# Implementation of a Chess Playing Artificial. Intelligence. Sean Stanek.

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Implementation of a Chess Playing Artificial Intelligence Sean Stanek

2 Overview Chess has always been a hobby of mine, and so have computers. In general, I like creating computer programs that can do things that humans could never dream to do, and as such, a computer artificial intelligence that plays chess is just such a program. Goals For this project, I plan to implement a working chess AI. The goal is to see how it responds to tweaking various variables, such as how offensive or how defensive it plays, point values of different pieces on the chessboard, branching factor, and search depth. I assume that an exhaustive search algorithm would be exponential in order, so a large depth might be unfeasible. However, a worthy goal of this project would be to create a chess AI that could exceed my own chess playing abilities. Implementation The obvious solution to finding the best move to make next on a chessboard is to exhaustively search the entire search space of any given state on a chessboard. There are 16 chess pieces on each player s side, each of which moves and captures enemy pieces differently. Additionally, to search the entire search space, each of these pieces should be moved to any and all spaces it can be. I score should be assigned to that move, and the best score should be used to decide which move to make.

3 This seems easy enough, but then realize that a chess AI that can only look at the current state and not into future states is no AI at all. Player A could be one move away from certain checkmate of Player B, but Player B would not even see this if he did not look even one move into the future. So, the obvious solution is to look at every possible combination of countermoves for every combination of moves, and try to figure out what the opponent would do. In fact, why not check every possible combination of countermoves for every possible combination of every possible combination of every possible Not possible. There are infinitely many combinations of moves much less sequences of moves that one can make on a chessboard. So, obviously a line must be drawn somewhere. Of course, the main obstacles that would be approached are space and time. Obviously using a depth-first search would not be too taxing on space, but definitely time. A breadth-first search would be taxing on both space and time. So, a depth-first search would be simplest and most efficient for now. For each move that the computer player can make, a recursion should be made. Each new chessboard s state should have all of its moves checked and scored. The best scores should be returned, and ultimately, the best score used in the decision to make a move. Because the AI will need to predict what the human player (or other player in general) will do, depending on the current state s player s turn, pieces captured by the AI will be

4 added to the score, and pieces of the AI s that get captured will be subtracted from the score. This is simply recursed to a desired depth, based on available time. Toward the middle of a game, as both players open up their sides of the chess board, more and more pieces will be exposed and have more opportunities to makes different moves. At the beginning of a chess game, a player can make only one of twenty different possible moves. In the middle of a game, a player could easily have sixty different possible moves. This could be a lot more taxing on time constraints, so instead of allowing all possible moves, it might be better to limit the search space by pruning the nodes with the current lowest scores before continuing on to recurse further. Obviously, if your king were about to be captured, you would want to eliminate that move from even being a possibility. So, simply eliminating that move from the current search space will prevent that path of losing from being taken. Modifying one or both of the maximum branching factor and maximum depth of recursion could change how the AI can work in a given time constraint. Obviously since we are not doing a completely exhaustive search of the game, we have to assign power values to each of the chess pieces to aid in deciding how to play the game. Each chess piece is assigned a value pawns are worth one point, knights and bishops are worth three points, a rook is worth five points, a queen nine points, and a king 200 points (you would never want your king to be captured). These numbers are just generally accepted numbers; however, there is no guarantee that a computer could actually have a better game with these numbers. If it placed more value on keeping its

5 knights instead of the rooks, it might in fact have a better chance of winning. This is one set of values that can be tweaked. Another set of values to be tweaked is the likelihood that the AI will attack or defend. Should capturing a rook be as important as keeping one s own rook? This can be different depending on the opponent to be played. If the opponent is a strong attacker, a good defense will frustrate the opponent (it certainly did to me). So, a couple values to assign more points for capturing a piece (attack) instead of losing a piece (defense) can be used to decide this. Analysis At any given state, there could be usually possible moves for a side. Let's call this number K. This number could be limited by a beam search maximum branching number. By trial, 20 seems to be a reasonable number that doesn't prune too much, but isn't too slow to go through many depths (the game state gets more complex as more pieces open up - a queen in the middle of the board could make 20 different moves by itself easily). We will call the pruned maximum branching factor k. The algorithm used is an exhaustive depth-first search that will terminate at a given depth d, and then continue throughout the rest of the search space. Additionally, the first level is always fully searched (i.e. not limited to the beam-search limit). Assuming this first level is depth 0, this means we have to perform O(K*k d ) node visits. In each node visit, we sort the array of scores in order to choose the best score, but also to use as the top N scores in the beam search. This sorting algorithm used is a bubble sort, but could actually be done with a

