DOCSLIB.ORG

A COMPUTER-ASSISTEDSTUDY of GO on M X N BOARDS* By

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A COMPUTER-ASSISTEDSTUDY of GO on M X N BOARDS* By A COMPUTER-ASSISTED STUDY OF GO ON M X N BOARDS* by Edward Thorp Mathematics Department University of California at Irvine Irvine, California and William E. Walden Computing Center Washington State University Pullman, Washington P 1 7V6Q 7-Aua..- _aX? a<_ <^A.rf. /XX" <=^r/if~**i iA^J^T^^M^ -cvaVlp. f-t^.t&tL. &Q fe-w. Asy(X cr/ Zifo- .^.yAy-i /frm<J<J! pen £X^ -Ovl^ . l^}-^JL ptZF/c. /2>£ V : Rp u> a-^-X : *~«^mU <=t<s~<3.<_~ Zytfy UF:^-UF:"- J..J.- lLA.^t'tCJ^yCT Ja^<2yLZA7a,,: UiUj Jy\jX~^J^L*^r2 _ ftSLs r //Vl.-^^^^y y * j « r * fyxv c s z>«2_ *■* aa: cx^y^ v-'/"X "/yx^.^y" L4J~)SV^~> /^-*-i-t^>-'L, _AIX <Av<^i. / it t r: /v <^ " A^ kA UcX^b, S £?>--;. CONTENTS 1. Introduction 1 2. Topology 3 3. Combinatorics 6 4. Rules H 5. Illustrative Game Trees for Tiny Boards 19 6. Evaluation of Tiny Boards 27 7. Heuristics 8. The Computer Program 9. Potential Uses of the Program 10. Miscellany Figures References A COMPUTER-ASSISTED STUDY OF GO ON M x N BOARDS ': by Edward Thorp and Wil liana Walden 1. Introduction: The game of Go is believed to have originated in China about four thousand years ago. It has been intensely cultivated in Japan for more than a thousand years and is now played throughout the world. For the history of Go, refer to Falkener (1961), or Smith (1956). Playing technique is discussed in Goodcll (1957), Lasher (i960), Morris (1951), Smith (1956), and Takagawa (1958). For those who worry about whether the study of games is useful, we remark that an interest in games of chance led Cardano, Fermat and Pascal to initiate the theory of probability. Providing a theoretical frame- work for poker was one of the objectives of Yon Neuman's theory of games. Recently one of the authors was faced with the problem of determining the optimum amount to bet on positive expectation situations in casino blackjack. Using results by Kelley (1956) and Breiman (1961), a theory of resource, allocation (synonyms are bet sizing and portfolio selection) was developed. This theory (Thorp 1969) supplants and refutes the theory of portfolio selection due to Markowitz (1959) which is generally accepted by economists. This research was supported in part by Grant AF-AFOSR 1113-66. 2 * We find Go a particularly promising game of skill to analyze. Tens of millions of people play it and it has been developed to an extremely high level, of skill. This means that computer analysis can be checked or tested again analysis by highly skilled human players. Also, the rules are few and simple, which suggests that the game may have significant theorems . There are several ways to study Go with the aid of a computer. Remus (1962) wrote a computer program, to learn "good" strategies and simulated the game on a smaller board. Another approach is to combine positional evaluation functions and tree computations, as has been done for chess. We study the game on an M X N board rather than the usual 19x19 board . First we give the complete tree calculation for tiny boards. Then we extend the analysis to larger boards. Previous studies of bridge and poker via tiny decks are, for instance, close in spirit to our approach. This paper continues our work in Thorp and Walden (1964). We suggest reading that paper before proceeding here. These approaches can be modified by combining man and machine. Our computer program, or others, can be used like a "super slide rule" to assist a human player in actual play. This might fit in with the project announced in Engelbart, 1968. One wonders why this isn't done in chess for instance. A contention sometimes made is that: two players who 3 * consult in a chess game don't generally do as well as the stronger player would have done alone. Whether or not this is true, we observe that with two consulting players, if there is much disparity, the abilities of the weaker player are nearly subsumed by those of the stronger player. Thus, the weaker player is redundant and only distracts the stronger player with fruitless discussions. With two equal players we might expect their different com- peting strategies to interfere with each other. But in a man-machine symbiosis, skills are complementary. Also, disputes do not arise: the man uses the machine when he wishes to, and not otherwise. The difference is that between calculating with a super slide rule and calculating with a committee. 