dip_noguero.doc - Decision Making System for the Game Oware...

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Decision Making System for the Game Oware By: Carlos Noguero Galilea Home University: Facultad de Informática de Madrid Date: 23/03/2004 Institut für Algorithmen und Kognitive Systeme (IAKS) Fakultät für Informatik - Universität Karlsruhe
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Index: Index: ................................................................................................................................. 1 1 - Introduction: .................................................................................................................. 3 2 - The Game of Oware: ...................................................................................................... 8 2.1 - Rules: ...................................................................................................................... 8 2.2 - Strategies: ............................................................................................................. 15 2.2.1 - Defensive: ....................................................................................................... 15 2.2.2 - Attack: ............................................................................................................. 16 2.2.3 - Kroo Building: .................................................................................................. 17 2.2.4 - Overloading: .................................................................................................... 17 2.2.5 - Pressure: ......................................................................................................... 18 2.2.6 - Counter attack: ............................................................................................... 19 2.3 – Game Phases: ....................................................................................................... 20 2.3.1 - Openings: ........................................................................................................ 20 2.3.2 - Middle Game: .................................................................................................. 22 2.3.3 - End Game: ...................................................................................................... 23 3 – Modelling a utility function: ......................................................................................... 25 3.1 - Searching trees for Oware: .................................................................................... 25 3.2 - Player’s Evolution: ................................................................................................. 29 3.3 - Decision Making and Utility Functions: .................................................................. 31 3.4 - Logic Representation: ............................................................................................ 33 3.4.1 - Unification: ...................................................................................................... 33 3.4.2 - Inference: ........................................................................................................ 34 3.5 - Production Systems: .............................................................................................. 35 3.5.1 - Backward Chaining: ......................................................................................... 36 3.5.2 - Production System for Oware: ......................................................................... 37 4 – The Program: ............................................................................................................... 41 4.1 – Prolog: ................................................................................................................... 41 5 – Conclusions: ................................................................................................................ 44 6 - References: .................................................................................................................. 47 Appendix 1: ...................................................................................................................... 49 Appendix 2: ...................................................................................................................... 57 1 - Introduction: 2
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This work comes from the study of a paper about multi-agent systems and utility functions [13]. After researching on these topics and other theories of AI a specific domain was selected. A game was chosen to apply these techniques and theories. Games and AI have a strong relationship, from a simple program that can play the game, to a complex system that tries to play as a human. Beneath all this there are multiple techniques and combinations that can be applied in game domains. Games provide some advantages over other problems for applying different techniques and measuring the results. One of the most important things is that games have a clearly defined set of rules. These rules limit the possibilities and outcomes of a game and therefore of the problem we are trying to study; as opposed to real world problems, where uncertainty is always present. Games have a clearly defined goal or objective, so that the result calculated by the system can be rated. They also have several degrees of complexity and they present different problems for which some techniques work better than others. All of these features make games an excellent domain in which to test and develop new or old AI theories. This is the domain we have chosen and in it we take a look at certain techniques, some of them used scarcely in games. Before any attempt to solve a game we must choose a representation for it. There are many representations used in AI, one widely used and studied is logic representation. With logic we can describe nearly any system, it is best used in systems that have little information so that the representation does not become complicated. With logic we can also use several methods of reasoning. Using rules is the simplest way to express this reasoning. We call one of these methods of reasoning a 'decision making system'. Decision making systems use logical representations of rules and facts to obtain new results using inference . This systems can work with a simple set of rules and, by means of a complex process, produce the desired conclusions. This is something that is common in games where the information is limited, mainly by the rules. In these cases
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