6 qsort or something better. But, being implemented as a bubble sort (there's only around 40 items to sort anyway), this equates to a runtime of O((K*k d )*K*K) = O(K 3 *k d ). In implementation, I can search through about 1.5 million nodes per second. Running a beam search, we can run a depth of four in a couple seconds. Of course, to get the most powerful computer AI, pruning nodes may not be an option, especially since many moves in chess are unseen combinations of other moves. This could require that no nodes be pruned, and a large depth be used. Assuming an average of 30 moves per state, and a maximum depth of 10, this would require visiting 30*30 10 or 18 million billion nodes, taking roughly 12 billion seconds or 374 years. It is obvious why chess is such a complex problem, and why computers have only recently been able to consistently defeat chess grandmasters, and running in massively parallel configurations at that. It is obvious that pruning MUST be done, and even then, depth is really a limitation. In practice, playing against my own AI, I enjoy using full searches (no beam width limit) and a depth of four. This takes the computer anywhere from five to twenty seconds (which is acceptable), and it is very intelligent and can predict many of my attacks before I make them. With a more specialized pruning algorithm, it should be possible to prune out more redundant nodes and be able to extend this AI beyond a depth of four, making it much more difficult to defeat. Conclusions A perfect chess AI is almost completely impossible. As opposed to simpler games, chess simply has a vast search space, both in the amount of possible moves that can be performed in each state and also in the number of moves needed to finish the game.

7 Searching all moves at every given state is time consuming and spends more time searching nodes that might not have to be searched, and does not allow the AI to search very far into the future of the game to predict what its opponent will do next, and thusly what move it should make next. On the other hand, pruning nodes and especially pruning them early on can allow the AI to search very far into the future, but at the cost of an incomplete search (and possibly losing the game long before it knows it could even possibly lose the game). The chess AI that beat world champion chess player Gary Kasperov was powered by one of the largest supercomputers that IBM could afford to throw at the task, as well as having an additional set of training data of openings and strategies that have defeated Kasperov in the past. Certainly powerful computers can beat the average player, but for how much longer can powerful chess masters beat the average computer?

### Artificial Intelligence in Chess

Artificial Intelligence in Chess IA in Chess is quite complex Even the fastest computer cannot solve the chess game (cannot analyze every possible situation) There are many ways of reducing the need of

### BASIC RULES OF CHESS

BASIC RULES OF CHESS Introduction Chess is a game of strategy believed to have been invented more then 00 years ago in India. It is a game for two players, one with the light pieces and one with the dark

### YourTurnMyTurn.com: chess rules. Jan Willem Schoonhoven Copyright 2016 YourTurnMyTurn.com

YourTurnMyTurn.com: chess rules Jan Willem Schoonhoven Copyright 2016 YourTurnMyTurn.com Inhoud Chess rules...1 The object of chess...1 The board...1 Moves...1 Captures...1 Movement of the different pieces...2

### How to Play Chess. The next diagram shows how the pieces are placed at the beginning of a game.

How to Play Chess Setup The players sit facing each other with the board between them. The board consists of 64 alternating colored squares. Regardless of the actual colors, the dark squares are named

### How to Play Chess. There are six different chess pieces. (King, Queen, Rook, Bishop, Knight, Pawn)

How to Play Chess The chess board is placed between the two players as shown in the diagram, White sitting on one side (the bottom of the diagram) and Black on the other side (the top of the diagram).