2. Topology: The game of Go is played on a rectangular board marked with two mutually perpendicular sets of parallel lines. The standard board has 19 lines in each direction. This produces 361 points of intersection. The two players, Black and White, move alternately beginning with Black. A move consists either of placing a piece Atone) on a vacant point of inter- section, or of passing. The object of the game is to capture stones and to surround territory. Two vertices are adjacent if they are on the same horizontal, or vertical line and there are no vertices between them. Classify vertices 4 into three types: black, white and vacant. Vertices v and w are connected if there is a chain (v., .... v ) of vertices of the same type such that v = v , 1 n l v is adjacent to v. , , 1-i § n I. and v =w. The v. need not be clis- i J l+l - n l tinct. In particular, we allow v= v for 1-i = n. Connectedness is an i equivalence relation (i. o. , it is reflexive, symmetric, and transitive). Thus, it partitions the board into disjoint equivalence classes. Call these equivalence classes groups. We will, distinguish between groups of stones and groups of spaces. If the vertices adjacent to a vertex in a given group are of the same type, that vertex is in the interior of the group. If the adjacent vertices are not of the same type, that vertex is a boundary point of the group. A vacant vertex adjacent to a black or to a white stone is a breathing space or degree of freedom (I. J. Good, 1965) for the group to which that stone belongs. Rule 1 ( Capture). If a group of stones has exactly one breathing space and the other player is permitted to move there (he may not be, because of the Ko rule or a rule prohibiting all cycles of even length, then if he does so, he captures that group. It is removed from the board and set aside. At the end of the game players receive one point for each captive. Rule 2 (Suicide is illegal). If a player's group of stones has exactly one breathing space, a move there by the player (which would deprive his own group of breathing space and cause it to be removed, i. c. , suicide) is illegal. If a single empty vertex is completely surrounded by stones of 5 the opposing color, a player can move there only if the move results in the removal of one or more of the adjacent men. (Otherwise, the move creates a group of one stone with no breathing space, which causes it to be removed, i. c. , suicide. ) A chain (v , v , . , v ) of vertices such that v. is adjacent to 12 n i v for 1-i = n - 1 is a path, If v= v and w= v , v and w are joined j — l n by path (v , v ). A group G surrounds a subset S of vertices the . n if (1) for each v in S, every path joining v to the edge of the board contains a member of G and (2) if II is any other group with this property every path joining S to H intersects G If an isolated, empty vertex v is surrounded by a group G of stones, then v is a special case of what is called an "eye". Note that a group of stones with two or more such isolated empty vertices cannot be captured because Rule 2 forbids a move to one isolated vacant inter- section while another remains. Any group with two eyes is impregnable. This principle of two eyes is fundamental in the game. There are other kinds of impregnable groups too; all such are called living. Figure I shows a Black group on a 1 X 3 board with two eyes. This is the smallest board which can have a group of stones with two eyes Isolated single vertices can be replaced by larger connected groups of vacant vertices in the above discussion, and each of these groups of vacant vertices is called an eye. However, if the group of empty vertices is large enough, the opponent may be able to build a living group inside. 6 In this case, he may or may not be able to prevent the creation of an eye. In practice this ambiguity about whether a surrounded group of vacant vertices is an eye does not seem to arise: we know of no example where the opponent, can destroy an eye by filling it with a living group. Of more immediate practical interest is the question of which eyes can be converted into two eyes if (a) the player whose group it is has the move, or (b) his opponent has the move. For instance, the Black player in Figure 2 can make two eyes if it is his turn by moving to the point x.
Load more

Recommended publications
  • The AGA Song Book up to Date
    3rd Edition Songs, Poems, Stories and More! Edited by Bob Felice Published by The American Go Association P.O. Box 397, Old Chelsea Station New York, N.Y., 10113-0397 Copyright 1998, 2002, 2006 in the U.S.A. by the American Go Association, except where noted. Cover illustration by Jim Rodgers. No part of this book may be used or reproduced in any form or by any means, or stored in a database or retrieval system, without prior written permission of the copyright holder, except for brief quotations used as part of a critical review. Introductions Introduction to the 1st Edition When I attended my first Go Congress three years ago I was astounded by the sheer number of silly Go songs everyone knew. At the next Congress, I wondered if all these musical treasures had ever been printed. Some research revealed that the late Bob High had put together three collections of Go songs, but the last of these appeared in 1990. Very few people had these song books, and some, like me, weren’t even aware that they existed. While new songs had been printed in the American Go Journal, there was clearly a need for a new collection of Go songs. Last year I decided to do whatever I could to bring the AGA Song Book up to date. I wanted to collect as many of the old songs as I could find, as well as the new songs that had been written since Bob High’s last song book. You are holding in your hands the book I was looking for two years ago.
