Collecting cognitive science data using games has the potential to be a powerful tool for recruiting participants and increasing their motivation. However, designing games that provide useful data is a difficult task that often requires significant trial and error. In this work, we consider how to apply ideas from optimal experiment design to designing games for cognitive science experiments. We use Markov decision processes to model players' actions within a game, and then make inferences about the parameters of a cognitive model from these actions. We present a general framework for finding games with high expected information gain based on this approach. We apply this framework to Boolean concept learning, inferring the difficulty of Boolean concepts from participants' behavior. We show that using games with higher expected information gain allows us to make this inference more efficiently.