### Introduction to Chess Strategy

Introduction to Chess Strategy Do you play poker? There are many similarities in strategies between chess and Texas holdem and chess players are starting to take notice. In both games, you must think a

### Setting up the Chessboard

Setting up the Chessboard Chess is a very old game. People believe that it originated in India in the fourth or fifth century but no one really knows who invented it. Chess is an intellectual competition

### This is a simple method for layering chess knowledge into a brain.

How to Teach Chess by Paula Rizzuto (Dec 2012) This is a simple method for layering chess knowledge into a brain This method requires 2 people I refer to them as teacher and learner, but the method can

### Making Decisions in Chess

Making Decisions in Chess How can I find the best move in a position? This is a question that every chess player would like to have answered. Playing the best move in all positions would make someone invincible.

### UIL Chess Puzzle Practice Material This year s UIL Chess Puzzle Test includes solve the mate positions similar to last year s, but it also tests

UIL Chess Puzzle Practice Material This year s UIL Chess Puzzle Test includes solve the mate positions similar to last year s, but it also tests other kinds of chess knowledge knowledge that relates directly

### AI and computer game playing. Artificial Intelligence. Partial game tree for Tic-Tac-Toe. Game tree search. Minimax Algorithm

AI and computer game playing Artificial Intelligence Introduction to game-playing search imax algorithm, evaluation functions, alpha-beta pruning, advanced techniques Game playing (especially chess and

### Frezcogames Chess Tours. Knight's Tour

Frezcogames Chess Tours Knight's Tour This ancient puzzle is very difficult, unless you use a well defined technique (you can find one at ). It can be made even more challenging, but still solvable, by

### Chess Rules! Most of the time when you play 2 games of chess, you won't be. thinking about the names of the squares, but you will need to

An Ancient Game Chess was invented somewhere in India or the Middle East 00-000 years ago. It was already an old, OLD game during the times of the castles, kings, and knights in Europe. A thousand years

### LOKA. CORE RULES The core of the Loka rules are the rules of chess. If you don t know them please have a look here:

LOKA Welcome to Loka. This is an early draft of the rules, which is of course subject to change as they are developed thanks to your feedback. CORE RULES The core of the Loka rules are the rules of chess.

### Script for How to Win a Chinese Chess Game

Script for How to Win a Chinese Chess Game Jinzhong Niu April 25, 2004 1 Presentation Set Up Chinese chess is played on a 10 9 board, on which either player has 16 pieces. Pieces are located at the intersections

Artificial Intelligence Adversarial Search Andrea Torsello Games Vs. Planning Problems In many problems you re are pitted against an opponent certain operators are beyond your control: you cannot control

### LINC Chess Student Workbook

LINC Chess Student Workbook This book belongs to: 1 Important Information My coach s name is: My LINC Site Coordinator is: My chess team meets twice a week: and To register for a tournament visit: www.kclinc.org/chess

### GLASS CHESS SET GENERAL RULES AND INFORMATION

GLASS CHESS SET 47884 GENERAL RULES AND INFORMATION THANK YOU for choosing a HARBOR FREIGHT TOOLS product. For future reference, please complete the owner s record below: Model Serial No. Purchase Date

### Lecture 2. Uninformed search

Lecture 2 Uninformed search " Reference: Preparing for week 1 Reading: Chapters 1 and 2.1, 2.2, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5 Assignment 1 has now been posted on the course LEARN site Uses MATLAB (a tutorial

### How to play. The Basic Game They look like ordinary checkers, but notice the KING CHECKERS on each side. YOUR GOAL: Capture your opponent s king!

How to play The Basic Game They look like ordinary checkers, but notice the KING CHECKERS on each side. YOUR GOAL: Capture your opponent s king! US Patent Publication No. US 8657289 B2, Feb 25, 2014 http://www.google.com/patents/us8657289

### Game set include: 40 wooden pieces The game board Instructions

Japanese Chess Game set include: 40 wooden pieces The game board Instructions www.shogi.cz info@shogi.cz /Shogicz Online Instructions: http://www.shogi.cz/instructions.pdf EN Detailed instructions to the

### Teaching Kids Chess in Three Lessons: Learning Strategies, Handicapping, and Questioning

1 Teaching Kids Chess in Three Lessons: Learning Strategies, Handicapping, and Questioning By Emily Walker Nelson Mississippi Association for Gifted Children 2 The World Chess Federation publishes widely

### COMP-424: Artificial intelligence. Lecture 7: Game Playing

COMP 424 - Artificial Intelligence Lecture 7: Game Playing Instructor: Joelle Pineau (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/comp424 Unless otherwise noted, all material posted

