046 – Puzzle Genres — Paper-And-Pencil Puzzles
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Paper and Pencils for Everyone
(CM^2) Math Circle Lesson: Game Theory of Gomuku and (m,n,k-games) Overview: Learning Objectives/Goals: to expose students to (m,n,k-games) and learn the general history of the games through out Asian cultures. SWBAT… play variations of m,n,k-games of varying degrees of difficulty and complexity as well as identify various strategies of play for each of the variations as identified by pattern recognition through experience. Materials: Paper and pencils for everyone Vocabulary: Game – we will create a working definition for this…. Objective – the goal or point of the game, how to win Win – to do (achieve) what a certain game requires, beat an opponent Diplomacy – working with other players in a game Luck/Chance – using dice or cards or something else “random” Strategy – techniques for winning a game Agenda: Check in (10-15min.) Warm-up (10-15min.) Lesson and game (30-45min) Wrap-up and chill time (10min) Lesson: Warm up questions: Ask these questions after warm up to the youth in small groups. They may discuss the answers in the groups and report back to you as the instructor. Write down the answers to these questions and compile a working definition. Try to lead the youth so that they do not name a specific game but keep in mind various games that they know and use specific attributes of them to make generalizations. · What is a game? · Are there different types of games? · What make something a game and something else not a game? · What is a board game? · How is it different from other types of games? · Do you always know what your opponent (other player) is doing during the game, can they be sneaky? · Do all of games have the same qualities as the games definition that we just made? Why or why not? Game history: The earliest known board games are thought of to be either ‘Go’ from China (which we are about to learn a variation of), or Senet and Mehen from Egypt (a country in Africa) or Mancala. -
Ai12-General-Game-Playing-Pre-Handout
Introduction GDL GGP Alpha Zero Conclusion References Artificial Intelligence 12. General Game Playing One AI to Play All Games and Win Them All Jana Koehler Alvaro´ Torralba Summer Term 2019 Thanks to Dr. Peter Kissmann for slide sources Koehler and Torralba Artificial Intelligence Chapter 12: GGP 1/53 Introduction GDL GGP Alpha Zero Conclusion References Agenda 1 Introduction 2 The Game Description Language (GDL) 3 Playing General Games 4 Learning Evaluation Functions: Alpha Zero 5 Conclusion Koehler and Torralba Artificial Intelligence Chapter 12: GGP 2/53 Introduction GDL GGP Alpha Zero Conclusion References Deep Blue Versus Garry Kasparov (1997) Koehler and Torralba Artificial Intelligence Chapter 12: GGP 4/53 Introduction GDL GGP Alpha Zero Conclusion References Games That Deep Blue Can Play 1 Chess Koehler and Torralba Artificial Intelligence Chapter 12: GGP 5/53 Introduction GDL GGP Alpha Zero Conclusion References Chinook Versus Marion Tinsley (1992) Koehler and Torralba Artificial Intelligence Chapter 12: GGP 6/53 Introduction GDL GGP Alpha Zero Conclusion References Games That Chinook Can Play 1 Checkers Koehler and Torralba Artificial Intelligence Chapter 12: GGP 7/53 Introduction GDL GGP Alpha Zero Conclusion References Games That a General Game Player Can Play 1 Chess 2 Checkers 3 Chinese Checkers 4 Connect Four 5 Tic-Tac-Toe 6 ... Koehler and Torralba Artificial Intelligence Chapter 12: GGP 8/53 Introduction GDL GGP Alpha Zero Conclusion References Games That a General Game Player Can Play (Ctd.) 5 ... 18 Zhadu 6 Othello 19 Pancakes 7 Nine Men's Morris 20 Quarto 8 15-Puzzle 21 Knight's Tour 9 Nim 22 n-Queens 10 Sudoku 23 Blob Wars 11 Pentago 24 Bomberman (simplified) 12 Blocker 25 Catch a Mouse 13 Breakthrough 26 Chomp 14 Lights Out 27 Gomoku 15 Amazons 28 Hex 16 Knightazons 29 Cubicup 17 Blocksworld 30 .. -
A Scalable Neural Network Architecture for Board Games
A Scalable Neural Network Architecture for Board Games Tom Schaul, Jurgen¨ Schmidhuber Abstract— This paper proposes to use Multi-dimensional II. BACKGROUND Recurrent Neural Networks (MDRNNs) as a way to overcome one of the key problems in flexible-size board games: scalability. A. Flexible-size board games We show why this architecture is well suited to the domain There is a large variety of board games, many of which and how it can be successfully trained to play those games, even without any domain-specific knowledge. We find that either have flexible board dimensions, or have rules that can performance on small boards correlates well with performance be trivially adjusted to make them flexible. on large ones, and that this property holds for networks trained The most prominent of them is the game of Go, research by either evolution or coevolution. on which has been considering board sizes between the min- imum of 5x5 and the regular 19x19. The rules are simple[5], I. INTRODUCTION but the strategies deriving from them are highly complex. Players alternately place stones onto any of the intersections Games are a particularly interesting domain for studies of the board, with the goal of conquering maximal territory. of machine learning techniques. They form a class of clean A player can capture a single stone or a connected group and elegant environments, usually described by a small set of his opponent’s stones by completely surrounding them of formal rules and clear success criteria, and yet they often with his own stones. A move is not legal if it leads to a involve highly complex strategies. -
