Board Games AI

2019 ◽  
pp. 68-80 ◽  
Author(s):  
Tad Gonsalves
Keyword(s):  
Machine Learning ◽  
Machine Learning Algorithms ◽  
Hard Problem ◽  
Game Playing ◽  
Evaluation Function ◽  
Board Game ◽  
Game Tree ◽  
Board Games ◽  
Np Hard Problem ◽  
Alpha Beta

The classical area of AI application is the board game. This chapter introduces the two most prominent AI approaches used in developing board game agents—the MinMax algorithm and machine learning—and explains their usage in playing games like Tic-Tac-Toe, Checkers, Othello, Chess, Go, etc. against human opponents. The game tree is essentially a directed graph, where the nodes represent the positions in the game and the edges the moves. Even a simple board game like Tic-Tac Toe (naughts and crosses) has as many as 255,168 leaf nodes in the game tree. Traversing the complete game tree becomes an NP-hard problem. Alpha-beta pruning is used to estimate the short-cuts through the game tree. The board game strategy depends on the evaluation function, which is a heuristic indicating how good the player's current move is in winning the game. Machine learning algorithms try to evolve or learn the agent's game playing strategy based on the evaluation function.

Board Games AI

2018 ◽  
pp. 144-155
Author(s):  
Tad Gonsalves
Keyword(s):  
Machine Learning ◽  
Machine Learning Algorithms ◽  
Hard Problem ◽  
Game Playing ◽  
Evaluation Function ◽  
Board Game ◽  
Game Tree ◽  
Board Games ◽  
Np Hard Problem ◽  
Alpha Beta

The classical area of AI application is the board games. This chapter introduces the two most prominent AI approaches used in developing board game agents – the MinMax algorithm and Machine Learning and explains their usage in playing games like tic-tac-toe, checkers, othello, chess, go, etc., against human opponents. The game tree is essentially a directed graph, where the nodes represent the positions in the game and the edges the moves. Even a simple board game like tic-tac toe (noughts and crosses) has as many as 255,168 leaf nodes in the game tree. Traversing the complete game tree becomes an NP-hard problem. Alpha-beta pruning is used to estimate the short-cuts through the game tree. The board game strategy depends on the evaluation function, which is a heuristic indicating how good the player's current move is in winning the game. Machine learning algorithms try to evolve or learn the agent's game playing strategy based on the evaluation function.

scholarly journals A Synthetic Player for Ayὸ Board Game Using Alpha-Beta Search and Learning Vector Quantization

2016 ◽  
Vol 9 (3) ◽  
pp. 1
Author(s):  
Oluwatobi, A. Ayilara ◽  
Anuoluwapo, O. Ajayi ◽  
Kudirat, O. Jimoh
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Vector Quantization ◽  
Search Algorithm ◽  
Learning Vector Quantization ◽  
Game Playing ◽  
Learning Approaches ◽  
Board Game ◽  
Significant Interest ◽  
Alpha Beta

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 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.

scholarly journals Free versus bound entanglement, a NP-hard problem tackled by machine learning

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Beatrix C. Hiesmayr
Keyword(s):  
Machine Learning ◽  
Large Family ◽  
Machine Learning Algorithms ◽  
Entangled States ◽  
Hard Problem ◽  
Np Hard ◽  
Entanglement Witnesses ◽  
Np Hard Problem ◽  
Bound Entanglement ◽  
Ppt Criterion

AbstractEntanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find $$82\%$$ 82 % to be free entangled, $$2\%$$ 2 % to be certainly separable and as much as $$10\%$$ 10 % to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining $$6\%$$ 6 % of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.

SIZES OF ORDERED DECISION TREES

2002 ◽  
Vol 13 (03) ◽  
pp. 445-458 ◽  
Author(s):  
HANS ZANTEMA ◽  
HANS L. BODLAENDER
Keyword(s):  
Machine Learning ◽  
Decision Tree ◽  
Decision Trees ◽  
Blow Up ◽  
Inductive Inference ◽  
Hard Problem ◽  
Minimal Size ◽  
Knowledge Based ◽  
Np Hard Problem ◽  
Decision Tables

Decision tables provide a natural framework for knowledge acquisition and representation in the area of knowledge based information systems. Decision trees provide a standard method for inductive inference in the area of machine learning. In this paper we show how decision tables can be considered as ordered decision trees: decision trees satisfying an ordering restriction on the nodes. Every decision tree can be represented by an equivalent ordered decision tree, but we show that doing so may exponentially blow up sizes, even if the choice of the order is left free. Our main result states that finding an ordered decision tree of minimal size that represents the same function as a given ordered decision tree is an NP-hard problem; in earlier work we obtained a similar result for unordered decision trees.

scholarly journals On Constructing Static Evaluation Function using Temporal Difference Learning

2013 ◽  
Vol 2 (1) ◽  
pp. 175-184
Author(s):  
Samuel Choi Ping Man
Keyword(s):  
Computer Game ◽  
Temporal Difference ◽  
Game Playing ◽  
Evaluation Function ◽  
Temporal Difference Learning ◽  
Board Games ◽  
Good Evaluation ◽  
Game State ◽  
Moderate Complexity ◽  
Static Evaluation