### LINC Chess Student Workbook

LINC Chess Student Workbook This book belongs to: _ 1 Important Information My coach s name is: _ My LINC Site Coordinator is: My chess team meets twice a week: and To register for a tournament visit:

### Chess Lesson Plans for Teachers Instructional Objectives for Chess: Day 1: Set up the board

Please take under consideration that this material is a kind of alternative for chess curriculum in chess in schools. As Chess in Schools Committee we are neutral for this material. Till FIDE Congress

### The Knights Handbook Miha ˇ Canˇcula

Miha Čančula 2 Contents 1 Introduction 6 2 How to play 7 2.1 Objective........................................... 7 2.2 Starting the Game...................................... 7 2.3 The Chess Server Dialog..................................

### OCTAGON 5 IN 1 GAME SET

Chess, Checkers, Backgammon, Dominoes and Poker Dice August 2012 UPC Code 7-19265-51821-3 HOW TO PLAY CHESS Chess Includes: 16 Dark Chess Pieces 16 Light Chess Pieces Board Start Up Chess is a game played

### Master Chess Computer

Cat. No. 60-2217 OWNER S MANUAL Please read before using this equipment. Master Chess Computer FEATURES Your RadioShack Master Chess Computer is one of the most versatile chess computers available. With

### Created by Peter McOwan and Paul Curzon of Queen Mary, University of London with support

Winning games: the perfect tictac-toe player Created by Peter McOwan and Paul Curzon of Queen Mary, University of London with support from EPSRC and Google Winning games: the perfect tic-tac-toe player

### Knowledge engineering in chess programming- Evaluation of a chess position-criteria and procedure

Knowledge engineering in chess programming- Evaluation of a chess position-criteria and procedure malugu_satyajit@yahoo.com vidyuth_koniki@yahoo.co.in Authors: M.Satyajit ¾ Cse-A Gitam K.B.N.Vidyuth ¾

### Software Requirement Specification. Chess. for. Prepared by: Mayra Aguas, Alfred Blackman, George D'Andrea, Paul Vu, and Gurvinder Singh.

Software Requirement Specification for Chess Prepared by: Mayra Aguas, Alfred Blackman, George D'Andrea, Paul Vu, and Gurvinder Singh. Contents: 1 INTRODUCTION 1 1.1 Purpose 1 1.2 Scope 1 1.3 Definitions....

### Software Design Description CHESS. for. Prepared by: Mayra Aguas, Alfred Blackman, George D'Andrea, Paul Vu, and Gurvinder Singh.

Software Design Description for CHESS Version 4.0 Approved March 4, 2010. Prepared by: Mayra Aguas, Alfred Blackman, George D'Andrea, Paul Vu, and Gurvinder Singh. Drexel University Revision History Name

### This Workbook has been developed to help aid in organizing notes and references while working on the Chess Merit Badge Requirements.

This Workbook has been developed to help aid in organizing notes and references while working on the Chess Merit Badge Requirements. Visit www.scoutmasterbucky.com for more information SCOUT S INFORMATION

### Chess Board. Square The e4 square. Central squares. Diagonal

Chess Board Square The e4 square Central squares Diagonal File The E-file White side and Black side Rank The 2 nd rank Board Showing The King side and the Queen side Chess Notation This system, known as

### Merels or Nine Men's Morris:

Byzantine Chess: Byzantine (circular) chess is played on a round board. The board is divided into four rows of sixteen squares each, with the center empty. The pieces are arranged in the manner shown in

### Computer Simulation (2) Game Playing

Computer Simulation (2) Game Playing Different Types of Games How many players? One Two Element of chance? Deterministic Nondeterministic Outcome Zero sum (what one player wins, the other loses) Non-zero

### SFTS CHESS TOURNAMENT 2015

SFTS CHESS TOURNAMENT 2015 General Instructions: 1. Players must arrive at the location by 12:30 PM to register. Games begin at 1.00 PM sharp. 2. Chess tournament will be played per the USCF rules. It

