This paper summarizes the AAIA'17 Data Mining Challenge: Helping AI to Play Hearthstone which was held between March 23, and May 15, 2017 at the Knowledge Pit platform. We briefly describe the scope and background of this competition in the context of a more general project related to the development of an AI engine for video games, called Grail. We also discuss the outcomes of this challenge and demonstrate how predictive models for the assessment of player's winning chances can be utilized in a construction of an intelligent agent for playing Hearthstone. Finally, we show a few selected machine learning approaches for modeling state and action values in Hearthstone. We provide evaluation for a few promising solutions that may be used to create more advanced types of agents, especially in conjunction with Monte Carlo Tree Search algorithms.