    [Show full text]
  • The Burden of Choice, the Complexity of the World and Its Reduction: the Game of Go/Weiqi As a Practice of "Empirical Metaphysics"
    See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/330509941 The Burden of Choice, the Complexity of the World and Its Reduction: The Game of Go/Weiqi as a Practice of "Empirical Metaphysics" Article in Avant · January 2019 DOI: 10.26913/avant.2018.03.05 CITATIONS READS 0 76 1 author: Andrzej Wojciech Nowak Adam Mickiewicz University 27 PUBLICATIONS 18 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Metrological Sovereignity, Suwerenność metrologiczna View project Ontological Politics View project All content following this page was uploaded by Andrzej Wojciech Nowak on 20 January 2019. The user has requested enhancement of the downloaded file. AVANT, Vol. IX, No. 3/2018 ISSN: 2082-6710 avant.edu.pl/en DOI: 10.26913/avant.2018.03.05 The Burden of Choice, the Complexity of the World and Its Reduction: The Game of Go/Weiqi as a Practice of “Empirical Metaphysics” Andrzej W. Nowak Institute of Philosophy Adam Mickiewicz Univesity in Poznań, Poland andrzej.w.nowak @ gmail.com Received 27 October 2018, accepted 28 November 2018, published in the winter 2018/2019. Abstract The main aim of the text is to show how a game of Go (Weiqi, baduk, Igo) can serve as a model representation of the ontological-metaphysical aspect of the actor–network theory (ANT). An additional objective is to demonstrate in return that this ontological-meta- phys⁠ical aspect of ANT represented on Go/Weiqi game model is able to highlight the key aspect of this theory—onto-methodological praxis.
    [Show full text]
  • 49Th European Go Congress Prague 2005
    49th European Go Congress Prague 2005 Bulletin 1 Contents The plans from the editorial team ....................................... 3 Introduction ................................................................ 4 Karate ....................................................................... 5 Commented game – Zhao Pei vs. Alexander Dinerstein ............. 6 New books ..................................................................9 Commented game – Cristian Pop vs. Kai Naoyuki .................. 10 Photos – life on congress ................................................ 12 Lithuania – travel impressions ..........................................14 Lithuania – The Violet Swarm has Turned Green.................... 15 Interview with Yan An and Chinese tsumego problems ............ 16 In the next bulletin • 13×13 tournament • Interview with Guo Juan, 5p • Vocabulary English – Czech – Japanese – Korean • Talk with Turkish champion Made by Vit ‘tasuki’ Brunner on GNU/Linux, written in Vim, typeset using TEX with sgf2tex package of fonts and macros. The plans from the editorial team We present you some commented games. Also we would like to introduce to you some of the players par- ticipating in the main tournament. Every Go Congress is a meeting of the veterans, who already took part in many Congresses, with players who show up for the first time. Also there are players present, from some countries, which did not take part before. Yet another category of players present here are those who took part in an EGC before, but came back to us only after a long break. We will re-introduce some of them to you. In every issue of the bulletin we will also print interviews with some of the professionals present. Every time we ask them to show us a set of life and death problems. The first problem will be easy, so everybody has a chance to solve. The second one is meant for the level of 1-digit kyu and the third will be for dan level players.
    [Show full text]
  • Learning to Play the Game of Go
    Learning to Play the Game of Go James Foulds October 17, 2006 Abstract The problem of creating a successful artificial intelligence game playing program for the game of Go represents an important milestone in the history of computer science, and provides an interesting domain for the development of both new and existing problem-solving methods. In particular, the problem of Go can be used as a benchmark for machine learning techniques. Most commercial Go playing programs use rule-based expert systems, re- lying heavily on manually entered domain knowledge. Due to the complexity of strategy possible in the game, these programs can only play at an amateur level of skill. A more recent approach is to apply machine learning to the prob- lem. Machine learning-based Go playing systems are currently weaker than the rule-based programs, but this is still an active area of research. This project compares the performance of an extensive set of supervised machine learning algorithms in the context of learning from a set of features generated from the common fate graph – a graph representation of a Go playing board. The method is applied to a collection of life-and-death problems and to 9 × 9 games, using a variety of learning algorithms. A comparative study is performed to determine the effectiveness of each learning algorithm in this context. Contents 1 Introduction 4 2 Background 4 2.1 Go................................... 4 2.1.1 DescriptionoftheGame. 5 2.1.2 TheHistoryofGo ...................... 6 2.1.3 Elementary Strategy . 7 2.1.4 Player Rankings and Handicaps . 7 2.1.5 Tsumego ..........................