Programming computers to play board games against human players has long been used as a measure for the development of artificial intelligence. The standard approach for computer game playing is to search for the best move from a given game state by using minimax search with static evaluation function. The static evaluation function is critical to the game playing performance but its design often relies on human expert players. This paper discusses how temporal differences (TD) learning can be used to construct a static evaluation function through self-playing and evaluates the effects for various parameter settings. The game of Kalah, a non-chance game of moderate complexity, is chosen as a testbed. The empirical result shows that TD learning is particularly promising for constructing a good evaluation function for the end games and can substantially improve the overall game playing performance in learning the entire game.DOI: 10.18495/comengapp.21.175184

scholarly journals The time spent on board games pays off : links between board game playing and competency motivation

2021 ◽  
Vol 19 (1) ◽  
pp. 119-131
Author(s):  
András Ferenc Dukán ◽  
Katalin Fried ◽  
Csaba Szabó
Keyword(s):  
Game Playing ◽  
Board Game ◽  
Board Games

Technical Elements of Machine Learning for Intellectual Property Law

2021 ◽  
pp. 11-27
Author(s):  
Anthony Man-Cho So
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Face Recognition ◽  
Intellectual Property ◽  
Speech Synthesis ◽  
Text Processing ◽  
Property Law ◽  
Game Playing ◽  
Board Game ◽  
Music Retrieval

Recent advances in artificial intelligence (AI) technologies have transformed our lives in profound ways. Indeed, AI has not only enabled machines to see (eg, face recognition), hear (eg, music retrieval), speak (eg, speech synthesis), and read (eg, text processing), but also, so it seems, given machines the ability to think (eg, board game-playing) and create (eg, artwork generation). This chapter introduces the key technical elements of machine learning (ML), which is a rapidly growing sub-field in AI and drives many of the aforementioned applications. The goal is to elucidate the ways human efforts are involved in the development of ML solutions, so as to facilitate legal discussions on intellectual property issues.

TrapAB: A New Position Search Algorithm in Chinese Chess Computer Game

2013 ◽  
Vol 380-384 ◽  
pp. 1621-1624 ◽  
Author(s):  
Jian Fang ◽  
Jian Chi ◽  
Hong Yi Jian
Keyword(s):  
Search Algorithm ◽  
Computer Game ◽  
Search Algorithms ◽  
Tree Search ◽  
Game Playing ◽  
Game Tree ◽  
Alpha Beta ◽  
Comparative Results ◽  
Potential Traps ◽  
Game Tree Search

In this paper, we propose an improved alpha-beta search algorithm, named trappy alpha-beta (simply), for game-tree in order to identify and set the potential traps in the game playing. can be regarded as an extension of the traditional alpha-beta search algorithm which ties to predict when the opponent might make a mistake and select such moves that can most likely lead the an opponent into the trap by comparing the various scores returned through iterative deepening technology. In our experiment, we test the performance of in comparison with three game-tree search algorithms, i.e., min-max, trappy minimax, and alpha-beta, by playing with four testing opponents, which are obtained form a typical Chinese chess computer game program-Xqwizard (http://www.xqbase.com). The comparative results show that our designedcan effectively find and set the traps in the playing with opponents.

scholarly journals Iterative Min Cut Clustering Based on Graph Cuts

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 474
Author(s):  
Bowen Liu ◽  
Zhaoying Liu ◽  
Yujian Li ◽  
Ting Zhang ◽  
Zhilin Zhang
Keyword(s):  
Machine Learning ◽  
Simple Formula ◽  
Clustering Algorithm ◽  
Graph Cut ◽  
Hard Problem ◽  
Running Time ◽  
Benchmark Datasets ◽  
Np Hard Problem ◽  
Graph Based Clustering ◽  
Min Cut

Clustering nonlinearly separable datasets is always an important problem in unsupervised machine learning. Graph cut models provide good clustering results for nonlinearly separable datasets, but solving graph cut models is an NP hard problem. A novel graph-based clustering algorithm is proposed for nonlinearly separable datasets. The proposed method solves the min cut model by iteratively computing only one simple formula. Experimental results on synthetic and benchmark datasets indicate the potential of the proposed method, which is able to cluster nonlinearly separable datasets with less running time.

scholarly journals Primary school teachers’ attitude to board-games and their board-game playing practice

2021 ◽  
Vol 14 (1) ◽  
pp. 182-187
Author(s):  
Ana JUHÁSZ
Keyword(s):  
Primary School ◽  
Elementary School Teachers ◽  
Teaching And Learning ◽  
Private Life ◽  
Game Playing ◽  
Board Game ◽  
School Teachers ◽  
Primary School Teachers ◽  
Board Games ◽  
Problem Solving Competency

Abstract: The usage of games in the process of teaching and learning is always advantageous, because children prefer to learn playfully. Board-games are particularly enjoyable for children. They do not learn consciously, but they enjoy playing together with their parents and siblings, because board-games bring together both family and friends. Playing board-games is not only a joyful activity, it also develops different skills of the player, as communication skills, strategy creating and problem solving competency, cooperation, etc. Nowadays there are many boardgames on sale, active board-game playing communities organize events, and a culture of playing board-games is developing. Thus integrating board-games in educational activities seems to be a natural process to follow. But this integration has many obstacles, as time and curriculum constrains, the lack of methodological knowledge of the teachers, inadequate choose of educational board-games for some subjects, etc. The aim of this research is to study primary school teachers’ attitude to playing board-games and their board-game playing practice. The results show that majority of the participating elementary school teachers love playing boardgames, almost half of them also play board games in their private life. Most of them bring these games to the classroom as well. Teachers love these games, because they are fun, teach logical thinking, make students creative, help them to relax, are team builders, motivate students to learn, get used to speed, develop attention, teach strategies, and are childhood favorites.

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