The problem of assigning a "fun value" to a game is an active area of research. Julian Togelius and Georgios Yannakakis are some of the big names looking at thi

The problem of assigning a "fun value" to a game is an active area of research. Julian Togelius and Georgios Yannakakis are some of the big names looking at this topic right now. One approach is to use tried-and-true statistical techniques to build models from user feedback. Often a player will be provided two variations of a game and asked which one was more fun. This input, combined with various other factors (how did the player perform? how many enemies were there in each version?) help construct some sort of classifier to automatically evaluate new game variations. An alternate approach, which I explored during my Master's research on the topic, was to analyze existing levels in commercially released videogames to construct a model of fun from that, as opposed to considering subjective human feedback. I chose to analyse Super Mario Brothers. It turns out you can see a very characteristic pattern in how the difficult portions of the levels are arranged. This pattern of difficulty takes the form of a rhythmic interplay of difficult and easier portions, and can be nicely described in terms of Flow and the Yerkes-Dodson law. We used this a criterion for evaluating automatically generated levels as a part of a larger system. The applications of this are pretty wide. Perhaps we could automatically evaluate web page interactions according to a certain model of fun to engage users? Perhaps we can detect when people are not having fun and automatically generate alternate designs?