Quantum Entangled Chess

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1 Carleton University Honours Project Quantum Entangled Chess Author: Alex Honeywell Supervisor: Dr. Tony White School of Computer Science April 12, 2011

2 Abstract In a quantum entanglement system containing two or more objects, one can- not describe the state of any single object without describing the entire system. The basics of these properties can be applied to games to provide a more unique experience. In particular, this project aims to apply quantum entanglement properties to the classical game of Chess in a mobile programming environment. The players will not be able to see their pieces, only the effect they have on the board. By effect, each piece will provide sight on only the squares that it would be able to move to. Sight from other pieces (including opponent pieces) will constructively interfere with each piece.

3 Acknowledgements Thanks to the authors of GNU Chess for creating the base chess engine used in this project, and to Dr. Tony White for supervising the project. i

4 Contents Acknowledgements List of Figures i iii 1 Introduction 1 2 Background Quantum Entanglement Developing for ios Objective-C Objectives 5 4 Application Design Putting the QE in QEC Code Structure Main View Flipside View The Chess Engine Results Gameplay Conclusions Contributions to Computer Science Future Work Bibliography 14 Appendix: Source Code A1 ii

5 List of Figures 2.1 Method Calling vs Messaging keyword The Board - Game Over AI Settings View QEC Class Diagram The Board - Starting View The Board - After a Few Moves iii

6 Chapter 1 Introduction When it comes to video games, the basic mechanics of the game can have a huge effect on its playability. Some simple games such as Klondike (aka Solitaire) pose as little more than timepassers. More complicated games such as Blizzard s World of Warcraft can easily take over a persons life. Those two examples outline common approaches to game mechanics, the former using simple card game strategies while the latter includes large computations to calculate the result of a single player performing a single action. As a result of its complexity, quantum mechanics are not usually seen in games outside of explaining the details of a system or plot device that exists only within the game setting. The goal of Quantum Entangled Chess (QEC) is to take a specific aspect of quantum mechanics, the entanglement property, and attempt to apply it to the classic game of Chess. It also looks to explore creating games on a mobile platform, specifically the Apple iphone and ios [1]. The game itself is played like real Chess with all the same rules, however there is one major difference: the player does not choose which piece to move, instead he chooses where a piece should move to. This provides the base upon which the quantum entanglement aspect of the game is built. In order to run this project, you must have access to Mac OS X with at least the latest version of Xcode 3 (Xcode 4 is preferred) and the ios 4.1 SDK. An iphone simulator is provided with Xcode. 1

7 Chapter 2 Background 2.1 Quantum Entanglement Quantum mechanics covers a large amount of subjects including particle states, wave functions, duality, and more. QEC looks only to take a relatively small sample of subject matter, the entanglement property, and to try and incorporate it into an old game in a new and novel way. In brief, the property of quantum entanglement is that of the state of a system containing two or more objects. If these objects are entangled, one cannot make any observations that describe one object without also describing the others. Instead of describing a system in the classical way of stating the properties of each object individually, quantum systems are better understood as a series of actions and their results. [2] 2.2 Developing for ios Announced January 2007 the Apple iphone is one of the most popular smart-phones in western society and helped revolutionize what people have come to expect from their mobile phone. ios (previously iphone OS) is the platform that runs on the iphone, ipod Touch, ipad, and the Apple TV. It shares its roots with Mac OS X and uses a multi-touch user interface provided by the Cocoa Touch framework. 2

8 The OS itself consists of four entities: Cocoa Touch: developed using Objective-C; supports the use of internal accelerometers (commonly used to orient the interface to always appear right-side-up by switching between landscape and portrait modes); gestures such as a swipe across the screen, tapping a specific point, pinching and reverse pinching Core Animation: OpenGL ES allows the use of smooth transitioning effects; professional-quality interface elements using the Quartz 2D API; resolution independence for switching between the iphone 4 s high resolution Retina display and the original smaller resolution Core Audio: access to a full-screen media player; live audio and video streaming over HTTP that optimizes for data networks or Wi-Fi connections; AV Foundation provides access to the devices camera and microphone, and support for media editing Core Data: data modelling using the well-known Model-View-Controller design pattern; translates source code into a graphical interface; built-in SQLite databases; provides access to the devices contacts, photos, calendar, other applications 2.3 Objective-C With Objective-C (ObjC) being a superset of C, Cocoa Touch also supports the use of C and C++ source code. While there are more differences between ObjC and C/C++, I will only outline the major ones that were observed during the development of this project. Instead of the well-known style of calling a method by its name which is linked to a direct section of code at compile time, ObjC uses the Smalltalk style of runtime-resolution message passing. An object receives a message at runtime and depending on its implementation, may or may not respond. Another difference is the use A class in ObjC has one of each and are comparable to the class declaration (.h) and definition (.cpp) of C++. ObjC uses 3