A Scalable Neural Network Architecture for Board Games
A Scalable Neural Network Architecture for Board Games Tom Schaul, Jurgen¨ Schmidhuber Abstract— This paper proposes to use Multi-dimensional II. BACKGROUND Recurrent Neural Networks (MDRNNs) as a way to overcome one of the key problems in flexible-size board games: scalability. A. Flexible-size board games We show why this architecture is well suited to the domain There is a large variety of board games, many of which and how it can be successfully trained to play those games, even without any domain-specific knowledge. We find that either have flexible board dimensions, or have rules that can performance on small boards correlates well with performance be trivially adjusted to make them flexible. on large ones, and that this property holds for networks trained The most prominent of them is the game of Go, research by either evolution or coevolution. on which has been considering board sizes between the min- imum of 5x5 and the regular 19x19. The rules are simple[4], I. INTRODUCTION but the strategies deriving from them are highly complex. Players alternately place stones onto any of the intersections Games are a particularly interesting domain for studies of of the board, with the goal of conquering maximal territory. machine learning techniques. They form a class of clean and A player can capture a single stone or a connected group elegant environments, usually described by a small set of of his opponent’s stones by completely surrounding them formal rules, have very clear success criteria, and yet they with his own stones. A move is not legal if it leads to a often involve highly complex strategies. -
Chapter 6 Two-Player Games
Introduction to Using Games in Education: A Guide for Teachers and Parents Chapter 6 Two-Player Games There are many different kinds of two-person games. You may have played a variety of these games such as such as chess, checkers, backgammon, and cribbage. While all of these games are competitive, many people play them mainly for social purposes. A two-person game environment is a situation that facilitates communication and companionship. Two major ideas illustrated in this chapter: 1. Look ahead: learning to consider what your opponent will do as a response to a move that you are planning. 2. Computer as opponent. In essence, this makes a two-player game into a one- player game. In addition, we will continue to explore general-purpose, high-road transferable, problem-solving strategies. Tic-Tac-Toe To begin, we will look at the game of tic-tac-toe (TTT). TTT is a two-player game, with players taking turns. One player is designated as X and the other as O. A turn consists of marking an unused square of a 3x3 grid with one’s mark (an X or an O). The goal is to get three of one’s mark in a file (vertical, horizontal, or diagonal). Traditionally, X is the first player. A sample game is given below. Page 95 Introduction to Using Games in Education: A Guide for Teachers and Parents X X X O X O Before X's O's X's game first first second begins move move move X X X X O X X O X O O O X O X O X O X O X O O's X's O's X wins on second third third X's fourth move move move move Figure 6.1. -
Ultimate Tic-Tac-Toe
ULTIMATE TIC-TAC-TOE Scott Powell, Alex Merrill Professor: Professor Christman An algorithmic solver for Ultimate Tic-Tac-Toe May 2021 ABSTRACT Ultimate Tic-Tac-Toe is a deterministic game played by two players where each player’s turn has a direct effect on what options their opponent has. Each player’s viable moves are determined by their opponent on the previous turn, so players must decide whether the best move in the short term actually is the best move overall. Ultimate Tic-Tac-Toe relies entirely on strategy and decision-making. There are no random variables such as dice rolls to interfere with each player’s strategy. This is rela- tively rare in the field of board games, which often use chance to determine turns. Be- cause Ultimate Tic-Tac-Toe uses no random elements, it is a great choice for adversarial search algorithms. We may use the deterministic aspect of the game to our advantage by pruning the search trees to only contain moves that result in a good board state for the intelligent agent, and to only consider strong moves from the opponent. This speeds up the efficiency of the algorithm, allowing for an artificial intelligence capable of winning the game without spending extended periods of time evaluating each potential move. We create an intelligent agent capable of playing the game with strong moves using adversarial minimax search. We propose novel heuristics for evaluating the state of the game at any given point, and evaluate them against each other to determine the strongest heuristics. TABLE OF CONTENTS 1 Introduction1 1.1 Problem Statement............................2 1.2 Related Work...............................3 2 Methods6 2.1 Simple Heuristic: Greedy.........................6 2.2 New Heuristic...............................7 2.3 Alpha- Beta- Pruning and Depth Limit................. -