### Game Playing in the Real World. Next time: Knowledge Representation Reading: Chapter 7.1-7.3

Game Playing in the Real World Next time: Knowledge Representation Reading: Chapter 7.1-7.3 1 What matters? Speed? Knowledge? Intelligence? (And what counts as intelligence?) Human vs. machine characteristics

### Game-Playing & Adversarial Search MiniMax, Search Cut-off, Heuristic Evaluation

Game-Playing & Adversarial Search MiniMax, Search Cut-off, Heuristic Evaluation This lecture topic: Game-Playing & Adversarial Search (MiniMax, Search Cut-off, Heuristic Evaluation) Read Chapter 5.1-5.2,

### Learning to play chess using TD(λ)-learning with database games

Learning to play chess using TD(λ)-learning with database games Henk Mannen & Marco Wiering Cognitive Artificial Intelligence University of Utrecht henk.mannen@phil.uu.nl & marco@cs.uu.nl Abstract In this

### The Sports Rules and Regulations

The Intramural Referee Handbook (Non-Traditional Sports) Rules are applied to all participating SUNY Purchase College Student/Staff/Faculty All Referees must uphold rules and regulation of every intramural

### FOUR DIMENSIONAL CHESS

FOUR DIMENSIONAL CHESS BEN Abstract. This is a quick introduction to four dimensional chess, with the mathematics in mind. 1. FIDE Chess We shall assume a basic knowledge of chess, but desire to reintroduce

### 1. The Chess Board and Pawn Movement

page 1-1 1. The Chess Board and Pawn Movement Objectives: 1. Name squares and chessmen at start of game 2. Set up the chessmen at the start of the game 3. State and apply rules of movement for the pawns

### How to Read and Write Algebraic Chess Notation

How to Read and Write Algebraic Chess Notation Algebraic notation (or AN) is a method for recording and describing the moves in a game of chess. It is now standard among all chess organizations and most

### Matrix Applications in Chess. Douglas Steiner

Matrix Applications in Chess Douglas Steiner November 18, 2009 Abstract This report illustrates basic applications of linear algebra for solving simple endgame positions in chess. 1 Introduction The game

### ITEC2620 Introduction to Data Structures

ITEC2620 Introduction to Data Structures Lecture 8b Search Trees Traversals Typical covered as graph traversals in data structures courses I ve never seen a graph traversal in practice! AI background Tree

### BIDDING CHESS JAY BHAT AND SAM PAYNE. 1 a b c d e f g h. at an otherwise respectable educational institution. SP s friend Ed had just returned

BIDDING CHESS JAY BHAT AND SAM PAYNE It all started with a chessboard and a bottle of raki at an otherwise respectable educational institution. SP s friend Ed had just returned from Turkey with a bottle

### HELPING YOUR CHILDREN WITH CHESS

HELPING YOUR CHILDREN WITH CHESS 1. WHY CHESS? (This section is extracted from Why Offer Chess in Schools by Jerry Meyers) We have brought chess to the schools because we believe it directly contributes

### Techniques to Parallelize Chess Matthew Guidry, Charles McClendon

Techniques to Parallelize Chess Matthew Guidry, Charles McClendon Abstract Computer chess has, over the years, served as a metric for showing the progress of computer science. It was a momentous occasion

### How to Write Chess Moves

Version 1.0 How to Write Chess Moves A Simple Guide for Beginners Written by Paul Macdonald 27 September 2012 Learning Chess Language You're going to quickly learn everything you need to know about reading

### Content. Game goals Chess board Piece movement Check Rooking Pawn promotion En passant Stalemate Draw Piece values. FER-Zagreb, Chess 2014/15 1

. Game rules Content Game goals Chess board Piece movement Check Rooking Pawn promotion En passant Stalemate Draw Piece values 1 Game goals Ultimate game goals i to checkmate the opponent s King. Other

### Manoj Kalathil. Currently residing in Muscat with his wife Lakshmi and two children Vedika and Vaiga

Manoj Kalathil Born in 1971 at Ernakulam to Sri. Karunakaran Kartha and Smt. Nalini Kunjamma. After graduation in Engineering and MBA he worked in various IT companies both in India and abroad. He is now

### ON THE CHESS BOARD. This week our problems derive from the chess board. However, they are not all chess related problems.

