Abstract: The Argo array provides nearly 4000 temperature and salinity profiles of the top 2000 meters of the ocean every 10 days. Still, Argo floats will never be able to measure the ocean at all times, everywhere. Optimized Argo float distributions should match the spatial and temporal variability of the many societally important ocean features that they observe. Determining these distributions is challenging because float advection is difficult to predict. Using no external models, transition matrices based on existing Argo trajectories provide statistical inferences about Argo float motion. We use the 24 years of Argo locations to construct an optimal transition matrix that minimizes estimation bias and uncertainty. The optimal array is determined to have a 2°×2° spatial resolution with a 90 day timestep. We then use the transition matrix to predict the probability of future float locations of the Core Argo array, the Global Biogeochemical Array, and the Southern Ocean Carbon and Climate Observations and Modeling (SOCCOM) array. A comparison of transition matrices derived from floats using Argos System and Iridium communication methods shows the impact of surface displacements, which is most apparent near the equator. Additionally, we demonstrate the utility of transition matrices for validating models by comparing the matrix derived from Argo floats with that derived from a particle release experiment in the Southern Ocean State Estimate (SOSE).