    [Show full text]
  • Go Books Detail
    Evanston Go Club Ian Feldman Lending Library A Compendium of Trick Plays Nihon Ki-in In this unique anthology, the reader will find the subject of trick plays in the game of go dealt with in a thorough manner. Practically anything one could wish to know about the subject is examined from multiple perpectives in this remarkable volume. Vital points in common patterns, skillful finesse (tesuji) and ordinary matters of good technique are discussed, as well as the pitfalls that are concealed in seemingly innocuous positions. This is a gem of a handbook that belongs on the bookshelf of every go player. Chapter 1 was written by Ishida Yoshio, former Meijin-Honinbo, who intimates that if "joseki can be said to be the highway, trick plays may be called a back alley. When one masters the alleyways, one is on course to master joseki." Thirty-five model trick plays are presented in this chapter, #204 and exhaustively analyzed in the style of a dictionary. Kageyama Toshiro 7 dan, one of the most popular go writers, examines the subject in Chapter 2 from the standpoint of full board strategy. Chapter 3 is written by Mihori Sho, who collaborated with Sakata Eio to produce Killer of Go. Anecdotes from the history of go, famous sayings by Sun Tzu on the Art of Warfare and contemporary examples of trickery are woven together to produce an entertaining dialogue. The final chapter presents twenty-five problems for the reader to solve, using the knowledge gained in the preceding sections. Do not be surprised to find unexpected booby traps lurking here also.
    [Show full text]
  • BULLETIN #3August
    Zhuyeqing Tea 55th European GO Congress Bordeaux 2011 € 0,50 August BULLETIN #3 3rd 2 CREDITS ■ Main Editor ■ Peter Dijkema ■ Writer ■ Peter Dijkema ■ Photos ■ Gérald Garlatti ■ Olivier Dulac ■ Layout ■ Gérald Garlatti WEATHER Wednesday, August 3rd Friday, August 5th Morning : 18°C / 64.4 °F Morning : 17°C / 62.6 °F Afternoon : 25°C / 77 °F Afternoon : 25°C / 77 °F Coast wind : 20 km/h Coast wind : - UV index : 7 UV index : 7 th Tuesday, August 4 Saturday, August 6th Morning : 16°C / 60.8 °F Morning : 16°C / 60.8 °F Afternoon : 26°C / 78.8 °F Afternoon : 25°C / 77 °F Coast wind : - Coast wind : - UV index : 7 UV index : 7 EDITORIAL 3 This third issue of the bulletin appeared later than we planned. The main reason is vacancies in the team of editors and reporters. Feel free to help us out. Request to all directors of side events: please report the results to us, so we can publish them in future bulletins. This number was written by me, with photos from Olivier Dulac, Redac’Chef while Gérald did the graphics. I hope you enjoy our work Peter Dijkema ■ We do a special dedication to Viktor Lin 5D and we great him a good health recovery. TABLE OF CONTENTS 4 ■ First week of the Main Tournament 5 ■ Tsumego solution 6 ■ Kifus of the Main Tournament 10 ■ Pair-Go 11 ■ Side Events 14 ■ Motoki’s Blog 14 ■ Annual General Meeting 15 ■ Weekend Tournament 16 ■ Impressions of the Pro’s 18 ■ Wbaduk event 19 ■ American Go Songs 22 ■ Professional News Bulletin #3 Wednesday , August 3 rd Printer : COREP Talence 4 FIRST WEEK ■ Top group of the Main Tournament On Thursday, both favourites kept on winning.