ON THE CHESS BOARD LAMC INTERMEDIATE - 3/09/14 This week our problems derive from the chess board. However, they are not all chess related problems. ABRIEF INTRODUCTION TO INDUCTION Consider the following

### Important USCF Rules - 6th Edition USCF Rulebook and Changes (Updated 10/12/ Changes are indicated in red)

Important USCF Rules - 6th Edition USCF Rulebook and Changes (Updated 10/12/2015 - Changes are indicated in red) Article 5: The Chess Clock 5E and 5F: Standard timer for sudden death The standard timer

### BPM: Chess vs. Checkers

BPM: Chess vs. Checkers Jonathon Struthers Introducing the Games Business relies upon IT systems to perform many of its tasks. While many times systems don t really do what the business wants them to do,

### Computer Chinese Chess

Computer Chinese Chess Tsan-sheng Hsu tshsu@iis.sinica.edu.tw http://www.iis.sinica.edu.tw/~tshsu 1 Abstract An introduction to problems and opportunities in Computer Chinese Chess. Open game Middle game

### Chess is one of the world s oldest and most popular

A Brief Summary of the Rules of Chess for the Intelligent Neophyte Chess is one of the world s oldest and most popular board games. Its longevity and popularity can probably be attributed to a number of

### solitaire Instructions, Hints & Solutions 8 to adult single player

solitaire Instructions, Hints & Solutions 8 to adult single player Solitaire Chess Welcome to Solitaire Chess, the single-player logic game that uses the rules of chess in simplified form to create a diabolical

### Making a non-computer or computer game fair for players vs. player, or player vs. computer

Making a non-computer or computer game fair for players vs. player, or player vs. computer AdamCon 17 July 15, 2005 Dale Wick Player vs. Player games establishes a relationship between the players which

### Introduction Solvability Rules Computer Solution Implementation. Connect Four. March 9, 2010. Connect Four

March 9, 2010 is a tic-tac-toe like game in which two players drop discs into a 7x6 board. The first player to get four in a row (either vertically, horizontally, or diagonally) wins. The game was first

### Organisation & Rules

Inter-school TEAM Chess Competitions Years 1 to 6 and Years 7 to 8 www.canterburychess.school.nz Organisation & Rules Entry eligibility... 2 Aims, entry criteria, format and timing... 3 Team and ranking...

### Game playing. Chapter 6. Chapter 6 1

Game playing Chapter 6 Chapter 6 1 Outline Games Perfect play minimax decisions α β pruning Resource limits and approximate evaluation Games of chance Games of imperfect information Chapter 6 2 Games vs.

### Chess Algorithms Theory and Practice. Rune Djurhuus Chess Grandmaster runed@ifi.uio.no / runedj@microsoft.com October 3, 2012

Chess Algorithms Theory and Practice Rune Djurhuus Chess Grandmaster runed@ifi.uio.no / runedj@microsoft.com October 3, 2012 1 Content Complexity of a chess game History of computer chess Search trees

### 1.3. Knights. Training Forward Thinking

1.3 Knights Hippogonal 2,1 movement. Captures by landing on the same square as an enemy piece. Can jump over other pieces Count one, two, turn. There has always been a horse in chess and the chess variants

### 4. Why is it that the best first search is more effective than hill climbing?

Abstract: The following questions and exercises are from chapter 3, Informed Search. This chapter covers the use of heuristics in search and how to evaluate the effectiveness of heuristics and search algorithms.

### Classifying Chess Positions

Classifying Chess Positions Christopher De Sa December 14, 2012 Chess was one of the first problems studied by the AI community. While currently, chessplaying programs perform very well using primarily

### Ian Stewart. Mathematics Institute University of Warwick Coventry CV4 7AL UK

The Never-Ending Chess Game Ian Stewart Mathematics Institute University of Warwick Coventry CV4 7AL UK What is mathematics? It seems impossible to give a succinct definition. The best one I know is 'what

### Problems and Search. Chapter 2

Problems and Search Chapter 2 Outline State space search Search strategies Problem characteristics Design of search programs 2 State Space Search Problem solving = Searching for a goal state 3 State Space

