Nowadays, video game developers record every virtual action performed by their players. As each player can remain in the game for years, this results in an exceptionally rich dataset that can be used to understand and predict player behavior. In particular, this information may serve to identify the most valuable players and foresee the amount of money they will spend in in-app purchases during their lifetime. This is crucial in free-to-play games, where up to 50% of the revenue is generated by just around 2% of the players, the so-called whales. To address this challenge, we explore how deep neural networks can be used to predict customer lifetime value in video games, and compare their performance to parametric models such as Pareto/NBD. Our results suggest that convolutional neural network structures are the most efficient in predicting the economic value of individual players. They not only perform better in terms of accuracy, but also scale to big data and significantly reduce computational time, as they can work directly with raw sequential data and thus do not require any feature engineering process. This becomes important when datasets are very large, as is often the case with video game logs. Moreover, convolutional neural networks are particularly well suited to identify potential whales. Such an early identification is of paramount importance for business purposes, as it would allow developers to implement in-game actions aimed at retaining big spenders and maximizing their lifetime, which would ultimately translate into increased revenue.