    [Show full text]
  • Tang Dynasty Games Magna Faire, AS LIV/2019
    Ouyang Yingzhao Tang Dynasty Games Magna Faire, AS LIV/2019 Weiqi (围棋) or Go ​ ​ A game of Strategy Perhaps better known by the name of it’s Japanese deritivie, Go, weiqi (围棋, wéi qí) is a territory control ​ ​ ​ ​ game played with a gridded board and 361 disc-shaped pieces. Unlike western Chess, there are no prescribed, piece-specific directional moves in Go, so that the combination possibilities are almost infinite. In the Tang Dynasty, one’s ability to play Go was a measure of a person’s gentility among the elites (men and women alike), along with calligraphy, music, and painting.1 The earliest reliable record of the game comes from 548 BCE, making it possibly the oldest game that has been continuously played.2 The standard size Go board consists of a grid of 19 by 19 intersections, but variant boards have existed throughout history. The earliest extant board, a fragment from the mausoleum of Emperor Jing (r. 157-141 BCE) is 17 by 17.3 Two more 17 by 17 boards were found in an Eastern Han Dynasty (dates) tomb and official Cao Teng’s tomb (mid-second century). A 15 by 15 board was found in a tomb dated to the late Western Han Dynasty, and similar variants may have survived into the Tang or Liao periods. (dates).4 The earliest 19 by 19 board is made of porcelain and dates to 595, and another is from the early Tang Dynasty, found in the tomb of Ran Rencai (598-652), who was Prefect of Yongzhou.5 To play weiqi, players take turns placing black and white stones on the board’s intersections.
    [Show full text]
  • History of Fermented Black Soybeans 1
    HISTORY OF FERMENTED BLACK SOYBEANS 1 HISTORY OF FERMENTED BLACK SOYBEANS (165 B.C. to 2011): EXTENSIVELY ANNOTATED BIBLIOGRAPHY AND SOURCEBOOK USED TO MAKE BLACK BEAN SAUCE. ALSO KNOW AS: FERMENTED BLACK BEANS, SALTED BLACK BEANS, FERMENTED SOYBEANS, PRESERVED BLACK BEANS, SALTY BLACK BEANS, BLACK FERMENTED BEANS, BLACK BEANS; DOUCHI, DOUSHI, TOUSHI, TOU-CH’IH, SHI, SHIH, DOW SEE, DOWSI (CHINESE); HAMANATTO, DAITOKUJI NATTO (JAPANESE); TAUSI, TAOSI (FILIPINO) Compiled by William Shurtleff & Akiko Aoyagi 2011 Copyright © 2011 by Soyinfo Center HISTORY OF FERMENTED BLACK SOYBEANS 2 Copyright (c) 2011 by William Shurtleff & Akiko Aoyagi All rights reserved. No part of this work may be reproduced or copied in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information and retrieval systems - except for use in reviews, without written permission from the publisher. Published by: Soyinfo Center P.O. Box 234 Lafayette, CA 94549-0234 USA Phone: 925-283-2991 Fax: 925-283-9091 www.soyinfocenter.com [email protected] ISBN 978-1-928914-41-9 (Fermented Black Soybeans) Printed 11 Dec. 2011 Price: Available on the Web free of charge Search engine keywords: History of fermented black soybeans History of fermented black beans History of Hamanatto History of Hamananatto History of black bean sauce History of shi History of shih History of salted black beans History of fermented soybeans History of douchi History of doushi History of preserved soybeans History of dow see History of tausi
    [Show full text]
  • Move Prediction in the Game of Go
    Move Prediction in the Game of Go A Thesis presented by Brett Alexander Harrison to Computer Science in partial fulfillment of the honors requirements for the degree of Bachelor of Arts Harvard College Cambridge, Massachusetts April 1, 2010 Abstract As a direct result of artificial intelligence research, computers are now expert players in a variety of popular games, including Checkers, Chess, Othello (Reversi), and Backgammon. Yet one game continues to elude the efforts of computer scientists: Go, also known as Igo in Japan, Weiqi in China, and Baduk in Korea. Due in part to the strategic complexity of Go and the sheer number of moves available to each player, most typical game-playing algorithms have failed to be effective with Go. Even state-of-the-art computer Go programs are weaker than high-ranking amateurs. Thus Go provides the perfect framework for devel- oping and testing new ideas in a variety of fields in computer science, including algorithms, computational game theory, and machine learning. In this thesis, we explore the problem of move prediction in the game of Go. The move prediction problem asks how we can build a program which trains on Go games in order to predict the moves of professional and high-ranking amateur players in other Go games. An accurate move predictor could serve as a powerful component of Go-playing programs, since it can be used to reduce the branching factor in game tree search and can be used as an effective move ordering heuristic. Our first main contribution to this field is the creation of a novel move prediction system, based on a naive Bayes model, which builds upon the work of several previous move prediction systems.