### Book One. Beginning Bridge. Supplementary quizzes and play hands. 2011 edition

Book One Beginning Bridge Supplementary quizzes and play hands 2011 edition Chapter One : Getting started with bridge TR1 How many points in each hand? TR2 Hands 1-8 for the first lesson TR3 MiniBridge

### UIL Chess Puzzle Practice Material This year s UIL Chess Puzzle Test includes solve the mate positions similar to last year s, but it also tests

#2 UIL Chess Puzzle Practice Material This year s UIL Chess Puzzle Test includes solve the mate positions similar to last year s, but it also tests other kinds of chess knowledge knowledge that relates

### Laboratory work in AI: First steps in Poker Playing Agents and Opponent Modeling

Laboratory work in AI: First steps in Poker Playing Agents and Opponent Modeling Avram Golbert 01574669 agolbert@gmail.com Abstract: While Artificial Intelligence research has shown great success in deterministic

### SMOOTH CHESS DAVID I. SPIVAK

SMOOTH CHESS DAVID I. SPIVAK Contents 1. Introduction 1 2. Chess as a board game 2 3. Smooth Chess as a smoothing of chess 4 3.7. Rules of smooth chess 7 4. Analysis of Smooth Chess 7 5. Examples 7 6.

### A Brief Survey of Chess AI: Strategy and Implementation Mark S. Montoya University of New Mexico CS 427 Fall 2012

A Brief Survey of Chess AI: Strategy and Implementation Mark S. Montoya University of New Mexico CS 427 Fall 2012 Introduction Chess AI seems to be a less popular area of research since the 1997 defeat

### Chess Player by Co-Evolutionary Algorithm

Chess Player by Co-Evolutionary Algorithm Agostinho Rosa Laseeb-ISR-IST, Av Rovisco Pais 1 1049-001 Lisboa, Portugal acrosa@laseeb.org Nuno Ramos Laseeb-ISR-IST, Av Rovisco Pais 1 1049-001 Lisboa, Portugal

### Adversarial Search and Game- Playing. C H A P T E R 5 C M P T 3 1 0 : S u m m e r 2 0 1 1 O l i v e r S c h u l t e

Adversarial Search and Game- Playing C H A P T E R 5 C M P T 3 1 0 : S u m m e r 2 0 1 1 O l i v e r S c h u l t e Environment Type Discussed In this Lecture 2 Fully Observable yes Turn-taking: Semi-dynamic

### CSE 212 Final Project: Chess Game

CSE 212 Final Project: Chess Game Rebecca Oehmen roehmen@nd.edu Cecilia Hopkins chopkins@nd.edu Ryan Lichtenwalter rlichten@nd.edu Abstract This project implements a classic version of Chess with a Graphical

### COMPREHENSIVE RULES OF BUGHOUSE (aka Transfer Chess aka Siamese Chess)

COMPREHENSIVE RULES OF BUGHOUSE (aka Transfer Chess aka Siamese Chess) 1. What is Bughouse? Bughouse is a variation of chess played by a team of two players against an opposing team. While one teammate

### BEST-REPLY SEARCH IN MULTI-PLAYER CHESS. Markus Esser. Master Thesis 12-13

BEST-REPLY SEARCH IN MULTI-PLAYER CHESS Markus Esser Master Thesis 12-13 Thesis submitted in partial fulfilment of the requirements for the degree of Master of Science of Artificial Intelligence at the

### Building Chess Endgame Databases for Positions with many Pieces using A-priori Information

Building Chess Endgame Databases for Positions with many Pieces using A-priori Information Eiko Bleicher Lehrstuhl Mathematische Optimierung Fakultät Mathematik und Informatik Friedrich-Schiller-Universität

### Problem Solving Through AI

2 Problem Solving Through AI 2.1 INTRODUCTION In the last chapter, we have tried to explain that Artificial Intelligence is the science and technology applied to make machines intelligent. The ultimate

### Chess. Strategy and Tactics For Novice Players P N B R Q K. XABCDEFGHY 8rsnlwqkvlntr( 7zppzppzppzpp' 6-+-+-+-+& 5+-+-+-+-% 4-+-+-+-+\$ 3+-+-+-+-#

