Designing and Developing an Intelligent Congkak

Congkak is the nation's traditional game which could soon be forgotten if no serious attention is given to it, but literature survey has not yet found any research publication that mentioned the use of neural network algorithm (NN) on Congkak. Therefore the project want to try to rectify this issue by trying to develop an Intelligent Congkak System that also implemented NN and try answer research question such as this: “What is the best Congkak evaluation function for training NN for game playing?” and “Can Min-Max algorithm (MM) be speeded up by using NN as a forward-pruning method?”. This issues can solved by programming the Congkak system based on previous work on Mancala and NN system, and then recording the performance of the related algorithm. As a result: the project had created a Congkak system that had featured 3 Artificial Intelligence (AI) agent, and discovered that the combination of NN and MM is slower than MM alone

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

Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

A synthetic player for Ayὸ board game using alpha-beta search and learning vector quantization

Game playing especially, Ayὸ game has been an important topic of research in artificial intelligence and several machine learning approaches have been used, but the need to optimize computing resources is important to encourage the significant interest of users. This study presents a synthetic player (Ayὸ) implemented using Alpha-beta search and Learning Vector Quantization network. The program for the board game was written in Java and MATLAB. Evaluation of the synthetic player was carried out in terms of the win percentage and game length. The synthetic player had a better efficiency compared to the traditional Alpha-beta search algorithm

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