The method assigns virtual people identifiers to events. The reach of a set of events is estimated as a simple count of distinct virtual people assigned to these events. This allows efficient serving of reach models at large scale. We formalize what it means for a reach model to be actionable and prove that any actionable reach model is equivalent to some virtual people model. We present algorithms for encoding reach models with virtual people and show that a wide variety of modeling techniques can be implemented with this approach.