Annai Women's College
Annai Women’s College (Arts and Science) Affiliated to Bharathidasan University – Tiruchirapalli. TNPL Road ,Punnam Chattram, Karur-639 136 Department of Computer Science, Computer Applications & IT Faculty Name : Mrs.V.Bhuvaneswari,Msc., M.phil., Major : I M.Sc(Computer Science) Paper Code : P16CSE2B Title of the Paper : Artificial Intelligence INDEX S.No Topics P.No 1 UNIT I: Introduction: AI Problems - Al techniques - Criteria for 3 to 24 success. Problems, Problem Spaces, Search: State space search - Production Systems 2 UNIT II: Heuristic Search techniques: Generate and Test - Hill 25 to 35 Climbing- Best-First - Means-end analysis. Knowledge representation issues: Representations and mappings - Approaches to Knowledge representations -Issues in Knowledge representations - Frame Problem. 3 UNIT III: Using Predicate logic: Representing simple facts in logic 36 to 43 - Representing Instance and is a relationships - Computable functions and predicates - Resolution. 4 UNIT III: Using Predicate logic: Representing simple facts in logic 44 to 53 - Representing Instance and is a relationships - Computable functions and predicates - Resolution. 5 UNIT V: Game playing – The mini max search procedure – Expert 54 to 82 System - Perception and Action Artificial Intelligence Annai Women’s College,Karur. (Arts and Science) Department of Computer Science. Class: I M.Sc (Computer Science) Staff Incharge: V.Bhuvaneswari M.Sc.,M.Phil., AP in CS Department. Artificial Intelligence UNIT I: Introduction: AI Problems - Al techniques - Criteria for success. Problems, Problem Spaces, Search: State space search - Production Systems UNIT II: Heuristic Search techniques: Generate and Test - Hill Climbing- Best-First - Means-end analysis. Knowledge representation issues: Representations and mappings - Approaches to Knowledge representations -Issues in Knowledge representations - Frame Problem. -
Gomoku-Narabe" (五 目 並 べ, "Five Points in a Row"), the Game Is Quite Ancient
Gomoku (Japanese for "five points") or, as it is sometimes called, "gomoku-narabe" (五 目 並 べ, "five points in a row"), the game is quite ancient. The birthplace of Gomoku is considered to be China, the Yellow River Delta, the exact time of birth is unknown. Scientists name different dates, the oldest of which is the 20th century BC. All this allows us to trace the history of similar games in Japan to about 100 AD. It was probably at this time that the pebbles played on the islands from the mainland. - presumably in 270 AD, with Chinese emigrants, where they became known under different names: Nanju, Itsutsu-ishi (old-time "five stones"), Goban, Goren ("five in a row") and Goseki ("five stones "). In the first book about the Japanese version of the game "five-in-a-row", published in Japan in 1858, the game is called Kakugo (Japanese for "five steps). At the turn of the 17th-18th centuries, it was already played by everyone - from old people to children. Players take turns taking turns. Black is the first to go in Renju. Each move the player places on the board, at the point of intersection of the lines, one stone of his color. The winner is the one who can be the first to build a continuous row of five stones of the same color - horizontally, vertically or diagonally. A number of fouls - illegal moves - have been determined for the player who plays with black. He cannot build "forks" 3x3 and 4x4 and a row of 6 or more stones, as well as any forks with a multiplicity of more than two. -
Knots, Molecules, and the Universe: an Introduction to Topology
KNOTS, MOLECULES, AND THE UNIVERSE: AN INTRODUCTION TO TOPOLOGY AMERICAN MATHEMATICAL SOCIETY https://doi.org/10.1090//mbk/096 KNOTS, MOLECULES, AND THE UNIVERSE: AN INTRODUCTION TO TOPOLOGY ERICA FLAPAN with Maia Averett David Clark Lew Ludwig Lance Bryant Vesta Coufal Cornelia Van Cott Shea Burns Elizabeth Denne Leonard Van Wyk Jason Callahan Berit Givens Robin Wilson Jorge Calvo McKenzie Lamb Helen Wong Marion Moore Campisi Emille Davie Lawrence Andrea Young AMERICAN MATHEMATICAL SOCIETY 2010 Mathematics Subject Classification. Primary 57M25, 57M15, 92C40, 92E10, 92D20, 94C15. For additional information and updates on this book, visit www.ams.org/bookpages/mbk-96 Library of Congress Cataloging-in-Publication Data Flapan, Erica, 1956– Knots, molecules, and the universe : an introduction to topology / Erica Flapan ; with Maia Averett [and seventeen others]. pages cm Includes index. ISBN 978-1-4704-2535-7 (alk. paper) 1. Topology—Textbooks. 2. Algebraic topology—Textbooks. 3. Knot theory—Textbooks. 4. Geometry—Textbooks. 5. Molecular biology—Textbooks. I. Averett, Maia. II. Title. QA611.F45 2015 514—dc23 2015031576 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. -
