We adapt a probabilistic latent variable model, namely GaP (Gamma-Poisson), to ad targeting in the contexts of sponsored search (SS) and behaviorally targeted (BT) display advertising. We also approach the important problem of ad positional bias by formulating a one-latent-dimension GaP factorization. Learning from click-through data is intrinsically large scale, even more so for ads. We scale up the algorithm to terabytes of real-world SS and BT data that contains hundreds of millions of users and hundreds of thousands of features, by leveraging the scalability characteristics of the algorithm and the inherent structure of the problem including data sparsity and locality. Specifically, we demonstrate two somewhat orthogonal philosophies of scaling algorithms to large-scale problems, through the SS and BT implementations, respectively. Finally, we report the experimental results using Yahoos vast datasets, and show that our approach substantially outperform the state-of-the-art methods in prediction accuracy. For BT in particular, the ROC area achieved by GaP is exceeding 0.95, while one prior approach using Poisson regression yielded 0.83. For computational performance, we compare a single-node sparse implementation with a parallel implementation using Hadoop MapReduce, the results are counterintuitive yet quite interesting. We therefore provide insights into the underlying principles of large-scale learning.