    [Show full text]
  • What Is the Project Title
    Artificial Intelligence for Go CIS 499 Senior Design Project Final Report Kristen Ying Advisors: Dr. Badler and Dr. Likhachev University of Pennsylvania PROJECT ABSTRACT Go is an ancient board game, originating in China – where it is known as weiqi - before 600 B.C. It spread to Japan (where it is also known as Go), to Korea as baduk, and much more recently to Europe and America [American Go Association]. This game, in which players take turn placing stones on a 19x19 board in an attempt to capture territory, is polynomial-space hard [Reyzin]. Checkers is also polynomial-space hard, and is a solved problem [Schaeffer]. However, the sheer magnitude of options (and for intelligent algorithms, sheer number of possible strategies) makes it infeasible to create even passable novice AI with an exhaustive pure brute-force approach on modern hardware. The board is 19 x19, which, barring illegal moves, allows for about 10171 possible ways to execute a game. This number is about 1081 times greater than the believed number of elementary particles contained in the known universe [Keim]. Previously investigated approaches to creating AI for Go include human-like models such as pattern recognizers and machine learning [Burmeister and Wiles]. There are a number of challenges to these approaches, however. Machine learning algorithms can be very sensitive to the data and style of play with which they are trained, and approaches modeling human thought can be very sensitive to the designer‟s perception of how one thinks during a game. Professional Go players seem to have a very intuitive sense of how to play, which is difficult to model.
    [Show full text]
  • Challenge Match Game 2: “Invention”
    Challenge Match 8-15 March 2016 Game 2: “Invention” Commentary by Fan Hui Go expert analysis by Gu Li and Zhou Ruiyang Translated by Lucas Baker, Thomas Hubert, and Thore Graepel Invention AlphaGo's victory in the first game stunned the world. Many Go players, however, found the result very difficult to accept. Not only had Lee's play in the first game fallen short of his usual standards, but AlphaGo had not even needed to play any spectacular moves to win. Perhaps the first game was a fluke? Though they proclaimed it less stridently than before, the overwhelming majority of commentators were still betting on Lee to claim victory. Reporters arrived in much greater numbers that morning, and with the increased attention from the media, the pressure on Lee rose. After all, the match had begun with everyone expecting Lee to win either 5­0 or 4­1. I entered the playing room fifteen minutes before the game to find Demis Hassabis already present, looking much more relaxed than the day before. Four minutes before the starting time, Lee came in with his daughter. Perhaps he felt that she would bring him luck? As a father myself, I know that feeling well. By convention, the media is allowed a few minutes to take pictures at the start of a major game. The room was much fuller this time, another reflection of the increased focus on the match. Today, AlphaGo would take Black, and everyone was eager to see what opening it would choose. Whatever it played would represent what AlphaGo believed to be best for Black.
    [Show full text]
  • Tsetlingo: Solving the Game of Go with Tsetlin Machine
    TsetlinGo: Solving the game of Go with Tsetlin Machine Kristoffer Lomeland Magelssen Trond Storebø SUPERVISORS Dr. Ole-Christoffer Granmo Master's Thesis University of Agder, 2020 Faculty of Engineering and Science Department of ICT UiA University of Agder Master's thesis Faculty of Engineering and Science Department of ICT c 2020 Kristoffer Lomeland Magelssen Trond Storebø. All rights reserved Abstract The Tsetlin Machine have already shown great promise on pattern recognition and text categorization. The board game GO is a highly complex game, and the Tsetlin Machine have not yet been tested extensively on strategic games like this. This thesis introduces TsetlinGO and aims to Solve the game of Go with Tsetlin Machine. For predicting the next moves a combination of Tsetlin Machine and Tree Search was used. In the thesis a 9x9 board size was used for the game of Go, to prevent the problem from becoming to complex. This thesis goes through hyper-parameter testing for classification of the Go board game. A solution with Tree Search and Tsetlin Machine combined is used to perform self-play and matches between Tsetlin Machines with different hyper-parameters. Based on the empirical results, our conclusion is that the Tsetlin Machine is more than capable for classifi- cation of the game of Go at various stages of play. Results from the experiments could be seen to achieve around 90%, while further climbing up to around 95% upon re-training. From examining the clauses, strong patterns was found that gave insight into how the machine works. The Tsetlin Machine was able to play complete games of Go, making connections on the board through use of pat- terns from the clauses.
    [Show full text]