Chess Strategy and Tactics For Novice Players P N B R Q K 8rsnlwqkvlntr( 7zppzppzppzpp' 2PzPPzPPzPPzP" 1tRNvLQmKLsNR! Copyright 1994, by Wisconsin Vortack, Inc. Second Edition 2002, Edited by Alessandro

### Roulette Wheel Selection Game Player

Macalester College DigitalCommons@Macalester College Honors Projects Mathematics, Statistics, and Computer Science 5-1-2013 Roulette Wheel Selection Game Player Scott Tong Macalester College, stong101@gmail.com

### Cribbage from Start to Finish!

Cribbage from Start to Finish! By: Mike Svendsen The goal of these instructions is to teach you how to play Cribbage. At first glance, cribbage may seem like an extremely complex game. But truly, the only

### Chess Algorithms Theory and Practice. Rune Djurhuus Chess Grandmaster runed@ifi.uio.no / runedj@microsoft.com September 23, 2014

Chess Algorithms Theory and Practice Rune Djurhuus Chess Grandmaster runed@ifi.uio.no / runedj@microsoft.com September 23, 2014 1 Content Complexity of a chess game Solving chess, is it a myth? History

### foundations of artificial intelligence acting humanly: Searle s Chinese Room acting humanly: Turing Test

cis20.2 design and implementation of software applications 2 spring 2010 lecture # IV.1 introduction to intelligent systems AI is the science of making machines do things that would require intelligence

### Math Circles: Invariants Part 1

Math Circles: Invariants Part 1 March 23, 2011 What is an Invariant? In the simplest terms, an invariant is something that doesn t change. As easy as that sounds, invariance is a very powerful property

### FROM CHESS NOVICE TO ADVANCED PLAYER

FROM CHESS NOVICE TO ADVANCED PLAYER IN 7 DAYS By Mato Jelic Chess essentials in combination with advanced strategies CONTENTS ABOUT CHESS HOW CHESS PIECES MOVE ALGEBRAIC CHESS NOTATION SPECIAL MOVES QUICK

### ARTIFICIAL INTELLIGENCE

Ho Chi Minh City University of Technology Faculty of Computer Science and Engineering ARTIFICIAL INTELLIGENCE Huỳnh Tấn Đạt Email: htdat@cse.hcmut.edu.vn Home Page: http://www.cse.hcmut.edu.vn/~htdat/

### MATE WITH BISHOP AND KNIGHT IN KRIEGSPIEL. Thomas S. Ferguson Mathematics Department UCLA Los Angeles, CA 90024

MATE WITH ISHOP AD IGHT I RIEGSPIEL Thomas S. Ferguson Mathematics Department UCLA Los Angeles, CA 90024 1. Introduction. In this paper we deal with the long unsolved problem of whether the king, bishop

### Human-like Chess Playing Program Petro Gordiievych

Human-like Chess Playing Program Petro Gordiievych What is the different between computer and human way to play chess? While current computers search for millions of positions a second, people hardly ever

### Tactical Analysis Board Games

DM842 Computer Game Programming: AI Lecture 9 Tactical Analysis Board Games Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Outline 1. Tactical Pathfinding

### The Cross-Platform Implementation

The Cross-Platform Implementation Of Draughts Game Valery Kirkizh State University of Aerospace Instrumentation Saint-Petersburg, Russia Introduction Age-old Russian game Draughts; Cross-platform implementation,

### AIMA Chapter 3: Solving problems by searching

AIMA Chapter 3: Solving problems by searching Ana Huaman January 13, 2011 1. Define in your own words the following terms: state, state space, search tree, search node, goal, action, transition model and

### Problem Solving and Blind Search

Plan: Problem Solving Blind Search Breadth-First Priority-First Depth-First Depth-Limited Iterative Deepening Constraint Satisfaction Problem Solving and Blind Search We talked last time about various

### NAME: Instructions for the Football Play-Calling Experiment - Offense

NAME: Instructions for the Football Play-Calling Experiment - Offense You are a football coach and your goal is to obtain as many yards as possible on this particular drive. You have two options: to run

### Artificial Intelligence Search I

Content: Search I Artificial Intelligence Search I Lecture 3 Introduction Knowledge, Problem Types and Problem Formulation Search Strategies General Search Problem 4 Criteria for Evaluating Search Strategies