A Hardware-based Minimax Implementation of a Blokus Duo Agent Reconfigurable Digital Systems - Technical Report

Artificial Intelligence (AI) is a term frequently encountered in every day life, thus proving its significant applicability on a wide range of fields. Among these fields, some of the more popular ones include playing games competitively and decision theory problems. The most dominant solutions to such problems are knowledge-based approaches and the Minimax algorithm. The performance of these approaches appears to be interesting in decision making problems that have either one or more of the following properties: a high branching factor, a deep tree or a moderate heuristic function to evaluate non-terminal nodes. An example of such a problem that comprises these properties is the game of Blokus Duo, a perfect information two player zero-sum game with a finite number of moves and no chance elements a.k.a a combinatorial game. The specific game drew our interest because it was the challenge of the ICFPT 2013 design conference, it is relatively new with few published heuristic functions but, most importantly, the first levels of the tree created have an exponentially increasing number of children nodes and the number of candidates is sometimes over 1000, properties that indicate its demanding nature. With the recent development of the MCTS algorithm, it has been commonly accepted that Minimax performs poorly in complex games, like Go. However, although Blokus Duo is a complex problem, it still has a much smaller game size than Go since the maximum length of the game is 42 moves. Thus we cannot predetermine whether a Minimax-based Blokus Duo player is adequately competitive. Taking this into consideration we decided to evaluate the performance of Minimax in a game that is demanding, but not too complex like Go. In addition, to the best of our knowledge the MHL lab of Technical University of Crete has not designed an architecture for a game that uses limited pieces in every round and therefore requires checking the availability of those pieces. However, it has developed many Minimax-based players such as [1] and [3]. This is another challenge, due to the fact that such games require a more complicated control, even if the algorithm we are implementing is a common Minimax algorithm. Taking into account the above, we concluded that the creation of a hardware-based Minimax Blokus Duo player is an interesting problem with an unpredictable outcome in terms of parallelism and performance. Chapter 2 introduces us to the Minimax algorithm, the rules of the Blokus Duo game, as well as critical strategies followed by professional players. Chapter 3 describes the results of the profiling performed on the respective software. We also analyze hardware opportunities and bottlenecks that this algorithm offers. In Chapter 4 we present the hardware-based implementation of the Blokus Duo player with detailed architecture diagrams and descriptions. Chapter 5 describes performance results, in terms of hardware resource utilization and speed up. Finally, in Chapter 6 a conclusion about the presented work is provided, followed by future work directions that are worth considering.