Using Entropy for Modeling Difficulty in the Asteroid Escape Sliding Puzzle

Developing a standarized metric for difficulty that can be applied to a large number of puzzles is not trivial. This does not come as a surprise because of the subjective factors involved in defining difficulty. However, studies that address the design and application of metrics that can be applied to multiple games are still important, because they can still be used to increase the quality of content generated by automated agents. We take a look at applying information entropy concepts in the game Asteroid Escape and compare the results with other metrics to assess difficulty used in games of similar characteristics. This approach is largely based on future work proposal from a previous study done on The Witness puzzles that yielded positive results on using an automatic method to assess the difficulty of user rated puzzles. This study also includes a modification of BFS and A* capable of finding every shortest solution. From the implementation, it is possible to look at contradicting results with the literature, where basic metrics had a better result correlating with an official definition of difficulty from the game designers. The impact expected from this study is to propose an update to the the corpus of puzzle games where the uncertainty metric for difficulty has been applied. As having an accurate assessment of difficulty can open the doors to other studies, such as improving the quality of the output from procedural content generation methods in games or propose an automated method of difficulty adjustment based on this metric.