9 obj->method(arg[,...]); (1) [obj method:arg[ alabel:arg2[...]]]; (2) Figure 2.1: C-style method calling (1) vs. ObjC-style message sending (2) the plus- and minus-signs to differentiate between a class method or an instance method instead of using the static keyword to define the former. A very useful aspect of ObjC is keyword. It is used to define member fields for a class, and when used in conjunction it can automatically generate getter and setter methods for those (nonatomic, retain) NSString * name (nonatomic, readonly) NSInteger id (2) Figure 2.2: A string called name with both a get and set method (1) and a read-only unique identifier (2) 4

10 Chapter 3 Objectives As mobile devices become more and more popular it has become increasingly beneficial to any software developer to have some experience with mobile programming. Since Apple s smartphone market share continues to grow ios is a very viable platform for future development. Thus ios was chosen to be an introduction to mobile programming. 5

11 Chapter 4 Application Design 4.1 Putting the QE in QEC A concession had to be made when developing QEC. Given that the base of the game is in fact Chess, the entanglement property of the game cannot exactly be applied to the starting board. Chess has specific starting locations for each piece, so in the beginning one can describe each and every object in the system without having to involve the others, contradicting the very essence of entanglement. However since the player has no knowledge of which piece is being moved it becomes increasingly difficult to determine what the underlying board looks like. Thus the only observations that can be made are what the results of an action are across the entire game. 4.2 Code Structure The ios SDK encourages almost forces a developer to use the Model-View-Controller design pattern, and QEC was designed accordingly. Using the Utility Application provided by Xcode (Apple s IDE for both ios and Mac OS X) as a starting point, QEC is split up into the following parts (see Figure 4.3 for a class diagram) Main View The Main View consists of the introduction screen, main menu, and Chess board. 6

12 MainViewController Going along with the MVC pattern the central coordinator of the application is the MainViewController. It determines which screen to display, sets up links between the BoardView and the SettingsController, and handles creating, pausing, and resuming games. BoardView The other central part of the application is the BoardView. It is here that the majority of the game logic resides. When first initialized, BoardView creates an 8-by-8 array of GridButtons and sets the actions for handling touch events. It also creates all the necessary labels that are required for displaying information about the game state. After this initialization the game computes the list of what are called PieceSights; if a Chess piece can move to a particular square of the board, that piece has sight on that square. A PieceSight contains the Origin-Coordinates (where the piece currently is), Vision-Coordinates (what square the piece can move to), which colour the piece is, if it s an en passant, castling, or capture move, what type of piece it is, and the integer representation of the move (see Section 4.2.3). Once the board is set up, no other code is executed until the player makes a move. When the player selects a square with vision the game selects the best move available to that square and performs it, then switches to the other player. The game proceeds like this until either a player has no valid moves or is in checkmate, at which point the game is over. Figure 4.1: Game Over 7

4.2.2 Flipside View The Flipside View is used to display game settings, including debugging settings used in development and AI settings, and the About Screen.

13 4.2.2 Flipside View The Flipside View is used to display game settings, including debugging settings used in development and AI settings, and the About Screen. The main settings screen is primarily used for debugging purposes, allowing certain piece types to be turned on and off and showing the piece types. The AI Settings (Figure 4.2) allows player vs. player, player vs. computer, computer vs. computer, and which type of AI is used. The two types are Always use brightest (vision), and Always use dimmest. If there is more than one square with the same vision value, a random square is selected with that value. Figure 4.2: The AI Settings View. When enabled, the UI expands to show which strategy the AI is using. 8

