The Characterization of Chance and Skill in Games [Elektronische Ressource] / Jakob Erdmann. Gutachter: Ingo Althöfer ; Matthias Löwe

The Characterization ofChance and Skill in GamesDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)vorgelegt dem Rat der Fakultät für Mathematik und Informatik derFriedrich-Schiller-Universität Jenavon Diplom-Informatiker Jakob Erdmanngeboren am 11.07.1980 in Königs WusterhausenGutachter1. Prof. Dr. Ingo Althöfer, FSU Jena2. Prof. Dr. Matthias Löwe, WWU MünsterTag der öffentlichen Verteidigung: 9. Juli 2010ContentsZusammenfassung ivOverview viAcknowledgements viiI The Chanciness of Two-Player Zero-Sum Games 11 Introduction 22 Previous Work 43 Terms and Concepts 54 The Concept of Influence 75 The Relative Influence of Chance 136 Chanciness 167 Simulation Results 188 Relevance of Chanciness for Human Agents 229 Conclusions and Open Problems 25II Chanciness and Controllabilityof N-Player General-Sum Games 2910 Introduction 3011 Previous Work 3212 Terms and Concepts 3613 The Concept of Influence 42ii14 Chanciness 5715 Controllability 6516 Other Influences 7217 Fundamental Results 7618 Approximation of Chanciness and Controllability 8219 Model Games 8920 “EinStein würfelt nicht!” and Variants Thereof 9521 Conclusion 108Bibliography 113Appendix 118A Lottery Chess 118B Lookup Sampling 119C Bounding chanciness and controllability for a Small Game.