Learning strategies for infinite games

F ur meine Eltern Acknowledgments First of all, I would like to thank my advisor, Prof. Dr. Wolfram Menzel, for all the support he gave to me during the work on this thesis. I am very grateful to Privatdozent Dr. Martin Kummer who introduced me into the world of games and who helped me so much to get this project started. I am glad that I had the opportunity to work with him. His broad knowledge, brilliance and teaching abilities were of inestimable use for me. I also appreciate his careful reading of the text and his many comments, which very much helped to improve the text. My best thanks go to Dr. (\Super-")Frank Stephan. Again and again, he deeply impressed me by the amazing speed and unlimited range of his mathematical skills, which I absolutely admire. It is a great pleasure to work with him. So often, he helped me out, when I got stuck in mathematical mud and couldn't see any further way to go. Next, I would like to thank my further co-authors Prof. Dr. John Case and Prof. Dr. Arun Sharma. I very much enjoyed collaborating with them. John inspired me so much by the many interesting discussions we had (not only about scientiic topics). I am very grateful to John for co-reviewing my thesis, in particular , for visiting Karlsruhe in order to be part of my thesis committee. My best thanks go to Arun, who made it possible for me to visit the University of New South Wales in Sydney two times (while it was winter in Germany). I had great and fruitful times in Australia, and I learned a lot from Arun, in particular, about the \business of science". My deepest thanks go to Prof. Dr. Roland Vollmar for acting as my co-referee, in times when he really had more important things to take care of. I very much enjoyed the friendly and warm way he (in particular) is chairing the \Graduiertenkol-leg", which I was a member of. I very much like to thank all my colleagues from the \Institut f ur Logik, Kom-plexitt at und Deduktionssysteme" for providing such a nice and friendly environment to work in, for many interesting discussions, for their comments, for all the great fun, for suuering my laugh, and for being reasonable players in our weekly soccer game. I am grateful to the Deutsche Forschungsgemeinschaft (DFG) for …