14 4.2.3 The Chess Engine After doing a little research into programming a Chess engine, it was determined that doing so would consume more time and resources than were available and could be considered out-of-scope for this project. After consultation a compromise was created, in which the adaption of an open-source Chess engine would suffice. GNU Chess [3] was chosen and implemented into QEC. The GNU Chess engine is used to determine the best move to make when there are more than one moves that can be made to a selected square. The selection process follows these steps (for details regarding how GNU Chess runs, please refer to its website [3]): 1. A player selects square xy 2. The function GenMoves is called to generate the list of all available moves and their ratings 3. The list of generated moves is compared against the list of sights on square xy 4. Generated moves that do not result in a piece being moved to square xy are discarded 5. The remaining moves are sorted by their rating, with negative ratings being discarded as well. A best-move rating is also tracked, initialized to zero. If the move rating is zero, the move is added to the zeromoves list. If the move rating is non-zero and worse than the best-move, discard it If the move rating is non-zero and better than the best-move, discard any previous moves in the plusmoves list. add this move to the new (now empty) list, and set the best-move rating to this moves rating If the move rating is non-zero and equal to the best-move, add it to the current plusmoves list 6. After all the sights are sorted, the final choice is made: If the plusmoves list is not empty, choose a random move from it, otherwise If the zeromoves list is not empty, choose a random move from it, otherwise 9

15 Choose a random move from the original list of sights The generated moves include castling, en passant, and pawn promotion, and each move is assigned an integer representation calculated as mv = (((f x + f y 8) << 6) (t x + t y 8)) where f is the origin square and t is the destination square. If the move is a castling move, mv is OR d with the CASTLING flag, similarly with ENPASSANT and CAPTURE. If the move would result in a promotion, four move-integers are generated instead of the original one, each OR d with one of QUEENPRM, ROOKPRM, BISHOPPRM, or KNIGHTPRM. Figure 4.3: Outline of the classes in QEC 10

16 Chapter 5 Results 5.1 Gameplay The gameplay between regular chess and QEC is vastly different. It is almost impossible to make a strategy given the innate randomness of the game. As a result the game quickly becomes one of simply hoping a move ends in a desired effect rather than strategizing move after move. This makes QEC a rather difficult game to win, where checkmate occurs more by chance than anything else, and there are no guaranteed sets of moves that will end in a checkmate. From the start of the game it would seem that QEC might be an easy game to play (Figure 5.1). However, after just a few moves by either player it quickly descends into chaos (Figure 5.2) 5.2 Conclusions Quantum mechanics are hard. Applying even a small section of quantum mechanics to a game while remaining playable is even harder. There are many aspects of Chess that came into focus and conflicted with the entanglement theory. For instance the point of capturing a piece. If you show the player that a Rook has been captured you are effectively giving away information about a specific part of the system, which violates quantum entanglement. However, if you provide no information whatsoever about pieces being captured players will have no way of knowing if the game is progressing or not, and most likely become bored quite quickly. Pawn promotion is another 11

17 Figure 5.1: The sight-map of the starting board. important part of Chess that conflicts with entanglement. Giving the player the choice of which piece to promote to gives away information about the system. If a player is in check the only legal moves are those that remove the player from that state and the available moves in such a case are usually quite clear in showing this. In the end, compromises had to be made. The player is informed of how many pieces have been captured, but not which ones. The Chess engine makes the decision for the player on which piece to promote a pawn to. Since the check state is very restrictive in what can and cannot happen there was no feasible way of not violating entanglement. 5.3 Contributions to Computer Science Since the objective of this project was to become familiar with mobile programming there were no outstanding contributions to the field, and unless quantum mechanics in casual gaming becomes more popular there is little doubt that this project will remain in its niche. 12

18 Figure 5.2: The sight-map of the board after a few moves have been made. 5.4 Future Work There remains a vast amount of work that could be done to improve QEC which would both provide the basics that most games have and improve upon the game itself. Currently, the game state is reset upon closing the application. Property lists could be utilized to save game settings and user information (such as player names for player vs. player). A save game system could also be setup by making use of the SQLite engine provided within ios. Expanding on the game itself, a more robust computer AI would definitely be an improvement, and a online multiplayer version of player vs. player could widen the audience. 13

19 Bibliography [1] Apple Inc. ios [Version 4.1]. [2] Bub, J. (2010) Quantum entanglement and information In Edward N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy, winter 2010 edition. [3] Waters, S., Kong-Sian, C., and Cracraft, S. GNU Chess chess/ [Version 5.08]. 14

20 Appendix: Source Code Included with this document are the source code files for the project. The following is the directory structure as viewed in Xcode gnuchess/ GNU Chess code with slight alterations in order to make it work with ObjC and the code written for this project. Main View/ All game action related code, including constants used throughout the project. Flipside View/ Game and AI settings, and the about screen. Application Delegate/ Main controller for the application. A1

21 Other Sources/ Common header file and main application entry point. Resources/ Game graphics, Cocoa Touch xib files, and application information property list. A2

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