RENJU for BEGINNERS Written by Mr. Alexander NOSOVSKY and Mr
RENJU FOR BEGINNERS written by Mr. Alexander NOSOVSKY and Mr. Andrey SOKOLSKY NEW REVISED EDITION 4 9 2 8 6 1 X 7 Y 3 5 10 1999 PREFACE This excellent book on Renju for beginners written by Mr Alexander Nosovsky and Mr Andrey Sokolsky was the first reference book for the former USSR players for a long time. As President of the RIF (The Renju International Federation) I am very glad that I can introduce this book to all the players around the world. Jonkoping, January 1990 Tommy Maltell President of RIF PREFACE BY THE AUTHORS The rules of this game are much simpler, than the rules of many other logical games, and even children of kindergarten age can study a simple variation of it. However, Renju does not yield anything in the number of combinations, richness in tactical and strategical ideas, and, finally, in the unexpectedness and beauty of victories to the more popular chess and checkers. A lot of people know a simple variation of this game (called "five-in-a-row") as a fascinating method to spend their free time. Renju, in its modern variation, with simple winnings prohibited for Black (fouls 3x3, 4x4 and overline ) becomes beyond recognition a serious logical-mind game. Alexander Nosovsky Vice-president of RIF Former two-times World Champion in Renju by mail. Andrey Sokolsky Former vice-president of RIF . CONTENTS CHAPTER 1. INTRODUCTION. 1.1 The Rules of Renju . 1.2 From the History and Geography of Renju . CHAPTER 2. TERMS AND DEFINITIONS . 2.1 Accessories of the game . -
3.4 Temporal Difference Learning 6 3.5 Ways of Learning 7 3.6 Features 8 4
Training a Back-Propagation Network with Temporal Difference Learning and a database for the board game Pente Valentijn Muijrers 3275183 [email protected] Supervisor: Gerard Vreeswijk 7,5 ECTS 22 januari 2011 Abstract This paper will give a view on how to make a back-propagation network which can play Pente by learning from database games with temporal difference learning. The aspects of temporal difference learning and neural networks are described. The method of how a neural network can learn to play the game Pente is also explained. An experiment is described and analyzed and shows how the neural network has learned the game of Pente and in what kind of behavior the learning strategy resulted. The best performance after training on one single game was reached with a learning rate of 0.001. After learning 300000 games from the database the network did not perform very well. A third experiment with 4000 self-play games was also conducted and showed that the network placed the game more to the middle of the board than to the sides which is some form of intelligence. First this paper will give a view of the aspects of temporal difference learning in neural networks and which choices in this project were made during testing. Then the game of Pente will be explained and the way of how this game can be learned by a neural network will be justified. At the end of this paper the experiments of this project will be explained and the results will be evaluated. Then the conclusions will be discussed and analyzed. -
Math-GAMES IO1 EN.Pdf
Math-GAMES Compendium GAMES AND MATHEMATICS IN EDUCATION FOR ADULTS COMPENDIUMS, GUIDELINES AND COURSES FOR NUMERACY LEARNING METHODS BASED ON GAMES ENGLISH ERASMUS+ PROJECT NO.: 2015-1-DE02-KA204-002260 2015 - 2018 www.math-games.eu ISBN 978-3-89697-800-4 1 The complete output of the project Math GAMES consists of the here present Compendium and a Guidebook, a Teacher Training Course and Seminar and an Evaluation Report, mostly translated into nine European languages. You can download all from the website www.math-games.eu ©2018 Erasmus+ Math-GAMES Project No. 2015-1-DE02-KA204-002260 Disclaimer: "The European Commission support for the production of this publication does not constitute an endorsement of the contents which reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein." This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. ISBN 978-3-89697-800-4 2 PRELIMINARY REMARKS CONTRIBUTION FOR THE PREPARATION OF THIS COMPENDIUM The Guidebook is the outcome of the collaborative work of all the Partners for the development of the European Erasmus+ Math-GAMES Project, namely the following: 1. Volkshochschule Schrobenhausen e. V., Co-ordinating Organization, Germany (Roland Schneidt, Christl Schneidt, Heinrich Hausknecht, Benno Bickel, Renate Ament, Inge Spielberger, Jill Franz, Siegfried Franz), reponsible for the elaboration of the games 1.1 to 1.8 and 10.1. to 10.3 2. KRUG Art Movement, Kardzhali, Bulgaria (Radost Nikolaeva-Cohen, Galina Dimova, Deyana Kostova, Ivana Gacheva, Emil Robert), reponsible for the elaboration of the games 2.1 to 2.3 3.