Material Symmetry to Partition Endgame Tables

Many games display some kind of material symmetry . That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards. Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple rel- atively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess , dominoes , and skat . In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables

Quixo Is Solved

Quixo is a two-player game played on a 5$\times$5 grid where the players try to align five identical symbols. Specifics of the game require the usage of novel techniques. Using a combination of value iteration and backward induction, we propose the first complete analysis of the game. We describe memory-efficient data structures and algorithmic optimizations that make the game solvable within reasonable time and space constraints. Our main conclusion is that Quixo is a Draw game. The paper also contains the analysis of smaller boards and presents some interesting states extracted from our computations.Comment: 19 page

Review of Kalah Game research and the proposition of a novel heuristic-deterministic algorithm compared to tree-search solutions and human decision-making

The Kalah game represents the most popular version of probably the oldest board game ever-the Mancala game. From this viewpoint, the art of playing Kalah can contribute to cultural heritage. This paper primarily focuses on a review of Kalah history and on a survey of research made so far for solving and analyzing the Kalah game (and some other related Mancala games). This review concludes that even if strong in-depth tree-search solutions for some types of the game were already published, it is still reasonable to develop less time-consumptive and computationally-demanding playing algorithms and their strategies Therefore, the paper also presents an original heuristic algorithm based on particular deterministic strategies arising from the analysis of the game rules. Standard and modified mini-max tree-search algorithms are introduced as well. A simple C++ application with Qt framework is developed to perform the algorithm verification and comparative experiments. Two sets of benchmark tests are made; namely, a tournament where a mid-experienced amateur human player competes with the three algorithms is introduced first. Then, a round-robin tournament of all the algorithms is presented. It can be deduced that the proposed heuristic algorithm has comparable success to the human player and to low-depth tree-search solutions. Moreover, multiple-case experiments proved that the opening move has a decisive impact on winning or losing. Namely, if the computer plays first, the human opponent cannot beat it. Contrariwise, if it starts to play second, using the heuristic algorithm, it nearly always loses. © 2020 by the authors.European Regional Development FundEuropean Union (EU); Ministry of Education, Youth and SportsMinistry of Education, Youth & Sports - Czech Republic [LO1303 (MSMT-7778/2014)]; internal grant agency of VSB Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, Czech Republic [SP2020/46

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

Monte-Carlo tree search using expert knowledge: an application to computer go and human genetics

Monte-Carlo Tree Search (MCTS la búsqueda en árbol mediante procesos estocásticos) se ha convertido en el algorítmo principal en muchos problemas de inteligencia artificial e informática. Esta tesis analiza la incorporación de conocimiento experto para mejorar la búsqueda. El trabajo describe dos aplicaciones: una en el 'juego del go' por el ordenador y otra en el campo de la genética humana. Es un hecho establecido que, en problemas complejos, MCTS requiere el apoyo de conocimiento específico o aprendido online para mejorar su rendimiento. Lo que este trabajo analiza son diferentes ideas de cómo hacerlo, sus resultados e implicaciones, mejorando así nuestra comprensión de MCTS. Las principales contribuciones al área son: un modelo analítico de las simulaciones que mejora la comprensión del papel de las simulaciones, un marco competitivo incluyendo código y datos para comparar métodos en etiología genética y tres aplicaciones con éxito: una en el campo de las aperturas en go de 19x19 llamada M-eval, otra sobre simulaciones que aprenden y una en etiología genética. Además, merece la pena destacar: un modelo para representar proporciones mediante estados llamado WLS con software libre, un resultado negativo sobre una idea para las simulaciones, el descubrimiento inesperado de un posible problema utilizando MCTS en optimización y un análisis original de las limitaciones